Target production network modeling and controlling a chemical production network

Abstract

The disclosure relates to a method for providing target production chain data for controlling and / or monitoring multiple production processes of a chemical production network. The target production chain data is associated with production parameters. The chemical production network is configured to produce multiple output materials from multiple input materials through various production processes. Production data related to the multiple production processes, including production parameters associated with the operation of the network, is provided. An original graph representation of the network is provided, featuring nodes and arcs that represent material flows between processes. Strongly connected components within this graph are determined, these components are contracted into single nodes, forming a contracted graph representation. A target graph representation is determined by expanding nodes of a skeleton graph derived from the contracted graph. Finally, the target production chain data is determined and provided for system control and monitoring.

Description

[0001] TARGET PRODUCTION NETWORK MODELING AND CONTROLLING A CHEMICAL PRODUCTION NETWORK

[0002] Technical Field

[0003] The disclosure relates to the field of controlling and monitoring chemical production networks.

[0004] Technical Background

[0005] The present disclosure relates to methods, apparatuses, systems, data structures, computing elements, production processes, products, computing nodes, manufacturing processes, physical entities for controlling and / or monitoring chemical production networks and for providing target production networks for such controlling / monitoring.

[0006] In an ongoing effort of reducing undesirable emissions of industrial processes, new technology is introduced to measure and purposefully improve the sustainability attributes of single products. Product carbon footprints are typically of special interest in this process. Product carbon footprints of a product portfolio along a cradle-to-gate process-network help provide transparency and allow for the determination of a cumulative carbon dioxide emission measure of materials purchased by customers as well as emissions attributed to a customers' products made from these materials.

[0007] This transparency is crucial for customers who are increasingly tracking emission contributions along the value chain and aiming at a reduction of such emissions, but it is also important to investors and authorities. For example, the European Union has announced specific regulation on industrial and vehicle batteries: Product carbon footprints must be thoroughly determined and will be used for categorization and defining thresholds for battery producers within the territory of the European Union.

[0008] To this end, software solutions applying business logic that provide a digital counterpart to an underlying material production process can be applied. A mass balance business model may to this end be integrated into a standardized end-to-end process. The aim is to be able to respond as automatically and flexibly as possible to the requirements of customers, who are increasingly demanding sustainable products in line with the mass-balance principle with only few changes of the existing supply chain process.

[0009] Summary

[0010] In an aspect the disclosure relates to a computer-implemented method for providing target production chain data for controlling and / or monitoring multiple production processes of a chemical production network. The target production chain data is associated with one or more production parameters per production process of the multiple production processes. The chemical production network is configured to produce multiple output materials from multiple input materials by the multiple production processes. The method includes providing production data associated with the multiple production processes, including one or more production parameters associated with the operation of the chemical production network. Based on the production data, an original graph representation associated with the chemical production network is provided. The original graph representation includes multiple nodes associated with the multiple production processes and multiple arcs. Each arc of the multiple arcs is associated with a material flow from one of the multiple production processes to another one of the multiple production processes. The method further includes determining multiple strongly connected components included in the original graph representation. Based on the original graph representation and the multiple strongly connected components, a contracted graph representation is determined. Per strongly connected component of the multiple strongly connected components, the respective strongly connected component of the original graph representation is contracted to a corresponding single node. The method further includes, determining a target graph representation by at least determining, based on the contracted graph representation, a skeleton graph and expanding multiple nodes of the skeleton graph. The method further includes, determining, based on the target graph representation, the target production chain data. The method further includes providing the target production chain data for controlling and / or monitoring the chemical production network.

[0011] In yet another aspect the disclosure relates to an apparatus for providing target production chain data for controlling and / or monitoring multiple production processes of a chemical production network. The target production chain data is associated with one or more production parameters per production process of the multiple production processes. The chemical production network is configured to produce multiple output materials from multiple input materials by the multiple production processes. The apparatus includes a production data interface configured to provide production data associated with the multiple production processes, including one or more production parameters associated with the operation of the chemical production network. The apparatus further includes a graph representation determination unit configured to determine, based on the production data, original graph representation data related to an original graph representation of the chemical production network. The original graph representation includes multiple nodes representing the multiple production processes and multiple arcs representing material flows between the production processes. The apparatus also includes a component analysis unit configured to determine multiple strongly connected components within the original graph representation. A graph contraction unit is configured to generate a contracted graph representation by replacing, per strongly connected component of the multiple strongly connected components, the respective strongly connected component with a single corresponding contracted node. Furthermore, the apparatus includes a target graph generator unit configured to generate a target graph representation at least by generating a skeleton graph based on the contracted graph representation and expanding multiple nodes of the skeleton graph. A target production chain data determination unit is configured to determine, based on the target graph representation, the target production chain data. Finally, the apparatus includes a target production chain data interface configured to provide the target production chain data for controlling and / or monitoring the chemical production network.

[0012] In yet another aspect the disclosure relates to a computer-implemented method for providing a target graph representation associated with a target production network. The method includes receiving an original graph representation of a chemical production network, the original graph representation including multiple nodes representing production processes and multiple arcs representing material flows between the production processes. The method further includes identifying multiple strongly connected components within the original graph representation. The method further includes, generating a contracted graph representation by respectively replacing the strongly connected components with a corresponding single node. The method further includes generating a skeleton graph based on the contracted graph representation. The method further includes expanding one or more nodes of the skeleton graph by replacing the respective node with a corresponding strongly connected component to generate the target graph representation. The method further includes providing the target graph representation.

[0013] In yet another aspect the disclosure relates to a computer-implemented method for controlling and / or monitoring a production operating system for a chemical production network. The chemical production network is configured to produce multiple output materials from multiple input materials by multiple production processes of the chemical production network. The production operating system is configured to determine, based on production input data, production output data for controlling and / or monitoring the chemical production network. The method includes providing an original graph representation associated with the chemical production network, wherein the original graph representation includes multiple nodes associated with the multiple production processes and multiple arcs, wherein, per arc of the multiple arcs, the respective arc is associated with a material flow from one of the multiple production processes to another one of the multiple production processes. The method further includes determining multiple strongly connected components included in the original graph representation. The method further includes determining a contracted graph representation, based on the original graph representation and the multiple strongly connected components, wherein, per strongly connected component of the multiple strongly connected components, the respective strongly connected component of the original graph representation is contracted to a corresponding single node. The method further includes determining a target graph representation by at least determining, based on the contracted graph representation, a skeleton graph and expanding multiple nodes of the skeleton graph. The method further includes, determining the production input data based on the target graph representation. The method further includes providing the production data output data obtained by operating the production operating system with the production input data. The method further includes providing the production data output data for controlling and / or monitoring the production operation system.

[0014] In yet another aspect of the disclosure relates to a method of automatically generating a synthetic network from a template network, the template network describing a real-world value chain for producing a plurality of end products, comprising:

[0015] Receiving, i.e. providing, a graph-representation of the template network, wherein the graph-representation of the template network comprises a plurality of first nodes, each of the first nodes representing a product that is one of: starting product, intermediate product, end product; and wherein the graph-representation of the template network comprises a plurality of arcs, each of the arcs connecting a respective pair of first nodes with a given direction, such that every pair of first nodes comprises a start node representing either a starting product or an intermediate product and comprises an end node representing either an intermediate product or an end product, and each arc comprising a respective value, the respective value indicating a respective product share of the start node in the end node of a respective pair; Receiving user input comprising information specifying characteristics of the synthetic network to be generated, wherein the characteristics at least comprise information about a selected part of the template network to serve as data basis for the automated generation of the synthetic network; automatically extracting a section of the graph-representation of the template network according to the information provided by the user input, and based on the extracted section: automatically generating the synthetic network as a bipartite graph.

[0016] In yet another aspect the disclosure relates to a data processing device comprising means for carrying out the method as described above and below.

[0017] In yet another aspect the disclosure relates to a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method as described above and below, e.g. cause the computer to perform the method for automatically deriving a synthetic network from a template network.

[0018] In yet another aspect the disclosure relates to a computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the method as described above and below.

[0019] In yet another aspect the disclosure relates to a system for automatically generating a synthetic network from a template network, the template network describing a real-world value chain for producing a plurality of end products, comprising a first interface which is configured to provide a graph-representation of the template network, wherein the graph-representation of the template network comprises a plurality of first nodes, each of the first nodes representing a product that is one of: starting product, intermediate product, end product; and wherein the graphrepresentation of the template network comprises a plurality of arcs, each of the arcs connecting a respective pair of first nodes with a given direction, such that every pair of first nodes comprises a start node representing either a starting product or an intermediate product and comprises an end node representing either an intermediate product or an end product, and each arc comprising a respective value, the respective value indicating a respective product share of the start node in the end node of a respective pair; further comprising a second interface which is configured to receive user input data comprising information specifying characteristics of the synthetic network to be generated, wherein the characteristics at least comprise information about a selected part of the template network to serve as data basis for the automated generation of the synthetic network; and comprising a computing unit, which is configured to extract a section of the graph-representation of the template network according to the information provided by the user input, and based on the extracted section: to generate the synthetic network as a bipartite graph.

[0020] In yet another aspect the present disclosure relates to a computer element with instructions, which when executed on one or more computing node(s) is configured to carry out the steps of the method(s) of the present disclosure or configured to be carried out by the apparatus(es) of the present disclosure. Any disclosure, embodiments and examples described herein relate to the methods, the systems, apparatuses, chemical products and computer elements lined out above and below. Advantageously, the benefits provided by any of the embodiments and examples equally apply to all other embodiments and examples.

[0021] Embodiments

[0022] There is a need to allow flexible and scalable evaluation, monitoring, and optimization of complex chemical production networks without relying on direct access to sensitive or operationally burdensome real-world production data, in particular to support the systematic validation of digital solutions and computational methods used for modeling, controlling, and analyzing such networks under varying structural and operational conditions.

[0023] An object of the present disclosure is to provide a method for robust and reliable evaluation, validation, and optimization of digital systems, computational models, and control logic associated with chemical production networks employing configurable representations of chemical production networks, particularly under varying structural, operational, and environmental conditions, and without requiring direct access to sensitive or large-scale real-world production data.

[0024] Business critical and strategic value chain applications implemented in software depend on correct and performant algorithms and tooling for test networks based on a template network fully describing a real-world production process, i.e. a value chain. There is a need for continuous and thorough validation testing, that is, testing techniques designed to simulate real-world scenarios, including performance and stress tests. These value chain applications process large amounts of data, e.g. related to hundreds of real-world production plants, many of which are interconnected and producing tens of thousands different products. There is a need to dynamically generate synthetic value chains that can be used to more robustly test the value chain applications. In particular, digital solutions to provide carbon footprints for tens of thousands of sales products are sought and developed.

[0025] Real-world value chains such as chemical value chains are rather large and exhibit complex flows, including cycles. For the development of a value chain solution this means that a large amount of data has to be handled, which is very time-consuming. Reading in the data, performing transformations, etc. takes a long time. Building and testing value chain applications, in particular in form of reduced models, is therefore tedious and time consuming, if possible at all. Large value chain size makes also debugging and automating tests difficult. Generating test cases and testing scaling behavior is therefore also tedious and time consuming. To test robustness of a value chain, a model has to be generally applicable. Therefore, generating smaller test cases and a broader set of test cases is desirable. This is challenging, however, as value chains consist of multiple associated data such as the production and supply connections, bill of materials in the individual production steps as well as capacities and costs. In addition, third party data sharing in externalization efforts is sometimes not desired or forbidden, such that a certain part of information comprised in a description of the real-world value chain has to be removed. It is hence yet another objective of the disclosure to improve and simplify the process of a model generation derived from one or more parts of a real-world value chain of a production process.

[0026] The method, system, apparatus, and computer program product of the present disclosure allow for robust and reliable generation, transformation, and analysis of configurable representations of chemical production networks, enabling scalable validation of control logic, performance testing of digital applications, simulation of structural and operational variations, secure external data sharing, and targeted environmental impact assessment, thereby improving and simplifying the process of model generation derived from one or more parts of a real-world value chain of a production process. Moreover, chemical production networks may be operated in a more robust and / or reliable manner, in particular by testing systems, methods and computer programs controlling and / or monitoring such production networks using generated graph representations associated with target networks. For example, specific structural features and / or edge cases may be targeted during testing by such generated graph representations.

[0027] Chemical production networks are among the most complex systems in industrial operations, involving thousands of interconnected processes, materials, and production steps. These networks are not only vast in scale but also structurally intricate, often containing cycles, dependencies, and dynamic flows that evolve over time. As companies increasingly rely on digital solutions and computational methods to model, monitor, and control these networks, for example for operational efficiency, sustainability tracking, or regulatory compliance, ensuring the robustness and reliability of these systems becomes mission-critical. However, testing such digital solutions is extremely challenging. Real-world production data is often sensitive, proprietary, or simply too large and unwieldy to use effectively in development environments. Moreover, using a single snapshot of a real value chain does not allow for testing edge cases, failure modes, or performance under varying structural conditions.

[0028] The present disclosure addresses this challenge by enabling the generation of synthetic, yet structurally realistic, representations of chemical production networks. These synthetic networks can be configured to reflect specific topologies, such as bipartite graphs, cycles, or subgraphs, and can be scaled in size and complexity to simulate a wide range of production scenarios. This capability is essential for validating the behavior of digital applications and control logic under stress, for inspecting failure modes, and for ensuring that systems perform reliably across different network configurations. It also supports the development and certification of software components used in regulated environments, where reproducibility, traceability, and coverage of test conditions are required.

