Method, device, medium, and product for state prediction of a physical system

Abstract

According to an embodiment of the present disclosure, a method, device, medium, and product for state prediction of a physical system are provided. The method includes obtaining a neural network that has been trained to determine changes in the state of a physical system over time, wherein the training data of the neural network indicates the states of multiple physical systems at multiple times; obtaining state data corresponding to the state of a target physical system at a first time; determining a unit feature representation of each of the multiple physical units based on at least the target value of the material property of each of the multiple physical units of the target physical system; and determining the state of the target physical system at a second time based on the state data by inputting at least the unit feature representation into the neural network. Through the above scheme, the generalization ability of the neural network can be significantly improved.

Description

Technical Field

[0001] Example embodiments of the present disclosure relate generally to the field of artificial intelligence (AI), and more particularly to methods, devices, media, and products for state prediction of physical systems. Background Art

[0002] The dynamics of physical systems study how the state of a physical system changes due to the action of forces. Modeling the dynamics of physical systems is crucial for the advancement of science and engineering. For example, in scientific and engineering research, one might want to simulate the motion of a sand pile, the deformation of a snow block after collision and compression, the deformation of an elastic body during a fall, or perform finite element mechanical (FEM) analysis of an elastic body over an irregular obstacle.

[0003] Building highly accurate physics simulators requires extensive domain knowledge and significant engineering effort. However, the approximate techniques used to ensure perceptual realism can cause such simulations to deviate from reality in the long run. With the continuous advancement of machine learning technology, neural network-based physics simulators (also known as "physics engines") have been proposed to learn the dynamic state changes of physical systems over time from large amounts of training data. Existing research has demonstrated the feasibility of machine learning techniques in improving the dynamic modeling of physical systems. Summary of the Invention

[0004] According to an example embodiment of the present disclosure, a scheme for state prediction of a physical system is provided.

[0005] In a first aspect of the present disclosure, a method for state prediction is provided. The method includes: obtaining a neural network that has been trained to determine a state change of a physical system over time, wherein training data of the neural network indicates states of multiple physical systems at multiple times; obtaining state data corresponding to a state of a target physical system at a first time, wherein the state data indicates multiple physical units included in the target physical system, material properties of the multiple physical units, and interactions between the multiple physical units; determining a unit feature representation of each of the multiple physical units based on at least a target value of the material property of each of the multiple physical units in the target physical system; and determining a state of the target physical system at a second time based on the state data by inputting at least the unit feature representation into the neural network.

[0006] In a second aspect of the present disclosure, an electronic device is provided. The device includes at least one processing unit; and at least one memory, the at least one memory being coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit. When the instructions are executed by the at least one processing unit, the device performs the following actions: obtaining a neural network, the neural network has been trained to be able to determine the state changes of a physical system over time, the training data of the neural network indicating the states of multiple physical systems at multiple times; obtaining state data corresponding to the state of a target physical system at a first time, the state data indicating the multiple physical units included in the target physical system, the material properties of the multiple physical units, and the interaction relationship between the multiple physical units; determining the unit feature representation of each of the multiple physical units based on at least the target value of the material property of each of the multiple physical units in the target physical system; and determining the state of the target physical system at a second time based on the state data by at least inputting the unit feature representation into the neural network.

[0007] In a third aspect of the present disclosure, a device for state prediction is provided. The device includes a network acquisition unit configured to acquire a neural network that has been trained to determine state changes of a physical system over time, wherein training data of the neural network indicates states of multiple physical systems at multiple times; a state acquisition unit configured to acquire state data corresponding to a state of a target physical system at a first time, wherein the state data indicates multiple physical units included in the target physical system, material properties of the multiple physical units, and interaction relationships between the multiple physical units; a feature representation determination unit configured to determine a unit feature representation of each of the multiple physical units based on at least target values of the material properties of each of the multiple physical units in the target physical system; and a state determination unit configured to determine the state of the target physical system at a second time based on the state data by inputting at least the unit feature representation into the neural network.

[0008] In a fourth aspect of the present disclosure, a computer-readable storage medium is provided, wherein a computer program is stored on the medium, and when the program is executed by a processor, the method of the first aspect is implemented.

[0009] In a fifth aspect of the present disclosure, a computer-readable storage medium is provided, wherein a computer program is stored on the medium, and when the computer program is executed by a processing unit, the method of the first aspect is implemented.

[0010] In a sixth aspect of the present disclosure, a computer program product is provided, wherein the computer program product comprises a computer program executable by a processing unit, the computer program comprising instructions for executing the method of the first aspect.

[0011] It should be understood that the contents described in the summary of the present invention are not intended to limit the key features or important features of the embodiments of the present disclosure, nor are they intended to limit the scope of the present disclosure. Other features of the present disclosure will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The above and other features, advantages and aspects of the embodiments of the present disclosure will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, wherein:

[0013] Figure 1 A schematic diagram illustrating an example environment in which embodiments of the present disclosure can be implemented;

[0014] Figure 2 A flowchart illustrating a process for state prediction of a physical system according to some embodiments of the present disclosure is shown;

[0015] Figure 3 A block diagram showing an example structure of a network application system according to some embodiments of the present disclosure;

[0016] Figure 4 An example algorithm for running a neural network according to some embodiments of the present disclosure is shown;

[0017] Figure 5 shows an example directed graph for modeling a physical system according to some embodiments of the present disclosure;

[0018] Figure 6 A block diagram illustrating an apparatus for state prediction of a physical system according to some embodiments of the present disclosure; and

[0019] Figure 7 A block diagram is shown of a computing device in which one or more embodiments of the present disclosure may be implemented. DETAILED DESCRIPTION

[0020] The following describes embodiments of the present disclosure in more detail with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are for illustrative purposes only and are not intended to limit the scope of protection of the present disclosure.