[0029] Beyond operational testing, the disclosure supports broader goals in sustainability and life cycle assessment. Synthetic networks can be used to simulate material flows and production mixes, enabling robust analysis of carbon footprints, resource usage, and environmental impact, in particular without exposing confidential data or relying on live systems. This is especially valuable in external collaborations, where sharing realistic but anonymized network structures facilitates joint development and benchmarking. By simplifying and automating the generation of testable network models, the disclosure empowers organizations to accelerate innovation, improve system reliability, and meet growing demands for transparency and environmental accountability in chemical production. By enabling the generation of configurable network representations, the disclosure enhances the precision and adaptability of digital systems used to control and monitor chemical production networks. These representations can be tailored to reflect specific structural characteristics, production logic, and material flow dynamics, allowing for targeted evaluation of control strategies and monitoring algorithms. This supports a wide range of technical effects, including improved responsiveness to process deviations, enhanced fault tolerance, and more accurate mapping of production data to environmental metrics. It also facilitates the simulation of production scenarios across different scales and configurations, enabling performance benchmarking, stress testing, and validation of system behavior under edge conditions. Furthermore, the ability to associate synthetic networks with realistic attribute distributions and labeling schemes contributes to better interpretability, traceability, and integration with business logic and compliance frameworks. Whether used in predictive monitoring, automated decision-making, or lifecycle-based impact analysis, the disclosure provides a robust foundation for secure, efficient, and transparent operation of chemical production systems.

[0030] In the following, embodiments of the present disclosure will be outlined by ways of examples. It is to be understood that the present disclosure is not limited to said embodiments and / or examples.

[0031] In an embodiment, the method includes providing selection data associated with one or more selection criteria for selecting at least a part of the contracted graph representation. The method further includes, determining a subgraph of the contracted graph representation by extracting the subgraph from the contracted graph representation based on the selection data, wherein the skeleton graph includes the subgraph. This may facilitate robust extraction of a subgraph from a contracted graph representation by using selection data associated with a designated segment of the chemical production network, thereby facilitating the derivation of a synthetic substructure correlated with physical production processes. This approach may furnish reliable digital test data related to monitoring and controlling production, manufacturing, and synthesis processes, potentially contributing to secure, stable operations and environmental impact reduction.

[0032] In an embodiment, expanding the multiple nodes of the skeleton graph includes replacing one or more of the multiple nodes of the skeleton graph by corresponding strongly connected components of the original graph representation. This may enable robust generation of synthetic network representations associated with chemical production processes by replacing selected nodes in a skeleton graph with corresponding strongly connected components derived from the original graph representation, thereby capturing complex cyclic dependencies present in physical production systems.

[0033] In an embodiment, the method further includes determining graph characterization data associated with the contracted graph representation, the graph characterization data including a value associated with a size of the contracted graph representation, and providing, based on the graph characterization data, one or more graph generation parameters including a value associated with a size of the skeleton graph. This may enable robust generation of synthetic graph parameters by determining graph characterization data associated with a contracted graph representation, including an indication of its size, and by providing graph generation parameters including an indication of the skeleton graph size.

[0034] In an embodiment, the graph characterization data associated with the contracted graph representation includes one or more values representing structural and topological properties of the graph. These values may comprise, for example, the total number of nodes, the total number of edges and / or arcs, the number of cycles, the minimum, maximum, and average length of cycles, and statistical distributions of nodes and edges across the graph. The graph characterization data may further include an indication of whether the graph is bipartite, as well as metrics describing the connectivity or clustering of nodes. Based on this graph characterization data, one or more graph generation parameters may be provided, including parameters specifying the desired size of the skeleton graph, its connectivity density, the presence or absence of cycles, and constraints on the structural layout such as enforcing bipartite topology or limiting cycle lengths. These parameters may be used to guide the generation of a synthetic graph representation that reflects the desired structural characteristics while maintaining similarity to the original graph representation. This enables the generation of configurable synthetic networks suitable for testing, monitoring, and optimization of chemical production networks under varied structural conditions. This approach may facilitate secure and stable simulation of digital test data related to physical chemical production processes, including manufacturing and synthesis, potentially supporting reliable monitoring and control and contributing to environmental impact reduction.

[0035] In an embodiment, a synthetically generated graph based on the graph generation parameters is determined. Determining the skeleton graph may include starting from the synthetically generated graph or adding the synthetically generated graph to the skeleton graph. This may enable to target certain edge cases for testing.

[0036] In an embodiment, the skeleton graph is determined by combining one or more synthetically generated graphs with one or more subgraphs extracted from the contracted graph representation. The synthetically generated graphs may be created based on graph generation parameters derived from graph characterization data, while the subgraphs may be selected based on selection criteria such as structural relevance, connectivity, or location within the contracted graph. To ensure that the combined structure forms a coherent and connected skeleton graph, arcs may be added between nodes of the synthetically generated graphs and nodes of the extracted subgraphs. This approach enables flexible and modular construction of the skeleton graph, allowing for the integration of realistic structural elements from the original graph with configurable synthetic components tailored to specific testing or monitoring scenarios.

[0037] In an embodiment, the method further includes prompting a user to provide graph generation input data associated with one or more graph generation parameters, and wherein providing the graph generation parameters includes setting at least one of the graph generation parameters based on the graph generation input data. Thereby generation of the synthetic network may be customized by the user and the user may select certain scenarios. In an embodiment, the method further includes determining strongly connected components characterization data including an indication of a probability distribution of a number of nodes per strongly connected component of the multiple strongly connected components of the original graph representation. Expanding the multiple nodes of the skeleton graph includes replacing one or more of the multiple nodes of the skeleton graph by a respective strongly connected component, wherein the respective strongly connected component is generated based on the strongly connected components characterization data. This may enable robust simulation of synthetic chemical production networks by utilizing strongly connected component characterization data to statistically expand a skeleton graph into synthetic components associated with physical production processes, including manufacturing, synthesis, and process monitoring. This may yield reliable digital proxies that facilitate secure and stable evaluation of production parameters, potentially contributing to environmental impact reduction and overall system reliability.

[0038] In an embodiment, the original graph representation is provided as a directed graph including multiple cycles. The multiple cycles may be, in absolute terms, more than 10, more than 100, or more than 1000 cycles. In relative terms, the number of the multiple cycles may be between 1 / 1000 and 1000 times the number of nodes in the original graph representation, or between 1 / 50 and 50 times the number of nodes. Moreover, the number of nodes that are maximally possible, may grow exponentially with the number of nodes.

[0039] In an embodiment, the skeleton graph is determined as a directed acyclic graph. This may facilitate generating the skeleton graph based on diverse standard algorithms known in graph theory. A more detailed structure resembling a chemical production network may then be provided by expanding multiple nodes.

[0040] In an embodiment, the original graph representation, the contracted graph, the skeleton graph and / or the target graph representation are weighted graphs. The edges or arcs of these graphs may have weights. These weights may be associated with a ratio of material, e.g. a material flow from one production process to another production process. This may be in absolute terms such as a physical weight or volume, it may be per time unit, or it may be specified relative to the total amount of material entering or leaving a production process associated with the respective node and may be unit-less or percentage and the like, e.g. all material entering a process may sum up to 100%, also the leaving material may sum up to 100% or, in relation to the input material, the output material may be also less than 100% due to losses.

[0041] In an embodiment, the contracted graph representation is determined as a directed acyclic graph by replacing, per strongly connected component of the original graph representation, the respective strongly connected component by a corresponding single node.

[0042] In an embodiment, the original graph representation includes multiple nodes associated with the multiple input materials, the multiple output materials and / or multiple intermediate materials, and includes multiple arcs, wherein, per arc of the multiple arcs, the respective arc is associated with a material flow from one of the multiple input materials or intermediate materials to one of the multiple production processes or from one of the multiple production processes to one of the multiple intermediate or output materials.

[0043] In an embodiment, the method further includes determining arc characterization data associated with, e.g. related to, the original graph representation, the arc characterization data including, per arc of the multiple arcs, a respective material identifier data associated with a respective material flow of a respective material and material ratio data associated with a ratio of the respective material provided as an input material or produced by a respective production process as an intermediate material being used as an input material by another respective production process. The method further includes generating, based on the arc characterization data, per arc of the skeleton graph and / or per arc of the target graph representation, one or more attributes associated with a respective material identifier data and material ratio data. The method further includes associating, per arc of the skeleton graph and / or per arc of the target graph representation, the one or more attributes with the respective arc. Associating may include setting, applying, or linking the attributes to the respective arc. The weights of arcs in the original graph representation, the contracted graph, the skeleton graph, and / or the target graph representation may also represent attributes. Hence, such weights may be generated or derived as part of the arc characterization data and subsequently associated with the respective arcs, for example by setting, applying, or linking them as attributes within the graph structure. This may enable incorporating these attributes into the synthetic target graph comprising expanded nodes and arcs.

[0044] In an embodiment, the arc characterization data determined from the original graph representation may be used to generate attributes for nodes of the target graph representation. For example, material identifier data and material ratio data associated with a given arc may inform the generation of attributes for adjacent nodes, such as production processes or material states. These attributes may be applied to arcs and nodes alike to reflect realistic production behavior, material flow dynamics, or environmental metrics. This ensures that the synthetic network maintains consistency in its structural and semantic representation, supporting robust testing and monitoring of chemical production networks and / or providing target production chain data, based on the target graph representation, for controlling the chemical production network.

[0045] In an embodiment, attributes for at least a part of the nodes and / or at least a part of the arcs of the target graph representation are generated, the attributes respectively comprising an attribute type and an attribute value, wherein the attributes are generated by at least one of: using a predefined rule set; sampling from a probability distribution of ratios of materials used for producing another material; applying a generative machine learning model. This may enable robust generation of attribute data associated with nodes and arcs of a synthetic graph-based representation of a chemical production network by employing methods including the application of predefined rule sets, sampling from probability distributions of material ratios, and utilizing generative machine learning models. This may provide reliable data related to physical production processes including manufacturing and synthesis operations. In an embodiment, determining the target graph representation includes transforming the target graph network according to one or more similarity requirements between the target graph prior to transformation and after transformation. An edit distance is used as a similarity requirement, wherein the edit distance is defined as a number of additions or removals of arcs. This may enable robust simulation of synthetic graph-based representations by applying similarity requirements. This may provide reliable digital test data related to monitoring and controlling production operations, including manufacturing and synthesis, thereby facilitating stable system evaluation and potentially contributing to environmental impact reduction.

[0046] In an embodiment, determining the target graph representation includes transforming the target graph network according based on addition and removal of arcs and nodes, wherein the transformation is performed until certain target criteria are reached and wherein the transformation may be optimized such that the target criteria are reached with a minimum necessary edit distance. This may enable to arrive a target graph representation, and hence, a target production chain as similar to as possible to the original graph representation and thus chemical production network.

[0047] In an embodiment, the method further includes annotating one or more arcs of the target graph representation with material identifier data and material ratio data associated with respective material flows.

[0048] In an embodiment, the method further includes providing one or more test criteria.

[0049] In an embodiment, the method further includes monitoring the chemical production network by evaluating the production output data against the test criteria to detect deviations, inefficiencies, or anomalies in the production processes. This may enable robust evaluation and control of chemical production networks by generating a synthetic graph-based representation associated with production steps and material flows, wherein production output data evaluated against predefined test criteria may facilitate reliable detection of deviations, inefficiencies, or anomalies.

[0050] In an embodiment, the method further includes controlling the chemical production network by adjusting one or more operational parameters of the production operating system based on the evaluation of the production output data against the test criteria.

[0051] In an embodiment, per arc of the arcs of the original graph representation, the respective arc correspondingly connects one of the nodes corresponding to one of the multiple production processes with another one of the nodes corresponding to another one of the multiple production processes.

[0052] In an embodiment, the disclosure may relate to a step carried out by a user, wherein the user executes a computer program that applies the generated synthetic network and analyzes properties of the synthetic network with the computer program in order to evaluate and / or optimize the technical value chain.

[0053] This embodiment may enable robust evaluation and optimization of technical value chains by applying a computer program to analyze the properties of a synthetic network associated with chemical production processes. It may provide reliable test data for programs and systems that monitor and control physical production entities. This may lead to secure and stable simulation of production parameters related to manufacturing and synthesis, potentially contributing to environmental impact reduction and enhancing overall system reliability.

[0054] In an embodiment, the graph representation of the template network may be provided as a directed graph.

[0055] This embodiment may enable enhanced testing and simulation of control systems associated with chemical production networks by providing a robust directed graph representation of the template network. The directed graph enables automated extraction of sections related to specific production stages. It comprises nodes representing starting, intermediate, and end products, and arcs associated with defined product shares. This may furnish reliable test data for systems monitoring or controlling chemical production, thereby contributing to stable operations, secure system integration, and environmental impact reduction.

[0056] In an embodiment, the graph representation of the template network may comprise at least one second node representing a production process step within the value chain.

[0057] This embodiment may enable more robust test data generation for programs or systems controlling or monitoring real chemical production networks. By integrating a production process step as a dedicated node within the graph representation of the template network, detailed process parameters may be associated with physical manufacturing activities. This may facilitate the construction of secure and stable synthetic networks comprising production-related information and may enhance reliability by providing simulation inputs correlated with actual production process steps, potentially contributing to environmental impact reduction.

[0058] In an embodiment, generating the synthetic network may comprise modifying the extracted section by adding or subtracting one or more arcs.

[0059] This embodiment may enable robust simulation of chemical production process dynamics by modifying the extracted section through selective addition or subtraction of one or more arcs. The resulting synthetic network may be stable, secure, and reliable for providing test data associated with programs or systems controlling or monitoring production operations. This approach may offer advantages including enhanced operational reliability and environmental impact reduction by generating data related to physical manufacturing, synthesis, or monitoring processes.

[0060] In an embodiment, the user input may comprise at least one of the following: a choice between the presence or absence of specific structural parts of the synthetic network to be generated; values attributed to arcs; data types for the values attributed to arcs; a permissible range for the values attributed to arcs; a specification of the sum of the values of a plurality of arcs arriving at or leaving a certain type of node; a name of a node; a desired total number of nodes of the synthetic network to be generated; a desired total number of strongly connected components of the synthetic network to be generated.

[0061] This embodiment may enable flexible generation of synthetic network test data by incorporating user input specifying detailed network characteristics including structural parts, arc values and associated data types, and connectivity constraints. This may establish a reliable digital proxy associated with physical chemical production networks. The method may further facilitate robust monitoring and secure controlling of production processes in manufacturing environments, potentially supporting stable operations and contributing to environmental impact reduction.