[0021] In the description of the embodiments of the present disclosure, the term "including" and similar terms should be understood as open inclusion, i.e., "including but not limited to". The term "based on" should be understood as "based at least in part on". The term "one embodiment" or "the embodiment" should be understood as "at least one embodiment". The term "some embodiments" should be understood as "at least some embodiments". Other explicit and implicit definitions may be included below.

[0022] As used herein, the term "model" can learn the association between corresponding inputs and outputs from training data, so that after training is completed, corresponding outputs can be generated for given inputs. The generation of the model can be based on machine learning technology. Deep learning is a machine learning algorithm that processes inputs and provides corresponding outputs by using multiple layers of processing units. A neural network model is an example of a model based on deep learning. In this article, a "model" may also be referred to as a "machine learning model", "learning model", "machine learning network" or "learning network", and these terms are used interchangeably in this article.

[0023] A "neural network" is a machine learning network based on deep learning. A neural network is capable of processing inputs and providing corresponding outputs. It typically includes an input layer, an output layer, and one or more hidden layers between the input and output layers. Neural networks used in deep learning applications typically include many hidden layers, thereby increasing the depth of the network. The layers of a neural network are connected in sequence so that the output of the previous layer is provided as input to the next layer, where the input layer receives the input of the neural network and the output of the output layer serves as the final output of the neural network. Each layer of a neural network includes one or more nodes (also called processing nodes or neurons), each of which processes the input from the previous layer.

[0024] Generally speaking, machine learning can be roughly divided into three phases: training, testing, and application (also known as inference). During the training phase, a given model can be trained using a large amount of training data, and parameter values are continuously updated iteratively until the model can obtain consistent inferences from the training data that meet the desired goals. Through training, the model can be considered to be able to learn the association between input and output (also known as input-output mapping) from the training data. The parameter values of the trained model are determined. During the testing phase, test inputs are applied to the trained model to test whether the model can provide correct outputs, thereby determining the model's performance. During the application phase, the model can be used to process actual inputs based on the parameter values obtained during training to determine the corresponding outputs.

[0025] As mentioned above, machine learning techniques can be used to train neural networks to model the dynamics of physical systems in order to predict the dynamic state of physical systems.

[0026] Figure 1 A block diagram of an environment 100 in which various implementations of the present disclosure can be implemented is shown. In the environment 100 of FIG1 , it is desirable to train and use a neural network 105 for determining the state of a physical system over time. Such a neural network 105 may also sometimes be referred to as a physics engine, a neural network-based physics engine, a physics simulator, or the like.

[0027] A physical system can typically be divided into multiple physical units, each of which interacts with the other. This interaction can be caused by the forces acting on these units. In the study of physical dynamics, one is often interested in how the positions of multiple physical units in a system change over time under the influence of external forces. At each point in time, the multiple physical units in the system and their interactions constitute the state of the system at that point in time.

[0028] Different physical systems correspond, for example, to various types of amorphous bodies, such as fluids, solids, gases, liquids, sand piles, and snow, or to different types of definite bodies, such as various elastic bodies and rigid bodies. Physical units in a physical system can be composed of corresponding types of materials, with different materials having different material properties. In some cases, a physical system can be composed of multiple materials, and thus different physical units within it may have different material properties.

[0029] It is expected that by training neural networks, the physical dynamics of different physical systems in various scenarios can be effectively simulated.

[0030] The environment 100 includes a network training system 110 and a network application system 120. Figure 1 In the example embodiment and some example embodiments described below, network training system 110 is configured to train neural network 105 using training data 115 to optimize parameter values of neural network 105, thereby obtaining trained parameter values. Neural network 105 is configured to be suitable for predicting a state of a physical system at a second time based on a state of the physical system at a first time. Such a neural network 105 may be referred to as a physics engine or a physics simulator.

[0031] As shown above, a physical system can be considered to be composed of multiple physical units, and there is an interaction relationship between the multiple physical units. Therefore, the physical system can be represented by graph data, in particular, a directed graph. A directed graph includes multiple nodes and directed edges connecting the multiple nodes. These edges can have directions to indicate the direction of the interaction between the physical units corresponding to the connected nodes. When characterizing a physical system, the granularity of the physical units can be divided as needed. For example, for a fluid system, the physical units can include particles; for example, in a system corresponding to water, the physical units can include water droplets. For a system corresponding to sand, the physical units can include sand grains. For an elastomer system, the physical units can include a grid in the elastomer.

[0032] The trajectory of the dynamic state change of the physical system can be expressed as (G 0 , G 1 ,...,G T ), where the directed graph Denotes the state of the physical system at time t (t=0, 1, ..., T). In the following, the symbol t indicating time is omitted if it does not cause ambiguity. Represents a set of nodes in a directed graph, each node Corresponding to a physical unit, ξ represents the material properties of the physical unit. Represents the interaction relationship between the physical units corresponding to the connected nodes, that is, Means node The physical unit and node whose corresponding material property is ξ There is an interaction relationship between the physical units whose corresponding material properties are η.

[0033] When training the neural network 105, the training data 115 includes state data indicating the state of each of the plurality of physical systems at a plurality of times. The state of the physical system at a time can be represented by a directed graph. For example, Figure 1 As shown schematically, the training data 115 may include a directed graph of the state of a physical system at a certain time, including multiple physical units 1-6. Some pairs of these physical units are connected by directed edges to indicate that these physical units have previously interacted with each other. The training data 115 may also include the state of the same physical system at the next one or more times to form a trajectory of state changes, for example (G 0 , G 1 ,...,G T In some examples, training data 115 may indicate changes in the state of the same physical system under the action of external forces over time.

[0034] The multiple physical systems involved in the training data 115 may be physical systems with the same material properties. For example, these physical systems are all for fluids with specific materials (e.g., liquid, sand, snow, etc.), for elastic bodies with specific materials, for certain physical systems used in finite element analysis, etc.