[0062] In an embodiment, on an input interface accepting the user input, the user may be given a choice between using the provided template network and using a user-defined skeleton network with user-specified structural characteristics for the generation of the synthetic network.

[0063] This embodiment may enable robust generation of synthetic networks comprising user-defined skeleton networks that simulate processes associated with real chemical production systems. This approach may produce reliable digital representations related to physical production, products, manufacturing, and synthesis. It may facilitate secure monitoring and control, ultimately contributing to environmental impact reduction.

[0064] In an embodiment, the template network may be transformed to the synthetic network according to one or more similarity requirements between the selected part of the template network and the synthetic network.

[0065] This embodiment may enable robust generation of test data associated with real chemical production networks by transforming a selected part of the template network into a synthetic network according to similarity requirements. This may provide a secure and stable digital representation related to physical processes controlling and monitoring production, including manufacturing and synthesis. It may contribute to improved assessments of process efficiency and potential environmental impact reduction.

[0066] In an embodiment, an edit distance may be used as a similarity requirement, wherein the edit distance is defined as a minimum number of additions or removals of arcs needed to transform the graph representation of the template network into the bipartite graph of the synthetic network.

[0067] This embodiment may enable robust generation of synthetic test data associated with chemical production networks by employing an edit distance similarity requirement to automatically derive a bipartite graph that preserves key structural relationships present in the template network. This may contribute to stable and secure system testing related to monitoring and controlling production, manufacturing, and synthesis processes. It may ensure that the digital representation is closely aligned with the physical operational environment, thereby supporting reliable performance validation and environmental impact reduction.

[0068] In an embodiment, the synthetic network may be derived from the template network by performing the following steps: computing a condensation graph of the graph representation of the template network; extracting a weakly connected subgraph from the condensation graph; modifying the extracted weakly connected subgraph within a predefined first edit distance to obtain a modified subgraph; identifying all strongly connected components represented by nodes of the modified subgraph; modifying each strongly connected component within a predefined second edit distance by adding arcs to the modified subgraph; and, for each of the added arcs, joining the modified strongly connected components.

[0069] This embodiment may enable robust derivation of a synthetic network through systematic condensation, extraction, and modification of graph components. It may provide reliable test data associated with digital representations of physical chemical production networks, including monitoring of production parameters and control of synthesis processes. The structured identification and modification of network subcomponents may support secure and stable evaluation of control programs related to physical production entities, including manufacturing and product synthesis, while contributing to environmental impact reduction.

[0070] In an embodiment, some or all of the first nodes of the synthetic network may be automatically labeled with human- readable descriptions.

[0071] This embodiment may enable the automatic assignment of human-readable labels to first nodes, thereby providing a robust mechanism for associating digital network elements with corresponding physical components involved in chemical production and monitoring. The labeling process may improve the reliability and stability of test data used for controlling production processes, including manufacturing and synthesis, and may contribute to secure oversight and environmental impact reduction associated with real chemical production networks.

[0072] In an embodiment, attributes for at least a part of the first nodes and / or at least a part of the arcs of the synthetic network may be automatically generated. Each attribute may comprise an attribute type and an attribute value. The attributes are generated by at least one of the following: using a predefined rule set; sampling from a probability distribution of shares of products in another product; applying a generative machine learning model.

[0073] This embodiment may enable more reliable simulation of test data by automatically generating robust attribute values associated with nodes representing products and arcs representing process flows in a digital model of a chemical production network. The assignment of attribute types and values based on predefined rule sets, probability distribution sampling, or generative machine learning models may allow for secure and stable evaluation of programs or systems monitoring and controlling production processes. This may contribute to environmental impact reduction through improved system validation.

[0074] In an embodiment the original graph representation may be used as a template, e.g. the chemical production network being a template network. Hence, in an embodiment the template network may describe, e.g. be associated with, a real-world technical value chain for a plurality of end products. The value chain may, in particular, be composed of a plurality of production product-steps and therefore product-states, in at least some of which starting products and / or intermediate products are compounded in predefined ratios to each other to form one of many other intermediate products or end products, respectively. Starting products can be raw materials.

[0075] The computer-implemented method of automatically generating a synthetic network from a template network and its related embodiments may serve not only to automatically generate a computer-executable synthetic network from such a template network describing a real-world technical value chain for a plurality of end products from scratch, but also to execute and analyze a computer program that makes use of, in particular comprising, the synthetic network. Alternatively, such a computer program is executed and analyzed manually by a user. In an embodiment, the real-world value chain may be described, e.g. represented, by the template network, which in turn is provided in form of a graph. A graph is a concept adopted from discrete mathematics that allows for modeling pairwise relations between objects. The objects are represented by nodes, also called vertices, which are connected by edges, also called arcs, in particular in case of directed edges. The set of arcs is a two-element-subset of the set of nodes, in particular of first nodes. Each arc is joining two vertices. The graph-representation of the template network comprises a plurality of first nodes. A node, in the context of graph theory can also be called a vertex. Each of the first nodes of the graph-representation of the template network belongs either to the category "intermediate product", or to the category "starting product" or to the category "end product". Pairs of first nodes are connected to each other by arcs, while the term 'arc' is describing a directed edge joining two nodes together. Hence, every pair of first nodes comprises exactly one start node and exactly one end node connected by an arc, which in turn means that nodes of the plurality of first nodes within a pair are adjacent to each other. The template network describing the value chain ends with end products at each of its potential paths through the nodes connected by edges. This does not preclude the possibility that the end node of one pair coincides with the start node of another pair. This is particularly the case when a chain of first nodes is part of one common path, which means that several intermediate products are on this path of first nodes and being fed into another intermediate product, or end product at the end of the path.

[0076] In an embodiment, every arc may have one particular value as an attribute. This value may describe the share of the product represented by each start node in an intermediate product or in an end product represented by an end node of the same pair of first nodes.

[0077] In other words, in some embodiments, the representation of the template network comprises a plurality of first nodes connected by a plurality of arcs, each of the arcs featuring exactly one value, describing the share of a preceding product in another product represented by the node at the end of the arc. The share describes a relative amount, i.e. a ratio of the product (starting product or intermediate product) of a start node within the product represented be the end note of a pair, which is the one of the first nodes in the graph-representation of the template network adjacent to the start node from the group of first nodes. The product (intermediate or end product) of the second node is in other words at least partially compounded of the product represented by the start node of each pair.

[0078] Hence, the arcs help to describe a bill of materials or consumption mix, in particular the share of other starting or intermediate products in every other intermediate or end product. The origin of every starting product and intermediate product is preferably known in advance, unless computed with the help of the values attributed to the arcs leading to the respective intermediate product, e.g. whether it is sourced from another company or produced within one's own company.

[0079] In another step, which can be done before or after the provision of a graph-representation of the template network, user input data comprising information specifying characteristics of the synthetic network to be generated, or at least a representation of it, are obtained. The user input specifies properties of the to be generated synthetic network such as its size and specification about the structural parts it contains; he may specify how certain data associated to parts of the template network should be constructed. Next to its size, the user may specify whether it should be a realistic synthetic network, i.e. whether to map a part of the template network realistically onto the synthetic network. The realistic map of a part of the value chain uses a structure for the synthetic network that resembles a real-world production network, i.e. the value chain, represented by the template network. Preferably, an input interface is provided, into which the user can input via a text file in a standard graph format, e.g. GML, a specific induced subgraph that is demanded to be present in the to be generated network.

[0080] The user input specifies a desired quality of the synthetic network, whereas at the same time loss of information in the process of deriving the synthetic network from the template network is at least accepted or even desired. The latter case may occur, when observing confidentiality requirements or other requirements to remove information is desired and allows for the isolation of relevant parts of the template network to a structurally similar derived and often downsized sub-scale, subset child network which is the synthetic network. Information about the template network might be subject to non-disclosure agreements with third parties, being restricted by one’s own confidentiality requirements, or does not represent the relevant and aspects to be investigated sufficiently or solely, e.g. when only relevant peculiarities of the template network are to be evaluated while ignoring other aspects that should be removed for this purpose that otherwise would contribute only irrelevant information.

[0081] The extraction of the chosen section of the graph-representation of the template network is in particular such that the extraction comprises a proper subset of a set of all features of the template network. In other words, deriving the synthetic subnetwork from the template network allows for generation of a raw or modified subsystem of the template network to allow for a targeted evaluation of properties of a part of the template network, or of a modified subsystem based on the part of the template network, if certain peculiarities are of special interest that are not or only weakly appearing in the template network.

[0082] For modifying the extracted part of the template network two basic operations as elementary digraph operations can be conducted:

[0083] - edge insertion: This introduces a new arc between a pair of nodes.

[0084] - edge deletion: This removes a single arc between a pair of nodes.

[0085] If the synthetic network is supposed to include a subnetwork, the subnetwork can be created manually or by a nested application of the computer-implemented method being used to produce the synthetic network itself.

[0086] The synthetic network may automatically be constructed in form of a graph-representation of itself with the properties of a bipartite digraph, e.g. being related to the first and the second nodes. Next to the bipartite property of the synthetic network, another objective of the computer-implemented method is to generate a meaningful synthetic network, i.e. its graph-representation should be weakly connected. A bipartite digraph is a digraph whose nodes can be divided into two disjoint sets U and V, such that every arc of the graph connects a node in U to one in V, or vice versa. U and V are called the parts of the graph.

[0087] The disclosure may simplify evaluation of existing parts of the value chain and testing of changes introduced to it by constructing one or more synthetic value chains with specific structural characteristics, suitable for the different testing purposes. While a template network describing a value chain of large size with a huge number of end products in the tens of thousands that may have been compounded by common intermediate products, may feature hundreds of thousands of nodes and millions of arcs, the synthetic networks can be large and complex like real-world networks as well. The method of automatically generating such a synthetic network allows for a user to specify various desired features of the synthetic network such as its size and which structural parts it contains. The at least partially automatically generated synthetic network can be used for robust testing of value chain applications. The synthetic network can then be used for robust computer-aided testing of value chain applications. Testing is in particular simplified on the synthetic network for the application of testing scaling behavior and correctness on edge cases.

[0088] Some embodiments of the disclosure may provide one or more further advantages:

[0089] The ability to test scaling behavior: By constructing synthetic networks of different sizes and densities it is possible to test the performance of software-applications under varying loads.

[0090] The correctness of behavior for specific network topologies: It is often the case that a software-application has to be tested on networks that show specific properties, e.g., the presence or absence of cycles. A cycle in a directed graph is a non-empty directed path in which the first and last nodes are equal. The method provides ready to use synthetic networks with the needed properties.

[0091] The Inspection of specific failure modes: The need to perform destructive testing may be experienced frequently. This is done by providing the application with networks with an unexpected structure and validate its robustness in such a scenario. Such synthetic networks adequate to this use can be generated with ease. Third party data sharing in externalization efforts: In collaboration efforts with external parties it is of great interest to share test instances of value chains that do not expose the actual value chain to kept secret, but that are structurally similar.

[0092] For the generated synthetic network certain structural properties specified beforehand can be guaranteed to hold.

[0093] According to another embodiment, the method of automatically generating a synthetic network from a template network further comprises the step, carried out by a user, of:

[0094] Executing a computer program that applies the generated synthetic network and analyzing properties of the synthetic network with the computer program to evaluate and / or optimize the technical value chain.

[0095] According to another embodiment, the graph-representation of the template network is provided as a directed graph. A directed graph is also called digraph. According to another embodiment, the graph-representation of the template network comprises at least one second node representing a production process step within the value chain.

[0096] According to another embodiment, generating the synthetic network comprises: modifying the extracted section by adding or subtracting one or more arcs. Constraints can be defined to what degree arcs can be subtracted or added, in particular with respect to a set comprising all arcs of the template network. For instance it may defined that the amount of arcs to be removed is subject to an upper bound, such as e.g. 10%. This ensures that structural properties of the template network are preserved to a certain degree also in the synthetic network. This pertains in particular to relevant properties defined beforehand.

[0097] According to another embodiment, the user input comprises at least one of the following demands for the synthetic network:

[0098] - a choice between the presence or absence of specific structural parts of the synthetic network to be generated;

[0099] - values attributed to arcs;

[0100] - data types for the values attributed to arcs;

[0101] - a permissible range for the values attributed to arcs;

[0102] - a specification of the sum of the values of a plurality of arcs arriving at or leaving a certain type of node;

[0103] - a name of a node;

[0104] - a desired total number of nodes of the synthetic network to be generated;

[0105] - a desired total number of strongly connected components of the synthetic network to be generated;

[0106] The expression "at least one of A, B and C" may mean "A, B, and / or C" in accordance to this disclosure. For example, it may be sufficient of e.g. only B is present. One from the group consisting of the items above is hence to be selected, or combinations thereof. Further possible combinations may be:

[0107] - A

[0108] - B

[0109] - C

[0110] - A and B

[0111] - A and C

[0112] - B and C

[0113] - A, B, and C.

[0114] Strongly connected components are important in graph theory because they can help identify strongly connected parts of a graph. For example, if it is desired to find all strongly connected subgraphs of a large directed graph, it can be started by finding all strongly connected components and continued by extracting the strongly connected subgraphs from each strongly connected component. To find all strongly connected components in a graph algorithms like Tarjan's algorithm or Kosaraju-Sharir's algorithm can be applied. The concept of strong connectivity applies specifically to directed graphs. Directed graphs are characterized by linking arcs of two nodes asymmetrically. In graph theory, a strongly connected component of a directed graph is a subgraph of the directed graph that comprises a path via edges with defined directions, i.e. arcs, from every node to every other node. In other words, every node in the strongly connected component has a way to reach every other node within the strongly connected component by following one or more arcs. In again other words, a strongly connected component is a maximal subset of nodes which can be reached from every node in the subset by following arcs. Hence, it is possible in this case to traverse the entire subgraph by following the direction of its arcs. A directed graph is strongly connected if every node v is reachable from every other node w (i.e. a directed path exists from w to v). The strongly connected components of a directed graph G form a partition of its node set into subgraphs that are themselves strongly connected. A condensation graph C(G) of G contains a node for each strongly connected component in G, and contains an arc between node I and node J if and only if there is an arc from any node in the strongly connected component I to any node in the strongly connected component J of G.