[0035] The neural network 105 can be configured as any neural network suitable for processing graph data, such as a graph neural network (GNN). Before training, the parameter values of the neural network 105 can be initialized, or pre-trained parameter values can be obtained through a pre-training process. Through the training process of the network training system 110, the parameter values of the neural network 105 are updated and adjusted. After the training is completed, the neural network 105 has trained parameter values. Based on such parameter values, the neural network 105 can be used to predict the state of the physical system.

[0036] exist Figure 1 In the embodiment of the present invention, the network application system 120 receives state data 130 representing the state of the target physical system at a certain time. The target physical system includes multiple physical units, and the multiple physical units have an interaction relationship. The material properties of each physical unit can be the same or different. The network application system 120 can be configured to use the trained neural network 105 to determine the state of the target physical system at a subsequent time. The target physical system can be dynamically similar to the physical system used to train the neural network 105, for example, it contains physical units with the same material properties. However, as will be discussed below, the values of these material properties may be the same, or they may be different.

[0037] exist Figure 1 In the present invention, the network training system 110 and the network application system 120 can be any system with computing capabilities, such as various computing devices / systems, terminal devices, servers, etc. The terminal device can be any type of mobile terminal, fixed terminal, or portable terminal, including mobile phones, desktop computers, laptop computers, notebook computers, netbook computers, tablet computers, media computers, multimedia tablets, or any combination of the foregoing, including accessories and peripherals of these devices or any combination thereof. Servers include but are not limited to mainframe computers, edge computing nodes, computing devices in cloud environments, etc.

[0038] It should be understood that Figure 1The components and arrangements in the illustrated environment are merely examples, and a computing system suitable for implementing the example embodiments described herein may include one or more different components, other components, and / or different arrangements. For example, although shown as separate, the network training system 110 and the network application system 120 may be integrated into the same system or device. The embodiments of the present disclosure are not limited in this respect.

[0039] When implementing dynamic simulations of physical systems based on machine learning, machine learning relies on training data. Therefore, existing solutions often lack generalization for unknown physical processes and substances. For example, if the physical systems involved in the training data include softer elastic materials and harder elastic materials, the trained neural network (i.e., physics engine) cannot be used to make preliminary predictions about the dynamic states of elastic materials with other elasticity levels. In other words, simulators based on machine learning can only simulate physical systems that have been seen in the training data, but cannot simulate physical systems that have not been seen. Considering the needs of practical applications, it is expected that the trained physics engine can be generalized to unseen physical systems.

[0040] According to embodiments of the present disclosure, an improved state prediction scheme for physical systems is proposed. This scheme incorporates feature representations related to material properties into the input of a neural network used to simulate the physical system. Material properties can include, for example, the viscosity of a fluid, the tilt angle of sand, or the Young's modulus of an elastomer. This scheme allows neural networks trained on physical systems with multiple different values of material properties to be generalized for state prediction of physical systems with other, unseen values of material properties.

[0041] Through the above scheme, the generalization ability of the neural network can be significantly improved, so that the trained neural network can maintain good prediction accuracy even for unseen material property values.

[0042] Figure 2 FIG. 2 is a flow chart showing a process 200 for predicting the state of a physical system according to some embodiments of the present disclosure. The process 200 may be implemented in Figure 1 120 network application systems.

[0043] At block 210 , the network application system 120 obtains a neural network 105 that has been trained to determine a state change of a physical system over time. The neural network 105 obtained by the network application system 120 may have been trained by the network training system 110 using the training data 115 .

[0044] Neural network 105 can be trained to simulate the dynamics of a physical system. Physical units with different material properties can exhibit different dynamic behaviors. As mentioned above, the physical units in the multiple physical systems involved in training data 115 can have corresponding material properties.

[0045] For example, for a fluid, material properties may include the viscosity of the fluid; for a sand pile, material properties may include the inclination angle of the sand pile; for snow, material properties may include the hardening coefficient of the snow; for a particle elastomer, material properties may include the hardness of the elastomer; for a physical system used for FEM analysis, such as for analyzing the collision deformation of an elastomer on an irregular obstacle, material properties may include the Young's modulus of the elastomer.

[0046] Within the same physical system, physical units may have the same material properties or different material properties. Across multiple physical systems included in training data 115, physical units with the same material property may have different values, for example, at least two different values. For example, one or more physical systems in training data 115 may include a first viscosity value for a fluid physical unit, while one or more other physical systems may include a second viscosity value for the fluid physical unit.

[0047] In the application of neural network 105, network system 120 predicts the dynamic state of a target physical system over time. Specifically, at block 220, network application system 120 obtains state data 130 corresponding to the state of the target physical system at a given time. Network application system 120 then utilizes neural network 105 to predict the state of the target physical system at a subsequent time.

[0048] The state data 130 indicates the multiple physical units included in the target physical system, the material properties of the multiple physical units, and the interaction relationships between the multiple physical units. For example, the state data may include a directed graph It indicates the state of a physical system at time t (t=0, 1, ..., T), where Represents a set of nodes in a directed graph, each node Corresponding to a physical unit, ξ represents the material properties of the physical unit; Represents the interaction relationship between the physical units corresponding to the connected nodes, that is, Means node The physical unit and node whose corresponding material property is ξ There is an interaction relationship between physical units whose material properties are η.

[0049] In some embodiments, when the state of the physical system is represented by graph data, the neural network 105 may include a graph neural network, and is therefore also referred to as a graph-based physics engine (GPE). The neural network 105 can be implemented using various types of machine learning architectures, such as a multi-layer perceptron (MLP) neural network.

[0050] In some embodiments, the neural network 105 may be configured to determine the position of each physical unit in the physical system at a next time based on the current state of the physical system. Based on the position changes of each physical unit, the state of the physical system at a next time may be determined.

[0051] In some embodiments, due to the interaction of forces between physical units, the neural network 105 is configured to determine the change in position of the physical units from the current position to the next time by determining the influence transmitted from one physical unit to another physical unit. In such an implementation, the neural network 105 can implement state prediction based on a message passing neural network (MPNN) architecture.