[0115] The choice between the presence or absence of specific structural parts of the synthetic network to be generated refers in particular to subgraphs, cycles, and connected components, of which the user can demand to be present or absent. The data types for the values attributed to arcs refer to data types as commonly known from software source code, e.g. ‘integer’ or ‘real’. These can be primitive data types, in other embodiments reference data types.

[0116] According to another embodiment, an input interface accepting the user input the user is given a choice between providing and using the template network and using a skeleton network with user-specified structural characteristics instead of the template network.

[0117] If the user prefers a rather realistic synthetic network representing a value chain of a given size, he will chose the template network. In contrast to this, a skeleton network with customized structural characteristics can be prescribed. Such skeleton networks are particularly useful for testing edge cases and debugging purposes. A structure according to the specified structural characteristics can be added, These structural characteristics to be specified by the user may comprise at least one of the following:

[0118] - a bipartite network;

[0119] - a synthetic network with exactly one cycle;

[0120] - an acyclic synthetic network;

[0121] - a synthetic network that contains a specified subnetwork.

[0122] One from the group consisting of the items above is hence to be selected, or combinations thereof. The term “at least one of’ is to be understood as a collection of items mutually connected with “and / or”.

[0123] According to another embodiment, the template network is transformed to the synthetic network according to one or more similarity requirements between the selected part of the template network and the synthetic network. This is to guarantee that the resulting synthetic network differs from the original template network only in negligible aspects. Various similarity metrics may be defined to ensure the computer-implemented method automatically generates a realistic synthetic network of any given number of nodes. Let GB be the template network, and let Gs be the synthetic network generated.

[0124] In some embodiments, the concept of similarity may have one or more similarity metrics, such as a combination of all of the following metrics:

[0125] A first similarity metric relates to a condensation graph C(GB) with the condensation graph C(Gs). Let s be the number of strongly connected components in Gs. The user may indicate the number of strongly connected components s in the system. If the user does not, this number s will be generated randomly.

[0126] Similarity metric 1 : There should exist an induced subgraph G in C(GB) of size s, such that the edit distance from C(Gs) to G does not exceed a given threshold T 1 . The method then constructs, based on input C(GB) a digraph G that matches similarity metric 1. An edit distance between two digraphs is defined as follows: An isomorphism of digraphs G and H is a bijection f: V(G)— >V(H) between the node sets of G and H, such that two nodes u and v of G form an arc uv in G if and only if f(u)f(v) is an arc in H. The edit distance between digraphs G and H is the length of a minimum sequence of elementary operations on G that transforms G into a digraph isomorphic with H.

[0127] G will constitute the ‘skeleton’ condensation graph of s nodes of the synthetic network. Strongly connected components need to be constructed representing the nodes of this graph G. To this end, similarity metric 2 is defined, which is based on the sizes of the strongly connected components.

[0128] Similarity metric 2: The sizes of the strongly connected components of Gs need to be sampled from a real probability distribution of strongly connected components in GB. The computer-implemented method then generates a list of sizes of strongly connected components that conform to similarity metric 2. For each node of G representing a strongly connected component, there exists a number of nodes that the respective strongly connected component must have.

[0129] In order to generate the complete Gs graph, the strongly connected components need to be created themselves and connected to each other according to G. The following similarity metric 3 deals with creating s strongly connected components in such a way that they are analogous to strongly connected components of the same size in GB: Similarity metric 3: Each strongly connected component of Gs must not exceed a given edit distance from some strongly connected components of the same size in GB. Each of the s strongly connected components of Gs should be generated according to similarity metric 3.

[0130] Furthermore, to assure that a pair of two strongly connected components of Gsare connected with a similar number of arcs as arcs between two strongly connected components of similar sizes in GB, similarity metric 4 is introduced: Similarity metric 4: Let Si and S2 be two strongly connected components of Gs of sizes Si and S2, respectively. The number of arcs connecting nodes of Si with nodes of S2 should be equal plus or minus a given percentage to the number of arcs connecting any two strongly connected components of sizes Si and S2 in GB. If there are no strongly connected components of sizes Si and S2 which are connected in GB, GB is searched for any two connects strongly connected components with sizes closest to Si and S2.

[0131] According to another embodiment, an edit distance is used as similarity requirement, wherein the edit distance is defined as a minimum number of addition or removal of arcs needed to transform the graph representation of the template network into the bipartite graph of the synthetic network.

[0132] In other words, a certain part from the template network is extracted and then modified according to a given edit distance.

[0133] According to another embodiment, the transformation of the template network is conducted by at least one of the two following elementary digraph operations: edge insertion to introduce a new arc between a pair of nodes; edge deletion to remove a single arc between a pair of nodes;

[0134] According to another embodiment, the synthetic network is derived from the template network with: computing a condensation graph of the graph-representation of the template network; extracting a weakly connected subgraph from the condensation graph; modifying the extracted weakly connected subgraph within a predefined first edit distance to a modified subgraph; identifying all strongly connected components represented by nodes of the modified subgraph; modifying each strongly connected component within a predefined second edit distance by adding arcs to the modified subgraph; for each of the added arcs: joining the modified strongly connected components; preferably in this order.

[0135] The computing of a condensation graph of the graph-representation of the template network may be done by identifying and contracting every strongly connected component to a single node. The condensation graph of a digraph D is built by adding one node per strongly connected component and an arc when an arc in D exists that connects the strongly connected components Ci and C2.

[0136] According to another embodiment, nodes of the synthetic network are labeled automatically with human-readable descriptions. Hence, the nodes of the synthetic network may be automatically decorated, giving them synthetic names. The user may customize the way this is done. To this end, the user may specify label rules for the nodes of the network, in order to give them meaningful names and make debugging and interpretation of results easier. The goal is to achieve artificial product names, that have nevertheless familiar parts that facilitate analysis, such as a company code, or a business process. The user can preferably specify a label rule for the nodes of each of the two partitions. A label rule for labeling a node is a concatenation of label terms. A label term is a text label, preferably concatenated with an integer that will be generated automatically. For a label term, the user may specify certain restrictions, that the integer generated by the system should respect. These restrictions comprise in particular one or more of the following: All in- or out-neighbors of a node within a part of the bipartition have the same label term; the label term should be constant across the same strongly connected component. Within these constraints, the labels are generated.

[0137] According to another embodiment, attributes for nodes and / or arcs of the synthetic network are automatically generated, the attributes each comprising an attribute type and an attribute value. The user may decorate the nodes and edges in the network with numerical attributes, according to configuration rules.

[0138] According to another embodiment, the attributes are generated by at least one of: using a predefined rule set; sampling from a probability distribution of shares of products in an another product; applying a generative machine learning model.

[0139] Hence, attributes for the individual nodes and / or arcs of the synthetic network may be created. An attribute preferably consists of an attribute type and a value. Methods for generating these attributes include using specified rule sets, sampling from conditional probability distributions, or using generative Al. As an example, the ratios of production nodes contributing to a consumption mix node can be sampled from a joint probability distribution where each ratio has support over real values from 0 to 1 and the sum of all ratios adds up to 1. An implementation of this is sampling from a unit-simplex. The probability distribution may also be dependent on the network structure or on other attributes. In an example, this could mean higher contributions to a consumption mix from the (production) nodes within the same company code, site or region. The goal in this case is to create artificial attributes whose values resemble the ones that come up in real value chains, such as ratios of bills of materials and consumption mixes, and clustering of nodes in production sites and regions.

[0140] Brief description of the drawings

[0141] In the following, the present disclosure is further described with reference to the enclosed figures. The same reference numbers in the drawings and this disclosure are intended to refer to the same or like elements, components, and / or parts.

[0142] Figs. 1 a-c illustrate examples of chemical processes with multi-input-multi output relations.

[0143] Fig. 2 illustrates a simplified schematic view of multiple chemical processes of the chemical production network. Fig. 3 illustrates a simplified schematic view of a sub-cluster of the chemical production network including multiple chemical processes.

[0144] Fig. 4 illustrates a simplified schematic view of multiple sub-dusters forming the chemical production network.

[0145] Fig. 5A illustrates a production node related to a network-based graph representation for a chemical production network.

[0146] Fig. 5B illustrates multiple connected first and second nodes related to a network-based graph representation for a chemical production network.

[0147] Fig. 6 illustrates a graph representation associated with a chemical production network.

[0148] Fig. 7A illustrates an example of a contracted graph representation.

[0149] Fig. 7B illustrates an example of graph characterization data.

[0150] Fig. 7C illustrates an example of strongly connected component data.

[0151] Fig. 8 illustrates a flow chart of a method for providing a target graph representation.

[0152] Fig. 9 illustrates an example of a target graph representation.

[0153] Fig. 10 illustrates a flow chart of another method for providing a target graph representation.

[0154] Fig. 11 illustrates a flow chart of a method of automatically generating a synthetic network from a template network or with an alternative according to an embodiment of the disclosure.

[0155] Fig. 12 illustrates an exemplary schematic template network from which according to an embodiment of the disclosure a synthetic network is derived.

[0156] Fig. 13 illustrates a method of automatically generating a synthetic network derived from a real value chain in a high level of abstraction.

[0157] Fig. 14 illustrates the method of Fig. 13 in a lower level of abstraction.

[0158] Fig. 15 illustrates a simplified schematic view of a chemical operating system.

[0159] Fig. 16 illustrates a flow chart of a method for controlling a production operating system.

[0160] Detailed description

[0161] The following embodiments are mere examples for implementing the method, the system or application device disclosed herein and shall not be considered limiting. The disclosure may be equally applicable to any industrial production networks producing any outputs or products from inputs by industrial processes.

[0162] In particular, chemical production networks include multi-input-multi-output chemical processes. This makes chemical production networks complex not only in the physical world, but also in their representation in digital systems that require a digital twin for monitoring such networks. One example for monitoring may be the monitoring of resource usage such as emissions or environmental impact of the chemical products produced by the chemical production network.

[0163] Monitoring and validating digital systems for chemical production networks may involve a range of challenges that stem from both structural complexity and operational constraints. Monitoring data may be highly decentralized, stored across different hierarchy levels such as chemical processes, plants, or production clusters. Gathering and integrating this data to form a coherent digital twin may require significant effort, especially when network-based monitoring data needs to be mapped to product-based logic or when emission data must be aligned with the digital representation.

[0164] The structural modeling of chemical production networks may also pose difficulties. These networks often exhibit multi-in multi-out process flows, cycles, and subgraphs, which may need to be accurately represented to reflect realistic production behavior. Constructing such digital twins may demand substantial computing resources, which in turn may lead to increased emissions and environmental impact due to the energy required for computation.

[0165] Testing digital solutions under realistic conditions may be further complicated by the limitations of real-world production environments. These environments may be too sensitive, confidential, or operationally constrained to serve as reliable testbeds. Live testing may introduce risks or require extensive computational resources, which may be costly and environmentally burdensome. To address these limitations, synthetic networks may be generated that structurally resemble real chemical production networks while allowing for flexible configuration and safe experimentation. These synthetic networks may support the validation of control logic, monitoring algorithms, and environmental assessment tools in a controlled, reproducible, and scalable manner.

[0166] Figs. 1a-c illustrate examples of chemical processes with multi-input-multi output relations as one non-limiting example of a industrial production network.

[0167] Chemical processes 100 may include different process steps for producing one or more output material(s) from one or more input material(s). The chemical process 100 may include at least one process step involving at least one chemical reaction. The chemical process 100 may produce from multiple input materials multiple output materials. Chemical processes or process steps include for example oxidation, reduction, hydrogenation, dehydrogenation, hydrolysis, hydration, dehydration, halogenation, nitrification, sulfonation, amination, alkylation, dealkylation, esterification, polymerization, polycondensation, catalysis, fermentation, mixing, separation, purification or the like. The process(es) or process steps may be performed sequentially in time and / or space to chemically, physically, mechanically and / or thermally transform input materials to output materials.

[0168] Fig. 1 a illustrates input materials 102 and 104 fed to the chemical process 100. The input materials 102 and 104 are chemically processed to output materials 106 and 108. The output materials 106 and 108 may include one main product and at least one by-product. In chemical reactions, the yield of one output material is typically below 100 %, because of side reactions and losses upon purification. Hence chemical processes may produce multiple output materials. The main product may signify the product of interest, and the by-product may signify the further output product that is unavoidably obtained by the chemical process. The by-product may be an intermediate which can be used as reagent in another chemical process. The chemical process including the feed of input materials and the produced quantity of output materials may be monitored by sensors 110 providing production monitoring data. Fig. 1 b illustrates input materials 102, 103, 104 fed to the chemical process 100. The input materials 102, 103, 104 are chemically processed to output materials 106, 108 as described in the context of Fig. 1a. In addition to the output materials 106, 108 a waste stream 112 may be produced by the chemical process. The waste stream may include any output material that cannot be used as reagent in another chemical process.

[0169] Fig. 1c illustrates input materials 102, 104 fed to the chemical process 100. The input materials 102, 104 are chemically processed to output materials 106, 108 as described in the context of Figs. 1 a and 1 b. In addition to the output materials 106, 108 a refeed stream of input material 114 may be produced and reused by the chemical process 100.

[0170] Fig. 2 illustrates a simplified schematic view of multiple chemical processes 204, 214, 216, 232 of the chemical production network. Fig. 2 illustrates the networked nature of the chemical production network. Multiple chemical processes 204, 214, 216, 232 are interlinked via their input-output material relation. For example, the output materials 206, 208 of chemical process 204 may be the input material of chemical processes 214, 216. Chemical process 214 may produce from the input materials 210 and 206 the output materials 218, 222 and waste stream 220. Output material 218 may exit the chemical production network as end products. The input material 210 may be fed to the chemical process 214 from the outside of the chemical production network. The input material 206 may be fed to the chemical process 214 from the chemical process 204 of the chemical production network. Similarly chemical process 216 may produce from the input materials 208 and 212 the output materials 224-230. Output material 228 may exit the chemical production network as end product. The output material 230 may be recirculated to chemical process 204 and fed into chemical process 204 as input material 202. Chemical process 232 may produce from the input materials 222, 224, 226 the output materials 234, 236. Output materials 234, 236 may exit the chemical production network as end products. This way the chemical production network may use interlinked or interrelated chemical processes to produce output products or end products leaving the chemical production network. The interlinking or interrelation may include at least one intermediate of one chemical process being used as input material to one or more chemical process(es) down-stream the one chemical process producing the at least one intermediate.

[0171] Fig. 3 illustrates a simplified schematic view of a sub-cluster 300 of the chemical production network including multiple chemical processes 312, 310, 318.

[0172] The chemical production network may include multiple plants performing chemical processes 312, 310, 318 and forming sub-duster 300 of the chemical production network. The sub-cluster 300 may be defined by the cluster boundary 301. The sub-cluster boundary 301 may signify input materials entering the sub-cluster 300 and output materials exiting the sub-cluster 300. The input material 302, 304 may be fed into chemical process 310. The input materials 306, 308 may be fed into chemical process 312. The output materials 320, 324 may be provided as end products of the subcluster 300 and exit the subcluster 300. The output materials 314 and 316 of chemical processes 310, 312 may be provided as input materials to chemical process 318. The output materials 322, 324 may be provided as end products of the subcluster 300 and exit the subcluster 300.

[0173] Fig. 4 Illustrates a simplified schematic view multiple sub-dusters 410, 412, 422 forming the chemical production network 400.

[0174] The chemical production network 400 may include multiple subclusters 410, 412, 422. The input materials 402, 404, 406, 408 may be fed to subclusters 410, 412. The chemical production network may be defined by the system boundary 401. The system boundary 401 may signify input materials entering the chemical production network 400 and output materials exiting the chemical production network 400. The output material 416 from subcluster 416 and the output material 418 from subcluster 412 may be fed as input material to subcluster 422. In addition, input material 414 may enter the chemical production network 400 and be fed to subcluster 422. The output materials 424, 426, 428 of sub-cluster 422 may exit the chemical production network as end products.

[0175] As illustrated in Figs. 1 to 4 the chemical production network 400 may include multiple chemical processes 100, which may be arranged in subclusters 410, 412, 422. The chemical processes 100 or subclusters 410, 412, 422 may be connected to form a network 400 with multiple production chains interrelated via their material flow. The chemical production network 400 may form part of a discrete product supply chain, wherein the discrete product is produced from one or more chemical outputs, chemical end-products or chemical output materials provided by the chemical production network 400.

[0176] The chemical production network 400 may include different entities such as chemical processes 100, chemical plants, sub-clusters 300, or combinations thereof. The chemical production network 400 may include multiple chemical plants including multiple chemical processes. The chemical plant may be operated by an operator associated with the output materials produced by the chemical plant. The sub-duster of the chemical production network may include one or more, e.g. multiple, chemical plants. The sub-cluster may be operated by an operating entity associated with the input and output materials of the sub-duster 300.

[0177] For generating the network-based and / or output material, e.g. end-product or product, based representation of a chemical production network different data sets related to different entities of the chemical production network may be gathered and processed. The different entities of the chemical production network 400 may include chemical processes 100, chemical plants and / or subclusters 300 forming the chemical production network 400 as illustrated in Figs. 1-4.

[0178] The gathering of data sets relating to different entities of the chemical production network may include gathering of production data associated with the chemical processes 100 and material flows from input materials to output materials per chemical process 100. The production data may be gathered per chemical process of the chemical production network 400. The production data may relate to production data measured per chemical process 100. The production data may include time series data measured during or on production. The production data may include time series data relating to measured production data according to production recipes per chemical process 100 or chemical process recipes. Production recipes may include measured input quantities per input material and / or measured output quantities per output material of the chemical process 100. The measured production recipes may be aggregated, such as averaged, over time such as per day, week, month, year or multiple days, weeks, months, years e.g. 1,2, or 3 years. The measured production recipes may be aggregated over time per input material and / or per output material of the chemical process 100. The aggregated production data may be provided per chemical process. The gathered or aggregated production data may relate to production quantities, such as volumes or amounts, of input material(s) and / or output material(s) per chemical process 100. The aggregated production data may include multi input-multi output relations for one or more chemical processes 100. In some embodiments the time series aggregation of production data is performed prior to generating the digital twin of the chemical production network.

[0179] The production data may include chemical process recipes or production recipes associated with the input and output materials per chemical process 100. The chemical process recipe or production recipe may include process identifiers associated with different chemical processes, input material identifiers associated with the different input materials, output identifiers associated with the different output materials, material types associated with input materials and / or output materials, quantities, such amounts or volumes, related to the input and / or output materials, ratios relating to relative quantities of the input and / or output materials or combinations thereof. The production data may include one or more, preferably multiple, structured data set(s) for chemical process recipe(s) or production recipe(s).

[0180] Since chemical processes 100 often adhere to multi-input-multi-output relations the production data provides a representation of a complex multi-input-multi-output network with multiple dependencies between multiple chemical processes 100. Such dependencies may include recirculation within a chemical process, recirculation between chemical processes, dependencies on input materials and output materials between multiple chemical processes and / or splits or forks of output materials to input materials for multiple chemical processes.

[0181] Fig. 5A illustrates a graph-based representation of a portion of a chemical production network, focusing on a single node 502 and its associated arcs. The node 502 may correspond to a representation of a production process. Multiple arcs 504, 506, 508, 510, and 512 are shown as directed connections associated with node 502, each encoding a material flow between processes. These arcs are annotated with metadata, e.g. the arcs may have attributes, including source and target process identifiers (e.g., FROM_PROCESS_ID and TO_PROCESS_ID), material identifiers (e.g., MATERIALJD), and associated quantities (e.g., QUANTITY), thereby capturing the directional and quantitative aspects of material transitions. The node 502 is annotated with metadata, e.g. may have attributes, in particular related to an identifier of the process - “PROCESSJD” -, which may be a unique name or number. The figure exemplifies how a node within the network can be connected to multiple upstream and downstream entities, and how such connections can be represented and analyzed using graph structures. This representation supports the extraction of production logic, flow dependencies, and process relationships, which may be used in subsequent steps such as graph condensation, subgraph extraction, or synthetic network generation.

[0182] Fig. 5B illustrates an alternative graph-based representation of a portion of a chemical production network, wherein both production processes and materials are modeled as distinct nodes. Node 514 may represent a production process within the chemical production network and may be referred to as a second node. Nodes 516, 518, 520, 522, and 524 may be associated with materials and may be referred to as first nodes. The materials may include input materials, intermediate materials, or output materials for the chemical production network. First nodes may relate to virtual tanks in a graph representation or may be associated with a material storage unit such as a physical tank of the chemical production network. Directed arcs 526, 528, 530, 532, and 534 connect the first nodes to and from the second node 514, thereby modeling the material flow into and out of the production process. In this representation, the identity of the material is encoded directly via the first nodes, and the arcs do not require separate annotation with material identifiers. Each arc may be annotated with a quantity value, such as QUANTITY: 'YYY' or QUANTITY: 'TTT', indicating the amount of material transferred between nodes. The directionality of the arcs may reflect the flow of material from input tanks to the process and from the process to output tanks. The material nodes may also be annotated with identifiers such as TANKJD and MATERIALJD, further specifying the material type and its associated storage or logical unit. This structure may allow for clearer separation between process logic and material flow, and may support enhanced interpretability, modularity, and traceability in graph-based modeling.

[0183] Moreover, this may facilitate aggregating equal material from different sources to simplify modeling and analysis. The representation shown in Fig. 5B may be used to construct synthetic networks that preserve the logical structure of real-world production systems while enabling flexible manipulation of material-process relationships, such as for simulation, testing, monitoring, optimization, or environmental impact assessment. Using first and second nodes, a graph representation associated with a chemical production network may be modeled as a bipartite network.

[0184] As illustrated in Fig. 5A and Fig. 5B, the node 502 and the node 514 may have an attribute associated with a location of the respective production process. Also some of the other nodes may have such an attribute, e.g. LOCATIONJD.

[0185] Fig. 6 illustrates an exemplary original graph representation 600. The original graph representation 600 is associated with a chemical production network.

[0186] The chemical production network may be a real-world chemical production network. The original graph representation may be used as a template for determining, e.g. deriving, other graph representations of other production networks based on it and may, in some embodiments, also be referred to as a template graph representation and / or the real-world chemical production network. Hence, this graph representation 600 may be “original” as it may be associated with the real-world chemical production network.

[0187] Fig. 6 schematically shows multiple nodes of the original graph network 600. Yet, as real-world chemical production networks typically may have a much larger amount of production processes, e.g. between 50.000 and 5.000.000 or more particularly between 100.000 and 500.000, and connections between them, e.g. between 200.000 and 6.000.000 or more particularly 700.000 and 2.000.000, the illustration of Fig. 6 may be associated with just a very small chemical production network or may be just a schematic simplified illustration to exemplary show certain features of such graph representation of chemical networks, which may yield an unexpected effect. The original graph representation 600 includes start nodes 610, 611 , 612, 613 and 614. The original graph representation 600 includes intermediate nodes 620, 621 , 622, 630, 631 , 632, 633, 634, 640, 650, 660 and 661. The original graph representation 600 includes end nodes 670, 671, 672, 673, 674, 675 and 676. One or more or all of the start nodes may, respectively, be associated with a feedstock for an input material, an entry point into the chemical production network for an input material, an input material and / or a production process, e.g. an entry process of the chemical production network, where an input material may enter the chemical production network. One or more or all of the intermediate nodes may, respectively, be associated with a production process such as an intermediate production process having, e.g., multiple input materials from the chemical production network fed into the respective production process, for, e.g., producing multiple output materials, which are then fed into other production processes of the chemical production network. The flow of materials, e.g. feeding input materials into respective production processes, is represented in the graph representation as arcs, e.g. directed edges, and is exemplarily illustrated in Fig. 6 by the arrows between the nodes. One or more or all of the end nodes may, respectively, be associated with an exit point out of the chemical production network for an output material, an output material and / or a production process, e.g. an exit process of the chemical production network, where an output material may leave the chemical production network.

[0188] As illustrated in conjunction with Fig. 7A, the nodes 620, 621 and 622 are a strongly connected component of the graph representing the chemical production network. The nodes 630, 631 , 632, 633 and 634 may be another strongly connected component of the graph. The nodes 660 and 661 may be yet another strongly connected component of the graph. Such nodes of a strongly connected components may be associated with production processes have the same location, being part of the same cluster and / or sub-cluster, wherein more diverse and / or higher material flows and cycles may typically be more likely when such production processes are located near to each other. Hence, the chemical production network and accordingly the graph representation may be viewed with two scales, one showing, e.g. local, strongly connected components, and the other showing a lower connection density and a lower amount of cycles, e.g. no cycles, yet on a larger scale, e.g. more distributed with higher distances between locations.

[0189] Fig. 7A illustrates a contracted graph representation 700. For example, the graph 700 illustrated in Fig. 7A may be a condensed graph of graph 600, wherein all strongly connected components have, respectively, been contracted to a respective single node. The start nodes 710, 711 , 712, 713 and 714 may be related to the start nodes 610, 611 , 612, 613 and 614. The contracted, also referred to as condensed, node 720 may be related to the nodes 620, 621 and 622. The condensed single node 730 may be related to the nodes 630, 631 , 632, 633 and 634. The condensed node 760 may be related to the nodes 660 and 661 . The end nodes 770, 771, 772, 773, 774, 775 and 776 may be related to the end nodes 670, 671 , 672, 673, 674, 675 and 676. Fig. 7B illustrates an example of graph characterization data 780, which is associated with the contracted graph representation shown in Fig. 7A. The contracted graph in Fig. 7A may be determined by replacing each strongly connected component of the original graph representation of the chemical production network with a single node, thereby simplifying the network structure while preserving its essential connectivity. The graph characterization data in Fig. 7B provides structural metrics that describe this contracted graph in quantitative terms.

[0190] The label NODE_COUNT: '17' indicates that the contracted graph comprises seventeen nodes, which may include nodes representing starting products, end products, and contracted strongly connected components. The label ARC_COUNT: '16' denotes that sixteen directed arcs are present, representing material flows or process transitions between these nodes. These counts reflect the overall size and connectivity of the contracted graph and are used to guide the generation of synthetic networks.

[0191] The labels AVG_IN_DEGREE: '...' and AVG_OUT_DEGREE: '...' are placeholders for the average number of incoming and outgoing arcs per node, respectively. These metrics provide insight into the directional complexity of the network and are relevant for evaluating the scalability and robustness of control logic applied to the production system. For example, a high average out-degree may indicate a production node that distributes material to many downstream processes, while a high in-degree may suggest aggregation of inputs from multiple sources.

[0192] The label QUANTITIES: '[..., ...]' represents a placeholder for a list of numerical values associated with the arcs, such as production volumes, material ratios, or flow intensities. These quantities may be derived from historical production data or simulated values and are used to inform the generation of synthetic networks that preserve realistic operational characteristics. For instance, a quantity value might represent the share of a precursor material in a downstream product or the throughput of a production step.

[0193] Together, the graph characterization data shown in Fig. 7B may serve as a foundational input for subsequent processing steps, including subgraph extraction, structural transformation within a defined edit distance, and expansion into synthetic networks. By capturing essential structural and quantitative properties of the contracted graph from Fig. 7A, this data enables the controlled generation of synthetic production networks that are structurally similar to the original system while allowing for anonymization, scaling, and targeted testing.

[0194] Fig. 70 illustrates an example of strongly connected component data 790, which may refer to the strongly connected component represented by node 720 in Fig. 7A. This data describes structural and quantitative properties of a group of nodes in the original graph representation of the chemical production network that are mutually reachable via directed paths. The data may be used to characterize the internal structure of such a component prior to its contraction into a single node in the contracted graph.