[0052] Typically, due to training using training data, neural network 105 is able to learn how to simulate physical systems having various values of material properties included in training data 115. As mentioned above, in conventional approaches, the trained neural network can only be applied to simulate physical systems having values of material properties that appeared in the training data, resulting in poor generalization capabilities of the neural network and limited use of the network.

[0053] In an embodiment of the present disclosure, to enable the trained neural network 105 to be generalized for use in predicting physical systems with unseen material property values, a feature representation related to the material property is introduced into the input features of the neural network 105. In this document, a "feature representation" is used to characterize the characteristics of an object (in this example, a material property with a specific value) in the form of a multidimensional vector, including multiple vector elements. Feature representation is sometimes also referred to as vector representation or embedding.

[0054] By introducing feature representations related to material properties into the input features, during model training, the feature representations related to material properties in the input features can be optimized to accurately represent the material property values that have appeared in the training data.

[0055] Specifically, when performing state prediction on a target physical system, the network application system 120 determines a unit characteristic representation for each of the multiple physical units of the target physical system based on at least the target values of the material properties of the multiple physical units in block 230. Depending on the material properties and material property values of each unit, the unit characteristic representation for each physical unit may be different.

[0056] At block 240 , the network application system 120 determines a state of the target physical system at a second time based on the state data by inputting at least the unit feature representation into the neural network 105 .

[0057] As will be described below, in addition to the unit feature representations of the physical units, the input to the neural network 105 may also include the relationship feature representations of the interaction relationships between the multiple physical units. The neural network 105 uses the physical units indicated by the state data, the material properties of the physical units, and the interaction relationships between the physical units to determine the state of the target physical system at the second time.

[0058] According to embodiments of the present disclosure, by continuously introducing material property values into input features, neural network 105 can be used to predict the temporal state changes of a target physical system with material property values not seen during training. In this way, the generalization capability of the trained neural network is improved, expanding the physical environment that can be used for prediction.

[0059] In some embodiments, as will be described in detail below, the internal processing of the neural network 105 may be improved by introducing the constraints of the law of conservation of momentum to increase the stability of neural network training and long-term operation.

[0060] Furthermore, in some embodiments, different discretized physical systems can be represented using different graph topologies, and a neural network with a unified architecture can be used to implement state prediction.

[0061] The above generally describes some embodiments of the present disclosure. Figure 3 An example processing flow of neural network 105 is described below. Figure 3 A block diagram illustrating an example structure of a network application system 120 according to some embodiments of the present disclosure is provided. Each module / component in the network application system 120 may be implemented by hardware, software, firmware, or any combination thereof. The network application system 120 is used to train the neural network 105 to predict the state of a physical system.

[0062] exist Figure 3 In the example of FIG, the neural network 105 implements state prediction based on MPNN. Figure 3 As shown, the neural network 105 may include an encoder 320, a processor 330, and a decoder 340. The network application system 120 includes an input feature determination module 210 configured to determine input features to be input to the neural network 105 for the target physical system to be predicted.

[0063] The network application system 120 can obtain state data 130 corresponding to the state of the target physical system at a first time. The input feature determination module 210 can determine the physical units included in the target physical system, the material properties of the multiple physical units, and the interactions between the multiple physical units from the state data 130. The input feature determination module 210 can also determine target values for the material properties of the multiple physical units from additional information associated with the target physical system.

[0064] As previously mentioned, input feature determination module 210 determines unit feature representations 312 for each of the multiple physical units of the target physical system based at least on target values of the material properties of the respective physical units. In some embodiments, input feature determination module 210 may also determine relationship feature representations 314 for the interaction relationships between the multiple physical units. The process of determining unit feature representations 312 and relationship feature representations 314 will be described in detail below. Unit feature representations 312 and relationship feature representations 314 are used as inputs to neural network 105.

[0065] In the neural network 105, the unit feature representation 312 and the relationship feature representation 314 are input to the neural network 105 as the original feature representations of the physical unit and the interaction relationship between the physical units, respectively. In some embodiments, the neural network 105 treats physical units with different material properties as different types of physical units, and thus applies processing operations specific to the material properties.

[0066] Specifically, encoder 320 in neural network 105 processes the input raw feature representations to map them into a latent vector space. Encoder 320 can encode each physical unit and each interaction relationship between two physical units to obtain an intermediate encoded representation 322 corresponding to each unit feature representation 312 and an intermediate encoded representation 324 corresponding to each relationship feature representation 314.

[0067] In some embodiments, when encoding a unit feature representation 312, the encoder 320 may utilize an encoding method corresponding to the material properties of the physical unit corresponding to the unit feature representation 312. In some embodiments, for a relationship feature representation 314, the encoder 320 may utilize an encoding method corresponding to the material properties of a pair of physical units corresponding to the relationship feature representation 314.

[0068] The processing of encoder 320 can be expressed as:

[0069]

[0070] In formula (1), represents the i-th node in the node set O in the directed graph used to represent the state of the target physical system at the first time, ξ represents the material property of the i-th physical unit corresponding to the node, The cell feature representation 312 representing the i-th physical cell, represents the encoding processing method used by the encoder 320 for the relational feature representation of the material attribute ξ, represents the intermediate feature representation 322 extracted by the encoder 320 for the i-th node.

[0071] In formula (1), Represents a node in a directed graph The physical unit and node whose corresponding material property is ξ The interaction relationship between physical units whose corresponding material properties are η, Relationship feature representation 314 representing interaction relationships, represents the encoding processing method used by the encoder 320 for the relationship feature representation for the material attribute ξ and the material attribute η; Indicates that the encoder 320 is The extracted intermediate feature representation 324.

[0072] The intermediate feature representation 322 and the intermediate feature representation 324 are provided to the processor 330. The processor 330 continues to explore the features of each physical unit in the state of the target physical system at the first time, so as to be used for predicting the position of each physical unit at the next time.

[0073] Specifically, in an MPNN-based architecture, the processor 330 can determine the message transmission from the source physical unit to the destination physical unit based on the intermediate feature representation 322 corresponding to the physical unit and the intermediate feature representation 324 corresponding to the interaction relationship between the physical units to generate a message feature representation from the source physical unit to the destination. The determination of the message feature representation is based on the unit feature representation corresponding to the source physical unit, the unit feature representation of the destination physical unit, and the relationship feature representation of the interaction relationship between the two physical units, and more specifically, based on the intermediate feature representation encoded from these feature representations. The message feature representation from the source physical unit to the destination can characterize the influence of the source physical unit on the destination physical unit. For example, in the case of an applied force, it can at least indicate the effect of the force from the source physical unit to the destination physical unit.

[0074] In some embodiments, the processor 330 may iteratively determine a message feature representation from one physical unit to another physical unit multiple times, thereby characterizing the influence of multiple neighboring nodes of a physical unit into the message feature representation. The message feature representation processor 330 may determine a final feature representation 342 for each physical unit based on the message feature representation to predict the location of the physical unit at the next time.

[0075] The processing of the processor 330 can be represented as follows, where the following processing is iteratively performed for L rounds, in the lth round of processing (l=1, . . . , L, where L can be a pre-configured value):

[0076] For all edges

[0077] For all edges

[0078] For all nodes

[0079] For all edges

[0080] In formula (2), Indicates that in the lth round of processing, the node i is determined The corresponding physical unit i to the j node The corresponding message feature representation of the j-th physical unit is, It represents the processing method used by the processor 330 for the material property ξ and the material property η. represents the intermediate feature representation extracted by the processor 330 for the i-th node in the l-th round of processing, which is based on the intermediate feature representation of the node in the previous round of processing And the aggregation result of the message feature representation from the adjacent physical unit to the i-th physical unit is determined, the aggregation processing of the message feature representation Material properties specific to the ith physical unit; Represents the node set corresponding to the adjacent physical units of the i-th physical unit. Indicates that in the first round of processing, the processor 330 processes the edge The extracted intermediate feature representation is based on the intermediate feature representation of the edge in the previous round of processing and to confirm.

[0081] After L rounds, the final feature representation obtained for each physical unit is 342 is provided to the decoder 340. The decoder 340 extracts the final feature representation 342 from each physical unit. The position of the physical unit at the next time (ie, the second time) is predicted 252, which can be expressed as:

[0082] For all nodes

[0083] In formula (3) represents the decoding process used by the decoder 340 for the material property ξ of the i-th physical unit, Indicates the position of the i-th physical unit at the second time.

[0084] Figure 4 An example algorithm 400 for operating the neural network 105 in the embodiments described above is shown.

[0085] The predicted positions 342 of each physical node in the target physical system at the second time are provided to the state determination module 350 in the network application system 120. The state determination module 350 can generate state data 352 representing the state of the target physical system at the second time, such as graph data representing the state, based on the state of the target physical system at the first time and by using the predicted positions of each physical unit at the second time.

[0086] It will be appreciated that, in the neural network 105 , the various material property-specific processing methods used by the encoder 220 , processor 230 , and decoder 340 described above may be represented by processing functions, the parameter values of which are determined during the training process of the neural network 105 .

[0087] In the present disclosure, by introducing feature representations related to material properties into input features, the trained neural network 105 can be used to predict more physical systems under the same material properties.

[0088] When determining the feature representation of each physical unit in the target physical system, the input feature determination module 310 may obtain the material properties and their values of each physical unit in the multiple physical systems involved in the training data 115. The input feature determination module 310 determines whether the target value of the material property of the physical unit is the same as the value of the material property of the physical unit in the physical system used to train the neural network 105.

[0089] For known values of material properties, there may be feature representations corresponding to these values. These feature representations have already been included in the input features of the neural network 105 during the training phase of the neural network. In some embodiments, if the same value of the same material property can be found, the input feature determination module 310 can directly use the feature representation corresponding to the known value of the material property as at least part of the unit feature representation 312 of the physical unit of the target network system.

[0090] In some cases, for certain physical units in the target physical system, if the target value of the material property of the physical unit is different from the value of the physical unit with the same material property in the training data 115, the input feature determination module 310 can determine whether the target value of the material property of the physical unit falls between two known values (sometimes referred to as a first value and a second value). If so, the input feature determination module 310 can determine a unit feature representation 312 for the physical unit in the target physical system based on at least a first feature representation corresponding to the first value of the material property and a second feature representation corresponding to the second value of the material property.

[0091] Specifically, the feature representation of the value of the same material property can be considered to conform to a continuous distribution. The input feature determination module 310 can use an interpolation operation to determine the target value corresponding to the material property of the physical unit in the target physical system from the first feature representation corresponding to the first value and the second feature representation corresponding to the second value, which can be expressed as follows:

[0092] Θ(λυ1+(1-λ)υ2)=λΘ(υ1)+(1-λ)Θ(υ2) (4)

[0093] Where v1 represents the first value of a material property, v2 represents the second value of the same material property, Θ(υ1) and Θ(υ2) represent the first characteristic representation corresponding to the first value and the second characteristic representation corresponding to the second value, respectively; Θ(λυ1+(1-λ)υ2) represents the characteristic representation corresponding to another value of the same material property (which is between v1 and v2).

[0094] In the example of formula (4), the interpolation of the first and second feature representations is performed using a continuous interpolation operation. The interpolation weights λ and (1-λ) of the first and second feature representations, respectively, can be calculated based on the difference between the target value of the material property of the physical unit in the target physical system and the first and second values. For example, if the difference between the target value and the first value is smaller, then λ is determined to be larger, and accordingly, (1-λ) is determined to be smaller.