[0195] The label NODEJD: '720' identifies the strongly connected component under consideration. The label

[0196] NODE_COUNT: '3' indicates that the component comprises three nodes in the original graph, each of which may represent a production process or a material state. The label ARC_COUNT: '3' specifies that three directed arcs are present within the component, connecting the nodes and forming its internal topology. The label CYCLE_COUNT: 'T indicates that the component includes one directed cycle, which may correspond to a recurring production loop or a recirculation of intermediate materials.

[0197] The label LOCATION_COUNT: 'T indicates that all nodes of the component are associated with the same location. This may reflect a localized cluster of production processes operating within a single site or facility. The label QUANTITIES: '[..., ...]' is a placeholder for numerical values associated with the arcs, such as production volumes, material ratios, or consumption shares. These values may be derived from historical production data or generated synthetically and may be used to simulate realistic operational behavior within the component.

[0198] The strongly connected component data shown in Fig. 70 may be part of a set of such data, with one data set provided for each strongly connected component of the original graph.

[0199] Graph characterization data may relate to structural metrics associated with a graph representation, in particular with the contracted graph. Such data may include, for example, the number of nodes, the number of arcs, average indegree and out-degree, the number of cycles, connectivity density, or aggregated quantities associated with material flows. Graph characterization data may be used to describe the overall structure of a graph at a higher level of abstraction, especially after strongly connected components have been contracted. Strongly connected component data may relate to detailed structural and quantitative properties of individual strongly connected components identified in the original graph representation prior to contraction. Such data may include, for example, the number of nodes and arcs within a component, the number and length of cycles, location identifiers, and material flow quantities. For example, the minimum length of a cycle may be 4, when using a bipartite graph representation such as one with nodes and arcs as illustrated with Fig. 5B, in particular, when a direct flow from an output material of a process back into the chemical process is removed from the graph representation by adapting the attributes associated with the material flows. While graph characterization data may be used to guide the generation of a skeleton graph or to define graph generation parameters for synthetic network construction, strongly connected component data may be used to preserve or reconstruct internal structure and flow dynamics that are no longer visible in the contracted graph. Their interplay may support multi-scale modeling, where the contracted graph provides a simplified backbone and the strongly connected component data enables reintroduction of localized complexity during expansion or synthetic graph generation.

[0200] These data sets may be used to guide the generation of synthetic networks by enabling the construction of synthetic components that reflect the size, connectivity, and flow characteristics of their real-world counterparts. By preserving such structural and quantitative features, the synthetic network may support robust testing of control logic, performance evaluation, and environmental impact analysis, while avoiding the use of sensitive production data. Fig. 8 illustrates a flow chart of a method for providing a target graph representation associated with a chemical production network. The method may be implemented by a computer program or system configured to process graph-based representations of production networks and to generate synthetic networks for testing, monitoring, or optimization purposes.

[0201] In an optional step 820, production data associated with multiple production processes may be provided. This production data may include one or more production parameters associated with the operation of the chemical production network, such as input and output quantities, material identifiers, process yields, or emission factors. The production data may serve as a basis for generating the original graph representation and may reflect real-world or simulated process behavior.

[0202] In step 802, an original graph representation associated with a chemical production network is provided. The original graph representation may comprise nodes representing production processes or material states, and directed arcs representing material flows between these nodes.

[0203] In step 804, multiple strongly connected components included in the original graph representation are determined. Each strongly connected component may represent a group of nodes that are mutually reachable via directed paths and may correspond to localized clusters of production processes.

[0204] In step 806, a contracted graph representation is determined based on the original graph representation and the multiple strongly connected components. In the contracted graph representation, each strongly connected component is replaced by a single node, thereby reducing the complexity of the network while preserving its essential connectivity.

[0205] In step 808, target network characteristics data is provided. This data may include selection data related to a subgraph of the contracted graph representation and at least one edit distance. The selection data may specify which part of the contracted graph is to be used for generating the target graph representation, and the edit distance may define the allowable structural modifications to be applied during transformation.

[0206] In step 810, the selected subgraph is extracted and modified. The modification may comprise adding and / or removing arcs within the specified edit distance, thereby transforming the structure of the subgraph while maintaining similarity to the original network. This transformation may be used to simulate edge cases, introduce structural variation, or anonymize sensitive production data.

[0207] In step 812, a target graph representation associated with a target production network is determined. This may comprise expanding multiple nodes of the modified subgraph. The expansion may be based on corresponding strongly connected components of the original graph representation, such that the expanded nodes reflect the size, connectivity, and flow characteristics of their real-world counterparts. The original graph representation may be provided based on production data associated with multiple production processes. In particular, the production data may include process identifiers, material flows, input and output quantities, and other production parameters that allow for the construction of a graph-based model of the chemical production network. Alternatively, the original graph representation may be retrieved from a database or data repository, for example as a previously generated or stored graph representation of a real-world or simulated production network. In some cases, the original graph representation may have been generated in a prior execution of the method or by a different system component and may be reused or modified in subsequent steps. This flexibility allows the method to operate on live data, historical data, or synthetic data, depending on the use case and system configuration.

[0208] Production data may be gathered per chemical process and may include time-aggregated measurement data such as input and output material quantities, material types, and process identifiers. The production data may reflect multi- input-multi-output relations per chemical process and may be structured as chemical process recipes. These recipes may include, for example, identifiers for input and output materials, material types (e.g. main product, by-product, waste), and associated quantities or ratios. Aggregation may be performed over configurable time intervals, such as days, months, or years, depending on the stability or variability of the production process. The aggregated production data may be used to generate structured input-output relations per chemical process, which may serve as a basis for constructing a digital representation of the chemical production network.

[0209] The original graph representation may be determined by transforming the production data into a graph-based data structure. This transformation may include mapping chemical processes to nodes and material flows to directed arcs, optionally including metadata such as material identifiers, flow quantities, or origin classifications. The graph representation may be generated dynamically from current or historical production data, or it may be retrieved from a database as a previously generated representation. In some cases, the original graph representation may be reused or updated from earlier runs of the method. The original graph representation may thus serve as a foundational data structure for further processing, including graph contraction, skeleton graph generation, and target network modeling. It may reflect the full complexity of the chemical production network, including multi-input-multi-output relations, recirculation, and inter-process dependencies, and may be used to support monitoring, simulation, or optimization tasks.

[0210] The target production chain data may be determined based on the target graph representation by reversing the logic used to construct the graph from production data. While the original graph representation may be derived from measured or aggregated production data, the target graph representation may instead serve as a structural model from which production input data is inferred. For example, the arcs of the target graph representation may define material flows between production processes, and the associated attributes— such as material identifiers, flow ratios, or production parameters— may be used to reconstruct input-output relations per process. These relations may include expected input quantities, output yields, or process-specific parameters such as energy consumption or emissions. The resulting target production chain data may thus represent a hypothetical or planned configuration of the chemical production network, suitable for simulation, testing, or operational planning.

[0211] The target production chain data may be provided to a production operating system for controlling and / or monitoring the chemical production network, e.g. as illustrated in Fig. 16. This may include adapting process parameters, adjusting material flow schedules, or reconfiguring production paths in response to simulated or real-time conditions. For example, if the target graph representation reflects a desired production scenario— such as a reduced-emission configuration or a failure-mode simulation— the production operating system may use the corresponding target production chain data to implement or test the scenario. Monitoring may involve comparing actual production behavior against the expected behavior defined by the target data, enabling the detection of deviations, inefficiencies, or anomalies. In this way, the target graph representation and the derived production chain data may support both proactive control and reactive monitoring of complex chemical production networks.

[0212] Fig. 9 illustrates an example of a target graph representation 900 associated with a target production network. The target graph representation may be derived from a modified subgraph of a contracted graph representation, as outlined in the method steps of Fig. 8. The graph shown in Fig. 9 comprises a set of nodes and directed arcs that reflect structural and operational characteristics of a chemical production network, while allowing for controlled variation and abstraction.

[0213] Nodes 912 and 913 may correspond to nodes 612 and 613 of the original graph representation shown in Fig. 6. These nodes may represent material states or production processes that serve as entry points into the network. Nodes 930, 931 , 932, 933, and 934 may correspond to the strongly connected component 730 of Fig. 7A and to nodes 630 through 634 of Fig. 6. These nodes may represent a group of production processes that are mutually reachable via directed paths and may form a cycle or localized cluster. Node 950 may correspond to node 750 of Fig. 7A and may represent another strongly connected component of the original graph. Node 970 may represent an end node, for example one of the output materials of the chemical production network.

[0214] The graph shown in Fig. 9 has been modified by adding and removing arcs, as permitted by the edit distance specified in the method of Fig. 8. These structural modifications may be applied to simulate edge cases, introduce variation, or anonymize sensitive production data. Despite these modifications, the graph is derived from the original graph representation and may retain structural features of the real chemical production network. Such features may include the presence of cycles, clustering of nodes by location, and realistic flow patterns.

[0215] Preserving these features may be important for performing testing, monitoring, or optimization of digital systems associated with chemical production networks. The nodes of a target graph representation, e.g. as illustrated in Fig. 9, may have different attributes such as process name, process identifier or material name / identifier than related nodes illustrated in Fig. 6. This may facilitate enhanced security when sharing data such as the target graph representation associated with chemical production networks. The nodes of a target graph representation may have same or similar names to related nodes of an original graph representation, which may simplify identification of them.

[0216] An original graph representation may relate to a graph-based data structure describing a chemical production network, wherein nodes may represent production processes or material states, and arcs may represent material flows between them. A contracted graph may relate to a simplified version of the original graph representation. This reduction in complexity may facilitate scalable analysis, enable structural abstraction, and support downstream graph transformations.

[0217] A contracted graph may relate to a graph structure derived from an original graph representation by replacing one or more strongly connected components with corresponding single nodes. This contraction may reduce complexity and facilitate scalable analysis, while optionally preserving certain strongly connected components for modeling purposes. For example, strongly connected components associated with production processes located at different sites may remain uncontracted to retain location-specific structure. A condensed graph may relate to a stricter form of contraction, wherein all strongly connected components of the original graph representation are replaced by respective single nodes, resulting in a directed acyclic graph. Using a condensed graph as the contracted graph may enable the application of specific graph algorithms that rely on acyclicity, such as topological sorting or hierarchical decomposition. The contracted graph may therefore serve as a flexible abstraction layer, whereas in some embodiments, the contracted graph may consist of, e.g. be determined as, a condensed graph, which may provide a canonical form suitable for algorithmic processing and structural analysis.

[0218] A skeleton graph may relate to a structural framework derived from the contracted graph, which may include one or more selected subgraphs, one or more synthetically generated graphs, or combinations thereof. The skeleton graph may serve as a basis for generating a target graph representation. A target graph representation may relate to a graph structure generated by expanding one or more nodes of the skeleton graph, optionally using strongly connected components or synthetic substructures, and may represent a configurable model of a chemical production network suitable for testing, monitoring, or optimization.

[0219] These graph representations may be used within the disclosed methods as successive data structures, each enabling different levels of abstraction and control. For example, the original graph representation may be transformed into a contracted graph, the skeleton graph may be derived or constructed from the contracted graph, and the target graph representation may be generated from the skeleton graph. The contracted graph and skeleton graph may be less complex than the original graph representation and may allow for modular manipulation, targeted transformation, and efficient generation of synthetic networks. Their interplay may support flexible workflows, where structural features from the original graph are preserved, abstracted, or selectively modified to meet specific testing or simulation requirements. The target graph representation may serve as input to control logic, simulation tools, or environmental impact assessment systems. By maintaining similarity to the original network while allowing for configurable transformation, the graph shown in Fig. 9 may support robust and reproducible evaluation of production systems under varying structural and operational conditions.

[0220] Fig. 10 illustrates a flow chart of a method for providing a target graph representation associated with a chemical production network. The method may be implemented by a computer program or system configured to process graph-based representations of production networks and to generate synthetic networks for testing, monitoring, optimization, or externalization purposes. Compared to the method shown in Fig. 8, the method of Fig. 10 does not rely on extracting a subgraph from a contracted graph representation but instead uses strongly connected component data to construct the target graph representation.

[0221] In step 1002, an original graph representation associated with a chemical production network is provided. The original graph representation may comprise nodes representing production processes or material states, and directed arcs representing material flows between these nodes. The graph may reflect a real-world value chain, including complex flows, cycles, and multi-input / multi-output relations.

[0222] In step 1004, multiple strongly connected components included in the original graph representation are determined. Each strongly connected component may represent a group of nodes that are mutually reachable via directed paths and may correspond to localized clusters of production processes, such as those operating within a single site or region.

[0223] In step 1006, strongly connected component characterization data is determined. This data may include, for each component, the number of nodes, the number of arcs, the number of cycles, location identifiers, and associated quantities. The quantities may represent production ratios, material shares, or consumption mixes. The characterization data may be used to guide the generation of synthetic components that reflect the structural and operational properties of their real-world counterparts.

[0224] In step 1008, a contracted graph representation is determined based on the original graph representation and the multiple strongly connected components. In the contracted graph representation, each strongly connected component is replaced by a single node. This transformation may reduce the complexity of the network while preserving its essential connectivity. The connectivity may be preserved in particular on a large scale, such that the overall structure, clustering, and inter-component relationships remain intact. Within individual strongly connected components, structural details may be modified, and some connections may be added or removed, but the global topology of the network may still reflect the original production logic.

[0225] In step 1010, graph characterization data is determined. This data may include global metrics of the contracted graph, such as the total number of nodes and arcs, average in-degree and out-degree, and aggregated quantities associated with arcs. These metrics may be used to inform the configuration of the target graph representation and to ensure that the synthetic network remains structurally realistic.

[0226] In step 1012, graph generation user input is obtained from a user. Hence, the user may be prompted to provide graph generation input data associated with one or more graph generation parameters. The user input may specify desired structural properties, size constraints, or similarity requirements for the target graph representation. For example, the user may define whether the resulting graph should include cycles, specific subgraphs, or a given number of strongly connected components.