[0095] Through such interpolation operations, for any target physical system, as long as the material properties of its physical units are the same as the material properties involved in the training data used to train the neural network 105, and the values of the material properties fall between the values seen by the neural network 105 from the training data, the neural network 105 can be utilized to perform accurate state prediction.

[0096] In some embodiments, for a physical unit, the unit feature representation 312 may also indicate other information in addition to material properties. For example, the input feature determination module 310 may also determine the unit feature representation 312 for the physical unit based on the velocity of the physical unit at a first time and / or the external force applied to the physical unit at a first time. The velocity and / or external force may be mapped to respective feature representations, which are then concatenated with the feature representation determined for the material properties to form the unit feature representation 312 for the physical unit.

[0097] It is understood that the unit characteristic representation 312 of the physical unit may also be determined based on other information associated with the physical unit. The embodiments of the present disclosure are not limited in this respect.

[0098] In some embodiments, when determining the relationship feature representation 314, the input feature determination module 310 may determine the relationship feature representation 314 of the interaction relationship between a pair of physical units having an interaction relationship based on the relative positions of the pair of physical units at a first time. Such a relationship feature representation 314 may characterize the relative positioning relationship between the pair of physical units. The state data 130 may specifically indicate the positions of each physical unit at the first time. In some embodiments, the relationship feature representation 314 may not characterize the position of each physical unit in the pair of physical units. This may enable the trained neural network 105 to naturally satisfy translation invariance.

[0099] In some embodiments of the present disclosure, as mentioned above, the law of conservation of momentum may also be introduced into the internal processing of the neural network 105. Specifically, the law of conservation of momentum may be used to constrain the determined message feature representation when determining the message transfer between two physical units. After determining the message feature representation from one physical unit to another physical unit, the processor 330 in the neural network 105 may directly determine the negative value of the message feature representation as the message feature representation from the other physical unit to the previous physical unit. This is reflected in the above equation (3) as the processing: The packet is the message characteristic representation from the jth physical unit to the ith physical unit. is the characteristic representation of the message from the i-th physical unit to the j-th physical unit The message characteristics from the source physical unit to the destination physical unit indicate the influence of the source physical unit on the destination physical unit. In the dynamics of the physical system, such influence reflects the action of force. Therefore, by The calculation of can reflect the law of conservation of momentum: all forces between two objects are equal in magnitude and opposite in direction.

[0100] The law of conservation of momentum is the most fundamental law in dynamical systems, which is a direct consequence of Newton's laws of motion. However, many previously developed machine learning-based physical system simulators have ignored this law and have not explicitly introduced it as a constraint in the neural network. In conventional MPNN schemes, The calculation is similar to These conventional solutions rely on the recognition that the neural network 105 is naturally able to learn message feature representations that satisfy the law of conservation of momentum from sufficient training data.

[0101] However, the inventors of this application found through research and experiments that by introducing This simple adjustment not only ensures momentum conservation but also reduces the computational effort required to represent message features in the neural network by half, without changing the number of network parameters. This computational effort, which accounts for the vast majority of the overall network computation in the MPNN architecture, also accounts for the majority of the overall network computation. Furthermore, the introduction of the momentum conservation constraint allows for faster convergence of neural network 105 training and greater stability.

[0102] Some embodiments of the present disclosure also provide special treatment for boundary physical elements in physical systems. When simulating the dynamics of real physical systems, challenging boundary conditions are often encountered. For example, the deformation of an elastic body upon encountering an irregular boundary is a significant issue in FEM analysis. In some embodiments of the present disclosure, physical elements at the boundaries of a physical system are identified as boundary physical elements. These boundary physical elements are also represented by boundary nodes in a directed graph. These boundary nodes can model the edges of the physical system.

[0103] When neural network 105 predicts the dynamic state of a physical system, boundary nodes (i.e., boundary physical units) can be treated as stationary nodes. Thus, the collision process between the material and the boundary can be modeled by message passing between the nodes corresponding to the material physical units and the boundary nodes. This approach allows neural network 105 to be trained under simple boundary conditions and generalize to more complex boundary conditions.

[0104] During the network application phase, for example, for a target physical system, one or more boundary physical units in the target physical system may be identified. When performing state prediction, the neural network 105 may not need to dynamically determine the positions of the boundary physical units, but may assume that the positions of the boundary physical units remain unchanged.

[0105] In some embodiments, by selecting appropriate graph topology structures to represent various types of physical systems, the state prediction architecture based on graph neural networks proposed in this disclosure can be uniformly and flexibly applied to various types of physical systems.

[0106] In some embodiments, if the physical system to be simulated is a particle-based discretized physical system for training, data based on a dynamic nearest neighbor graph can be used to characterize this type of physical system. Figure 5 An example directed graph for modeling a physical system according to some embodiments of the present disclosure is shown. Figure 5 In FIG, a directed graph 510 is used to represent a physical system using a dynamic nearest neighbor graph.

[0107] Particle-based discretization systems include amorphous bodies composed of materials with no fixed shape, such as liquids, sand, and snow. Particle-based discretization systems are modeled using a dynamic nearest neighbor graph, whereby two particles are connected if their distance is less than a threshold r. The graph topology of the dynamic nearest neighbor graph reflects the fact that the interaction strength between two particles vanishes as their distance increases. As the physical system deforms during the unfolding simulation, the nearest neighbor graph needs to be updated at each time point to reflect the deformation of the physical system.

[0108] In some embodiments, if the physical system to be simulated is a grid-based discretized physical system, a static multi-scale grid graph is used to represent this type of physical system. The static multi-scale grid graph may include a graph topology across multiple time points. Figure 5 The directed graph 520 in

[0065] utilizes a static multi-scale grid graph to represent the physical system.

[0109] In a static multi-scale grid graph, a node is set for each grid point, and only nodes in the same grid unit are connected by edges to reflect the structure of the grid. In order to consider the integrity and long-range interactions during the solid deformation process, a multi-scale grid graph topology can be used. Taking a two-dimensional structure as an example, several grids (for example, four grids) in the same grid unit can be merged into a "macro grid", such as Figure 5 The macrogrids 521, 522, 523 are shown. However, a new "virtual node" can be used to represent the macrogrid, and the connectivity between the virtual nodes can be refined into "virtual edges" in the graph. Figure 5 In the example, virtual node 531 represents macrogrid 521, virtual node 532 represents macrogrid 522, and virtual node 533 represents macrogrid 523. Furthermore, multiple adjacent macrogrids can be further merged into a larger macrogrid, until the entire system is merged into a single, largest macrogrid. These virtual nodes and virtual edges are used only to describe the macrostructure and establish high-speed paths for force transmission, rather than representing actual physical units or the movement of physical units in the physical system. This approach can effectively describe shaped bodies (e.g., elastomers and other materials that can deform without changing their overall shape).

[0110] For physical systems represented by dynamic nearest neighbor graphs or static multi-scale grid graphs, dynamic simulation can be implemented similarly using the architecture of the neural network 105 described above to determine the state changes of the physical system over time.

[0111] Figure 6 A block diagram of an apparatus 600 for checking consistency between a document and an abstract according to some embodiments of the present disclosure is shown. The apparatus 600 may be implemented as or included in the network application system 120. Each module / component in the apparatus 600 may be implemented by hardware, software, firmware, or any combination thereof.

[0112] As shown in the figure, the device 600 includes a network acquisition unit 610, which is configured to obtain a neural network. The neural network has been trained to be able to determine the state changes of the physical system over time, and the training data of the neural network indicates the states of multiple physical systems at multiple times. The device 600 also includes a state acquisition unit 620, which is configured to obtain state data corresponding to the state of the target physical system at a first time, and the state data indicates the multiple physical units included in the target physical system, the material properties of the multiple physical units, and the interaction relationship between the multiple physical units. The device 600 also includes a feature representation determination unit 630, which is configured to determine the unit feature representation of each of the multiple physical units based on at least the target value of the material property of each of the multiple physical units in the target physical system. The device 600 also includes a state determination unit 640, which is configured to determine the state of the target physical system at a second time based on the state data by inputting at least the unit feature representation into the neural network.

[0113] In some embodiments, the characteristic representation determination unit 630 is configured to: for a given physical unit among a plurality of physical units, determine a plurality of values that physical units in a plurality of physical systems have that have the same material property as the physical unit; and if the target value of the material property of the given physical unit is between a first value and a second value among a plurality of values, determine the unit characteristic representation of the given physical unit based at least on a first characteristic representation corresponding to the first value of the material property and a second characteristic representation corresponding to the second value.

[0114] In some embodiments, the feature representation determination unit 630 is configured to: determine a first interpolation weight for the first value and a second interpolation weight for the second value based on the differences between the target value and the first value and the second value, respectively; and perform interpolation of the first feature representation and the second feature representation using the first interpolation weight and the second interpolation weight.

[0115] In some embodiments, the characteristic representation determination unit 630 is further configured to determine the unit characteristic representation of each of the multiple physical units based on at least one of the following: the velocity of each of the multiple physical units at the first time, and the external forces applied to the multiple physical units respectively at the first time.

[0116] In some embodiments, the device 600 further includes: a relationship feature representation determination unit configured to determine the relationship feature representations of the interaction relationships between multiple physical units, each relationship feature representation being determined based at least on the relative positions of a pair of physical units having an interaction relationship at a first time.

[0117] In some embodiments, the state determination unit 640 is configured to: determine, by a neural network, a first message feature representation from a first physical unit among a plurality of physical units to a second physical unit, the first message feature representation characterizing the influence from the first physical unit to the second physical unit; determine the negative value of the first message feature representation as a second message feature representation from the second physical unit to the first physical unit, the second message feature representation characterizing the influence of the second physical unit on the first physical unit; and determine, by the neural network, the state of the target physical system at a second time based at least on the first message feature representation and the second message feature representation.

[0118] In some embodiments, the state determination unit 640 is configured to determine a position of each of the plurality of physical units in the target physical system at a second time.

[0119] In some embodiments, the plurality of physical units include at least one boundary physical unit at a boundary of the physical system, wherein a position of the at least one boundary physical unit remains unchanged when determining the positions of the plurality of physical units at the second time.

[0120] In some embodiments, the state data includes graph data, the graph data includes multiple nodes and multiple directed edges between the multiple nodes, the multiple nodes respectively represent multiple physical units in the target physical system, and the multiple edges respectively represent the interaction relationship between the multiple physical units.

[0121] In some embodiments, the neural network is trained on a particle-based discretized physical system, and the graph data includes data based on a dynamic nearest neighbor graph. In some embodiments, the neural network is trained on a grid-based discretized physical system, and the graph data includes data based on a static multi-scale grid graph.

[0122] Figure 7 shows a computing device in which one or more embodiments of the present disclosure may be implemented.

[0123] like Figure 7 As shown, computing device 700 is in the form of a general-purpose computing device. Components of computing device 700 may include, but are not limited to, one or more processors or processing units 710, memory 720, storage device 730, one or more communication units 740, one or more input devices 750, and one or more output devices 760. Processing unit 710 may be a real or virtual processor and is capable of performing various processes according to programs stored in memory 720. In a multi-processor system, multiple processing units execute computer-executable instructions in parallel to increase the parallel processing capabilities of computing device 700.

[0124] The computing device 700 typically includes a plurality of computer storage media. Such media can be any available media accessible to the computing device 700, including but not limited to volatile and non-volatile media, removable and non-removable media. The memory 720 can be a volatile memory (e.g., registers, cache, random access memory (RAM)), a non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. The storage device 730 can be a removable or non-removable medium and can include a machine-readable medium, such as a flash drive, a disk, or any other medium that can be used to store information and / or data (e.g., training data for training) and can be accessed within the computing device 700.