[0227] In step 1014, graph generation parameters are determined based on the graph characterization data and the graph generation user input. These parameters may include the number of nodes to be included in the target graph, the number of strongly connected components, and the allowable edit distance for structural modifications.

[0228] In step 1016, the strongly connected component characterization data is modified based on the graph generation user input. This modification may include adjusting the size, connectivity, or flow properties of individual components to match the desired configuration. For example, the user may specify that certain components should be bipartite, acyclic, or contain specific structural motifs.

[0229] In step 1018, target network characteristics data is provided. This data may include the modified strongly connected component characterization data and the graph generation parameters, and may serve as input for the generation of the target graph representation. The strongly connected component data may be used to define structural properties of the target network, for example by sampling from a probability distribution or a conditional probability distribution derived from the original graph representation. Such conditional distributions may be associated with contextual factors such as production site, region, or process type. A subset of the strongly connected component data may be selected, for example to reflect only certain types of production clusters or to exclude components with specific characteristics. Additionally, the method may include prompting a user to provide input specifying desired properties of the target chemical production network, such as the presence of specific structural motifs, failure modes, or real- world constraints. The target network characteristics data may thus combine statistical patterns from the original network with user-defined requirements to guide the generation of a structurally realistic and purpose-specific target graph representation.

[0230] In step 1020, a skeleton graph is determined based on the graph generation parameters of the target network characteristics data. The skeleton graph may define the high-level structure of the target graph, including the connectivity between components. The skeleton graph may be generated manually, or by applying graph-theoretic algorithms such as condensation, sampling, or generative construction. In step 1022, a target graph representation associated with a target production network is determined by expanding multiple nodes of the skeleton graph based on the target network characteristics data. The expansion may be performed using the modified strongly connected component characterization data, rather than relying on corresponding components from the original graph. The expansion may include automatic labeling of nodes, generation of attributes for arcs, and synthesis of production ratios using rule sets, probability distributions, or generative models. The target graph representation may be used for robust testing of control logic, performance evaluation, and environmental impact analysis, and may support external collaboration without exposing sensitive production data.

[0231] Fig. 11 shows a method of automatically generating a synthetic network 1 . This may also be referred to as target graph representation. First a graph-representation of the template network 3 is received S 1 , i.e. obtained and provided. The template network 3 is specified by a graph representation and describes a complex value chain of a large number of chemical processes for producing final materials as end products. Such a graph representation may also be referred to as original graph representation, wherein it is, in particular, associated with a chemical production network, e.g. it may be a digital twin of a real chemical production network. In a simplified manner, such a graphrepresentation of a template network 3 is depicted in a very simplified form in Fig. 12, where for the sake of simplicity only one of its first nodes 4 is referenced as such. While the plurality of first nodes 4 in the graph describes product states and mixes, the graph may also comprise one or more second nodes describing process steps, which do not necessarily change the mixture of a product. Each from the plurality of first nodes 4 represents a respective material state that is either a starting product or an intermediate product or an end product. Arcs between the nodes with a given direction feature a respective value representing a respective product share of the start node in the end node of a respective pair of nodes 4. Hence, the arcs describe contributing product shares of materials in one specific first node 4. As described above, in reality the graph representation of the template network 3 is expected to be huge. There can be more than 3x105nodes, more than 9x105edges, among which it can be calculated for instance to be 1 ,0x105weakly connected components and more than 3x105strongly connected components. A manual transformation to a synthetic network is thus extraordinarily complex if not impossible at all. Instead of performing a manual transformation, the user has only to define his desired specification of the desired value chain to be represented by a simplified version of the template network 3 if the use of it is desired, i.e. by a synthetic network 1. Such a synthetic network 1 is depicted in a simplified version in Fig. 12 on the right. The user may specify to desire a bipartite graph which is depicted in Fig. 12 to be recognized as such by having two-colored nodes that are connected in sequentially alternating colors. To this end, the user can provide S2 his input on an input interface 5, where it is received S2, i.e. obtained, by a computer conducting the computer implemented method. His input data may be validated in step V and analyzed whether processable and usable. It follows a decision step D, whether the template network 3 is desired for generation of the synthetic network 1. In Fig. 11, the left column stands for 'yes’, the right column for ‘no’. Both branches fulfill the purpose of generating a synthetic network 1 , while only the left branch after D, i.e. the choice for using the template network 3 as a data source leads to automatically extracting S3 a section of the graph-representation of the template network 3 according to the information provided by the user input as part of automatically generating S4 the synthetic network 1. If chosen 'yes’ in D, the template network 3 is read R, and information comprised by the graph-representation of the template network 3 is received. In this branch of the decision, the synthetic network 1 is derived from the template network 3, wherein the desired size of the synthetic network 1 is user-specified and the following steps are conducted: computing S31 a condensation graph of the graph-representation of the template network 3; extracting S32 a weakly connected subgraph from the condensation graph; modifying S33 the extracted weakly connected subgraph within a predefined first edit distance to a modified subgraph; identifying S34 all strongly connected components represented by nodes of the modified subgraph; modifying S35 each strongly connected component within a predefined second edit distance by adding arcs to the modified subgraph; for each of the added arcs: joining S36 the modified strongly connected components;

[0232] If, however, at the choice D, ‘no’ is chosen (right column after choice D in Fig. 11), a skeleton network 9 is given by the user and its structure to meet specifications predefined S30 by the user. The user, in this branch, may demand a synthetic network 1 with exactly one cycle and / or an acyclic synthetic network 1 and / or a synthetic network 1 that contains a specified subnetwork. With one of the two branches being completed, the computer-implemented method automatically labels S5 first nodes 4, and if present, second nodes, of the synthetic network 1 with human-readable descriptions. Attributes for nodes and / or arcs of the synthetic network 1 are automatically generated S6, the attributes each comprising an attribute type and an attribute value. The attributes are generated by using a predefined rule set and / or sampling from a probability distribution of shares of products in an another product and / or applying a generative machine learning model. Thereby, the automated production of the synthetic network 1 is complete and can have the shape as depicted in Fig. 12 on the right, featuring exemplary nine nodes in a bipartite graph connected by directed edges, i.e. arcs. The synthetic network 1 represents also a value chain of a chemical production process of an end product and is, when completed, packaged in a Python library and distributed, and can be analyzed by the user by executing a computer program using this Python library. Properties of the synthetic network 1 can be analyzed with the computer program to evaluate and / or optimize the technical value chain. A plurality of varied synthetic networks 1 can be produced for evaluating different properties of these, while transferring results to optimize the real-world value chain or for conducting an evaluation of the production process in particular for attributing emission measurements to end products with the help of contributed emission shares by product components.

[0233] Fig. 13 shows a method of automatically generating a synthetic network 1 based on a real value chain in a high level of abstraction. In this computer-implemented method, first, a real-world value chain is observed, analyzed, and described by a template network 3. To this end, sufficient data describing the real world value chain to generate a template network 3 is given. The computer-implemented method then transforms and modifies T in a series of operations the template network 3 such that a synthetic network 1 with desired properties is obtained. The set of operations within the transformation T comprises the steps S1 , S2, S3, S4, i.e. receiving S1 of a graphrepresentation of the template network, receiving S2 user input, automatically extracting S3 a section of the template network 3, and automatically generating S4 the synthetic network. As a result, the synthetic network 1 is obtained and can be used in computer analysis tools. Details of steps S3 and S4 can be found in Fig. 14.

[0234] Fig. 14 shows the method of Fig. 13 of automatically generating a synthetic network 1 derived from a real value chain in a lower level of abstraction. Once the template network 3 is read S1 and the user input is received S2 (cf. e.g. Fig. 11), the template network 3 is available for computing S31 a condensation graph C of the graph-representation of the template network 3. After this, a weakly connected subgraph S from the condensation graph C is extracted S32. In the schematic example of Fig. 14, the nodes of the weakly connected subgraph S are denoted by 'a', 'b' and 'c'. In the following step, the extracted weakly connected subgraph S is modified S33 within a predefined first edit distance to obtain a modified subgraph. All strongly connected components of this modified subgraph are identified S34 and each of the strongly connected components is modified S35 within a predefined second edit distance by adding arcs to the modified subgraph; these strongly connected components are represented by nodes of the modified subgraph; the added arcs in section ‘S34.S35’ right column of Fig. 14 are drawn as dashed lines for better recognizability, as opposed to the maintained arcs, which are drawn as solid lines. Finally, for each of the added arcs, the modified strongly connected components are joined S36 (cf. the two strongly connected components in the most right column of section S36 in Fig. 14). This results in a completed structure of nodes comprising at least a plurality of first nodes 4, of which in Fig. 14 only one is denoted as such for sake of simplicity. All of first nodes 4 are then ready to be labeled S5 automatically with human-readable descriptions and for attributes of the first nodes 4 to be automatically generated S6 and added to the then completed synthetic network 1 , cf. Fig. 11 .

[0235] Fig. 15 illustrates, in accordance with at least one embodiment, a simplified schematic view of a production operating system 1500 that is data-connected to a chemical production network 1510.

[0236] The chemical production network may comprise multiple production processes and may be configured to convert input materials into output materials. Input materials may be fed into the chemical production network at an entry point 1512, and output materials may leave the network at an exit point 1514.

[0237] The operating system may simulate, monitor, or control the chemical production network and may generate output data reflecting production outcomes, material flows, or computed properties. The production operating system may be implemented as a computer program product.

[0238] Feedstock 1520 may be associated with input materials entering the chemical production network. Output materials 1522 may be associated with products leaving the chemical production network. The production operating system 1500 may be configured to track input and output materials per feedstock, per production process, and per product.

[0239] The production operating system 1500 may be connected to a production database 1502. The production database may store structured data sets including input materials per feedstock 1530, input materials per production process 1532, and output materials per production process 1534. These data sets may be used to construct or validate graph-based representations of the chemical production network.

[0240] The production operating system may further comprise production parameter calculation logic 1504. This logic may be configured to compute production properties 1538, which may include material ratios, process yields, or environmental metrics. The system may also store data describing output materials per product 1536, which may support traceability and validation of production outcomes.

[0241] Fig. 16 illustrates a flow chart of a method for controlling and / or monitoring a production operating system for a chemical production network. The method may be implemented by a system configured to operate on a graph-based representation of a chemical production network and to evaluate production behavior based on predefined test criteria.

[0242] In step 1602, a target graph representation is provided. The target graph representation may describe a chemical production network in terms of nodes and arcs, where nodes represent production processes or material states and arcs represent material flows..

[0243] In step 1604, one or more test criteria are provided. The test criteria may include performance thresholds, structural constraints, environmental metrics, or validation rules. These criteria may be used to evaluate the behavior of the production operating system when applied to the target graph representation.

[0244] In step 1606, production input data is determined based on the target graph representation. The input data may include material identifiers, quantities, process configurations, or environmental attributes. The input data may be generated automatically from the graph structure or configured manually by a user. The production input data may be determined based on the target graph representation by interpreting the graph structure as a forward model of material and process dependencies. For each node in the graph, representing a production process, the incoming arcs may define the required input materials and their respective quantities or shares, while the outgoing arcs may define the expected outputs. This structure may be used to generate a complete set of production input data, including material requirements, process configurations, and inter-process dependencies. The production input data may be used to initialize or update a production operating system, for example by configuring process parameters, scheduling material flows, or allocating resources. In this way, the target graph representation may serve as a blueprint for operating the chemical production network under specific structural or operational assumptions.

[0245] In step 1608, production output data is obtained by operating the production operating system with the production input data.

[0246] In step 1610, the production output data is evaluated against the one or more test criteria. The evaluation may include checking for compliance, detecting anomalies, validating environmental properties, or assessing performance under varying conditions. In step 1612, one or more production parameters of the production operating system are adjusted in response to the evaluation. The adjustment may be performed automatically or manually and may include modifying control logic, updating configuration settings, or refining process models. The method may support iterative testing, optimization, and validation of production systems using configurable graph-based representations.

[0247] For example, the chemical production network may be adapted according to the target graph representation, wherein connections and material flows may be changed and / or production processes may be added or removed.

[0248] Test criteria may relate to one or more conditions, constraints, or expected behaviors that are used to evaluate the correctness, robustness, or domain conformity of a chemical production network model or its associated computational methods. These criteria may be defined by domain experts, derived from physical or chemical laws, or configured by a user to reflect specific production scenarios. For example, test criteria may include mass balance constraints, such as ensuring that the sum of input quantities to a process is greater than or equal to the sum of output quantities, or that the total mass is conserved when emissions and waste streams are accounted for. Test criteria may also include structural constraints, such as the absence of mass-generating cycles, or the requirement that certain materials appear only as outputs or only as inputs in specific subgraphs.

[0249] The evaluation of test criteria may be performed automatically by applying rule-based or algorithmic checks to the target graph representation and associated production data. For example, the system may verify that all input weights to a process node are strictly positive and that the main output yield is normalized to a reference value, such as 1 kg of main product. Additional checks may include verifying that no negative input quantities occur, that selfinputs (i.e. a product used to produce itself) are correctly normalized, and that no singularities arise in matrix-based consolidation steps, such as those used in product carbon footprint allocation. If violations of test criteria are detected, the system may flag the issue, suggest conservative corrections, or prompt the user for domain-compliant adjustments in accordance with regulatory frameworks.

[0250] Test criteria may also be domain-specific or user-defined to reflect real-world production logic or to simulate failure modes. For example, a user may specify that a certain node represents a known synthesis step (e.g. ammonia synthesis) and that the presence or absence of key substances (e.g. NH4) in the input or output should trigger a classification or validation rule. In synthetic network generation, test criteria may be used to ensure that generated networks reflect plausible chemical transformations, for example by sampling from synthesis databases or applying forward or retrosynthesis logic. The system may further prompt the user to define test criteria interactively, allowing for the insertion of known process behaviors, expected anomalies, or edge cases to be validated during simulation or monitoring.

[0251] The present disclosure has been described in conjunction with preferred embodiments and examples as well. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed disclosure, from the studies of the drawings, this disclosure and the claims. Any steps presented herein can be performed in any order. The methods disclosed herein are not limited to a specific order of these steps. It is also not required that the different steps are performed at a certain place or in a certain computing node of a distributed system, i.e. each of the steps may be performed at different computing nodes using different equipment / data processing.

[0252] As used herein ..determining" also includes ..initiating or causing to determine", “generating" also includes ..initiating and / or causing to generate" and “providing” also includes “initiating or causing to determine, generate, select, send and / or receive”. “Initiating or causing to perform an action” includes any processing signal that triggers a computing node or device to perform the respective action.

[0253] In the claims as well as in the description the word “comprising” or “including” or similar wording does not exclude other elements or steps and shall not be construed limiting to the elements or steps lined out. The indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation or further elements may be included.

[0254] Providing in the scope of this disclosure may include any interface configured to provide data. This may include an application programming interface, a human-machine interface such as a display and / or a software module interface. Providing may include communication of data or submission of data to the interface, in particular display to a user or use of the data by the receiving node, entity or interface.

[0255] Various units, circuits, entities, nodes or other computing components may be described as “con-figured to” perform a task or tasks. Configured to shall recite structure meaning “having circuitry that” performs the task or tasks on operation. The units, circuits, entities, nodes or other computing components can be configured to perform the task even when the unit / circuit / component is not operating. The units, circuits, entities, nodes or other computing components that form the structure corresponding to “configured to” may include hardware circuits and / or memory storing program instructions executable to implement the operation. The units, circuits, entities, nodes or other computing components may be described as performing a task or tasks, for convenience in the description. Such descriptions shall be interpreted as including the phrase “configured to.” Any recitation of “configured to” is expressly intended not to invoke 35 U.S.C. § 112(f) interpretation.

[0256] In general, the methods, apparatuses, systems, computer elements, nodes or other computing components described herein may include memory, software components and hardware components. The memory can include volatile memory such as static or dynamic random-access memory and / or nonvolatile memory such as optical or magnetic disk storage, flash memory, programmable read-only memories, etc. The hardware components may include any combination of combinatorial logic circuitry, clocked storage devices such as flops, registers, latches, etc., finite state machines, memory such as static random-access memory or embedded dynamic random-access memory, custom designed circuitry, programmable logic arrays, etc.

[0257] Moreover, any of the methods, method steps, processes and actions described or illustrated herein may be implemented using executable instructions in a general-purpose or special-purpose processor and stored on. A processor may be a processor of any suitable type, and is preferably a processor configured for parallel processing of at least a hundred or a at least a thousand threads in parallel, e.g. a graphical processing unit (GPU). For instance, the processor comprises at least a hundred or a at least a thousand parallel processing cores. In particular, the processor may comprise at least one (preferably at least a thousand) compute unified device architecture (CUDA) core(s), which may allow for using a graphical processing unit as the processor, which may increase computational efficiency. For instance, the processor may comprise at least one (e.g. at least a hundred) streaming multiprocessor cores, which may allow for increasing the data throughput. As a further example, the processor may comprise one or more (e.g. at least a hundred) tensor core(s). A tensor core may be specifically adapted to perform matrix operations and may allow to accelerate large matrix operations. A tensor core may be configured to perform mixed-precision matrix multiply and accumulate calculations in a single operation. For instance, a tensor core may perform mixed-precision floating-point matrix arithmetic, specifically utilizing FP16 (half-precision) inputs to produce either full-precision (FP32) or half-precision (FP16) outputs. In the case of FP16 output, a tensor core may provide a performance boost by storing the intermediate accumulation results in FP32 format, thereby maintaining the precision necessary for accurate results. For example, a processor may comprise several thousand tensor cores, each capable of performing 64 floating point FMA (Fused Multiply-Add) operations per clock cycle. With these capabilities, such a GPU may allow for hundreds of TFLOPs (Tera Float-ing-Point Operations per Second) of performance in mixed-precision computations. Furthermore, a tensor core may support a variety of numerical formats, including IEEE standard half-precision, single-precision, and double-precision floating-point formats, as well as a range of integer for-mats.

[0258] A processor may be a processor of any suitable type, and is preferably a processor configured for parallel processing of at least a hundred or at least a thousand threads in parallel, e.g. a graphical processing unit (GPU). For instance, the processor comprises at least a hundred or a at least a thousand parallel processing cores. In particular, the processor may comprise at least one (preferably at least a thousand) compute unified device architecture (CUDA) core(s), which may allow for using a graphical processing unit as the processor, which may increase computational efficiency. For instance, the processor may comprise at least one (e.g. at least a hundred) streaming multiprocessor cores, which may allow for increasing the data throughput. As a further example, the processor may comprise one or more (e.g. at least a hundred) tensor core(s) and / or (e.g. at least a hundred) tensor processing units (TPUs) . A tensor core may be specifically adapted to perform matrix operations and may allow to accelerate large matrix operations. A tensor core may be configured to perform mixed-precision matrix multiply and accumulate calculations in a single operation. For instance, a tensor core may perform mixed-precision floating-point matrix arithmetic, specifically utilizing FP16 (half-precision) inputs to produce either full-precision (FP32) or half-precision (FP16) outputs. In the case of FP16 output, a tensor core may provide a performance boost by storing the intermediate accumulation results in FP32 format, thereby maintaining the precision necessary for accurate results. A tensor processing unit may be an application-specific integrated circuit (ASIC). It may comprise a matrix multiplication unit (MXU), which may be specifically adapted or configured for dense linear algebra operations. TPUs may be configured to handle large-scale matrix operations efficiently, which may provide high computational throughput for Al tasks. A TPU may be equipped with on-chip high-bandwidth memory (HBM), which may enhance the capability for the use of larger models and batch sizes. TPUs may be connected in groups called Pods, which may scale up workloads with minimal code changes. An MXU may be specifically configured for performing matrix multiplications. A TPU may comprise a tensor core. For example, a processor may comprise several thousand tensor cores, each capable of performing 64 floating point FMA (Fused Multiply-Add) operations per clock cycle or (e.g. at least several hundred) tensor processing units (TPUs) being specifically configured for accelerating machine learning (ML) workloads, particularly for cloud-based applications. Additionally, Field-Programmable Gate Arrays (FPGAs) and Application-Specific Integrated Circuits (ASICs) may provide flexibility and performance benefits for specific Al tasks.. With these capabilities, such a GPU may allow for hundreds of TFLOPs (Tera Floating-Point Operations per Second) of performance in mixed-precision computations. Furthermore, a tensor core may support a variety of numerical formats, including IEEE standard half-precision, single-precision, and double-precision floating-point formats, as well as a range of integer formats.

[0259] A processor may be a central processing units (CPU) configured with an advanced architecture, such as Intel’s Xeon Scalable processors or AMD’s EPYC series. A CPU may be configured for sequential processing and general- purpose computing. These CPUs may incorporate vector instruction sets, such as AVX-512, to accelerate mathematical computations that may e.g. enhance Al model training and inference. Furthermore, CPUs may integrate Al accelerators i.e. a CPU may be specifically configured for deep learning workloads.

[0260] The processor may be coupled to memory having a memory bandwidth of at least a hundred gigabytes per second, which may allow efficient handling of extensive data sets and may allow faster reading, processing, and writing compared to a general-purpose processor such as a computational processing unit. The memory may be a high- capacity memory configured to manage the data-intensive nature of Al applications, providing necessary bandwidth and storage capacity for complex datasets. The memory may for instance be DDR4, DDR5, High Bandwidth Memory (HBM) and / or GDDR6X memory, which may improve data transfer rates and reduce latency. Such memory may enhance e.g. modeling and real-time sensor data for monitoring and control. Further, the memory may be operated with memory optimization techniques, such as caching and prefetching, which may enhance the execution speed of Al algorithms. Non-volatile Memory (NVM) technologies, including NAND Flash and 3D XPoint, may provide persistent storage solutions with high-speed access, which may enhance rapid data storage and retrieval for Al applications. Any disclosure and embodiments described herein relate to methods, systems, apparatuses, devices, chemicals, materials, computer program elements lined out above and vice versa. Advantageously, the benefits provided by any of the embodiments and examples equally apply to all other embodiments and examples and vice versa. All terms and definitions used herein are understood broadly and have their general meaning.

Claims

47Claims1 . A computer-implemented method for providing a target production chain data for controlling and / or monitoring multiple production processes of a chemical production network, wherein the target production chain data is associated with one or more production parameters per production process of the multiple production processes, the chemical production network being configured to produce multiple output materials from multiple input materials by the multiple production processes, the method including:- providing production data associated with the multiple production processes including one or more production parameters associated with the operation of the chemical production network;- providing, based on the production data, an original graph representation associated with the chemical production network, wherein the original graph representation includes multiple nodes associated with the multiple production processes and multiple arcs, wherein, per arc of the multiple arcs, the respective arc is associated with a material flow from one of the multiple production processes to another one of the multiple production processes;- determining multiple strongly connected components included in the original graph representation;- determining a contracted graph representation, based on the original graph representation and the multiple strongly connected components, wherein, per strongly connected component of the multiple strongly connected components, the respective strongly connected component of the original graph representation is contracted to a corresponding single node;- determining a target graph representation by at least determining, based on the contracted graph representation, a skeleton graph and expanding multiple nodes of the skeleton graph;- determining, based on the target graph representation, the target production chain data; and- providing the target production chain data for controlling and / or monitoring the chemical production network.

2. The method according to claim 1, wherein the method further includes:- providing selection data associated with one or more selection criteria for selecting at least a part of the contracted graph representation; and- determining a subgraph of the contracted graph representation by extracting the subgraph from the contracted graph representation based on the selection data, wherein the skeleton graph includes the subgraph.

3. The method according to claim 2, wherein expanding the multiple nodes of the skeleton graph includes replacing one or more of the multiple nodes of the skeleton graph by corresponding strongly connected components of the original graph representation.

484. The method according to any of the preceding claims, wherein the method further includes:- determining graph characterization data associated with the contracted graph representation, the graph characterization data including a value associated with a size of the contracted graph representation; and- providing, based on the graph characterization data, one or more graph generation parameters including a value associated with a size of the skeleton graph.

5. The method according to claim 4, wherein the method further includes:- determining a synthetically generated graph based on the graph generation parameters;- and wherein determining the skeleton graph includes starting from the synthetically generated graph or adding the synthetically generated graph to the skeleton graph.

6. The method according to claim 4 or claim 5, wherein the method further includes:- prompting a user to provide graph generation input data associated with one or more graph generation parameters;- and wherein providing the graph generation parameters includes setting at least one of the graph generation parameters based on the graph generation input data.

7. The method according to any of the preceding claims, wherein the method further includes:- determining strongly connected components characterization data including an indication of a probability distribution of a number of nodes per strongly connected component of the multiple strongly connected components of the original graph representation;- and wherein expanding the multiple nodes of the skeleton graph includes replacing one or more of the multiple nodes of the skeleton graph by a respective strongly connected component, wherein the respective strongly connected component is generated based on the strongly connected components characterization data.

8. The method according to any of the preceding claims, wherein the original graph representation is provided as a directed graph including multiple cycles.

9. The method according to any of the preceding claims, wherein the skeleton graph is determined as a directed acyclic graph.

10. The method according to any of the preceding claims, wherein the contracted graph representation is determined as a directed acyclic graph by replacing, per strongly connected component of the original graph representation, the respective strongly connected component by a corresponding single node.4911. The method according to any of the preceding claims, wherein the original graph representation includes multiple nodes associated with the multiple input materials, the multiple output materials and / or multiple intermediate materials and includes multiple arcs, wherein, per arc of the multiple arcs, the respective arc is associated with a material flow from one of the multiple input materials or intermediate materials to one of the multiple production processes or from one of the multiple production processes to one of the multiple intermediate or output materials.

12. The method according to claim 11 , wherein the method further includes:- determining arc characterization data associated with the original graph representation, the arc characterization data including, per arc of the multiple arcs, a respective material identifier data associated with a respective material flow of a respective material and material ratio data associated with a ratio of the respective material provided as an input material or produced by a respective production process as an intermediate material being used as an input material by another respective production process;- generating, based on the arc characterization data, per arc of the skeleton graph and / or per arc of the target graph representation, one or more attributes associated with a respective material identifier data and material ratio data; and- associating, per arc of the skeleton graph and / or per arc of the target graph representation, the one or more attributes with the respective arc.

13. The method according to any of the preceding claims, wherein attributes for at least a part of the nodes and / or at least a part of the arcs of the target graph representation are generated, the attributes respectively comprising an attribute type and an attribute value, wherein the attributes are generated by at least one of:- using a predefined rule set;- sampling from a probability distribution of ratios of materials used for producing another material;- applying a generative machine learning model.

14. The method according to any of the preceding claims, wherein determining the target graph representation includes transforming the target graph network according to one or more similarity requirements between the target graph prior to transformation and after transformation; and wherein an edit distance is used as a similarity requirement, wherein the edit distance is defined as a number of additions or removals of arcs.5015. An apparatus for providing a target production chain data for controlling and / or monitoring multiple production processes of a chemical production network, wherein the target production chain data is associated with one or more production parameters per production process of the multiple production processes, the chemical production network being configured to produce multiple output materials from multiple input materials by the multiple production processes, the apparatus including:- a production data interface configured to provide production data associated with the multiple production processes including one or more production parameters associated with the operation of the chemical production network;- a graph representation determination unit configured to determine, based on the production data, an original graph representation data related to an original graph representation of the chemical production network, the original graph representation including multiple nodes representing the multiple production processes, and multiple arcs representing material flows between the production processes;- a component analysis unit configured to determine multiple strongly connected components within the original graph representation;- a graph contraction unit configured to generate a contracted graph representation by replacing, per strongly connected component of the multiple strongly connected components, the respective strongly connected component with a single corresponding contracted node;- a target graph generator unit configured to generate a target graph representation at least by generating a skeleton graph based on the contracted graph representation and expanding multiple nodes of the skeleton graph;- a target production chain data determination unit configured to determine, based on the target graph representation, the target production chain data; and- a target production chain data interface configured to provide the target production chain data for controlling and / or monitoring the chemical production network.

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