[0125] The computing device 700 may further include additional removable / non-removable, volatile / non-volatile storage media. Figure 7As shown in FIG, a disk drive for reading from or writing to a removable, non-volatile disk (e.g., a "floppy disk") and an optical drive for reading from or writing to a removable, non-volatile optical disk may be provided. In these cases, each drive may be connected to a bus (not shown) by one or more data media interfaces. Memory 720 may include a computer program product 725 having one or more program modules configured to perform various methods or actions of various embodiments of the present disclosure.

[0126] The communication unit 740 enables communication with other computing devices via a communication medium. Additionally, the functionality of the components of the computing device 700 can be implemented as a single computing cluster or multiple computing machines that can communicate via a communication connection. Thus, the computing device 700 can operate in a networked environment using logical connections to one or more other servers, network personal computers (PCs), or other network nodes.

[0127] Input device 750 may be one or more input devices, such as a mouse, keyboard, or trackball. Output device 760 may be one or more output devices, such as a display, a speaker, or a printer. Computing device 700 may also communicate with one or more external devices (not shown) via communication unit 740, as needed, such as storage devices, display devices, or the like, with one or more devices that allow a user to interact with computing device 700, or with any device that allows computing device 700 to communicate with one or more other computing devices (e.g., a network card, a modem, etc.). Such communication may be performed via an input / output (I / O) interface (not shown).

[0128] According to an exemplary implementation of the present disclosure, a computer-readable storage medium is provided, on which computer-executable instructions are stored, wherein the computer-executable instructions are executed by a processor to implement the method described above. According to an exemplary implementation of the present disclosure, a computer program product is also provided, which is tangibly stored on a non-transitory computer-readable medium and includes computer-executable instructions, and the computer-executable instructions are executed by a processor to implement the method described above.

[0129] Various aspects of the present disclosure are described herein with reference to flowcharts and / or block diagrams of methods, apparatuses, devices, and computer program products implemented according to the present disclosure. It should be understood that each block of the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer-readable program instructions.

[0130] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine such that, when these instructions are executed by the processing unit of the computer or other programmable data processing device, a device is generated that implements the functions / actions specified in one or more blocks in the flowcharts and / or block diagrams. These computer-readable program instructions can also be stored in a computer-readable storage medium, where these instructions cause the computer, programmable data processing device, and / or other device to operate in a specific manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing various aspects of the functions / actions specified in one or more blocks in the flowcharts and / or block diagrams.

[0131] Computer-readable program instructions can be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operational steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0132] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple implementations of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of a module, program segment or instruction comprises one or more executable instructions for realizing the logical function of the specification. In some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented using a dedicated hardware-based system that performs the function or action of the specification, or can be implemented using a combination of dedicated hardware and computer instructions.

[0133] While various implementations of the present disclosure have been described above, the foregoing description is intended to be illustrative, not exhaustive, and not limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is selected to best explain the principles of the implementations, their practical applications, or improvements to existing technologies, or to enable others skilled in the art to understand the various implementations disclosed herein.

Claims

1. A method for state prediction, comprising: obtaining a neural network that has been trained to determine a change in state of a physical system over time, wherein training data for the neural network indicates states of a plurality of physical systems at a plurality of times; Obtaining state data corresponding to a state of a target physical system at a first time, the state data indicating a plurality of physical units included in the target physical system, material properties of the plurality of physical units, and interaction relationships between the plurality of physical units, the state data including graph data; determining a cell characteristic representation for each of the plurality of physical cells in the target physical system based at least on a target value of a material property for each of the plurality of physical cells; as well as The state of the target physical system at a second time is determined based on the state data by inputting at least the unit feature representation into the neural network, wherein, Based on determining that the neural network is trained for a particle-based discretized physical system, the graph data includes data based on a dynamic nearest neighbor graph, and based on determining that the neural network is trained for a grid-based discretized physical system, the graph data includes data based on a static multi-scale grid graph.

2. The method of claim 1 , wherein determining a cell characteristic representation of each of the plurality of physical cells comprises: For a given physical unit among the plurality of physical units, determining a plurality of values of physical units in the plurality of physical systems that have the same material property as the physical unit; as well as If the target value of the material property of the given physical unit is between a first value and a second value among the multiple values, the unit characteristic representation of the given physical unit is determined based on at least a first characteristic representation corresponding to the first value of the material property and a second characteristic representation corresponding to the second value.

3. The method of claim 2 , wherein determining the cell characteristic representation of the given physical cell comprises: determining a first interpolation weight for the first value and a second interpolation weight for the second value based on differences between the target value and the first value and the second value, respectively; as well as The interpolation of the first feature representation and the second feature representation is performed using the first interpolation weights and the second interpolation weights.

4. The method of claim 1 , wherein determining a cell characteristic representation of each of the plurality of physical cells further comprises: The unit characteristic representations of each of the plurality of physical units are also determined based on at least one of: a velocity of each of the plurality of physical units at the first time, and an external force applied to each of the plurality of physical units at the first time.

5. The method according to claim 2, further comprising: Relationship feature representations of the interaction relationships between the plurality of physical units are determined, each relationship feature representation being determined based at least on relative positions of a pair of physical units having the interaction relationship at the first time.

6. The method of claim 1 , wherein determining the state of the target physical system at the second time comprises: determining, by the neural network, a first message feature representation from a first physical unit to a second physical unit among the plurality of physical units, wherein the first message feature representation represents an influence of the first physical unit on the second physical unit; determining a negative value of the first message characteristic representation as a second message characteristic representation from the second physical unit to the first physical unit, wherein the first message characteristic representation represents an influence of the second physical unit on the first physical unit; and A state of the target physical system at a second time is determined by the neural network based on at least the first message feature representation and the second message feature representation.

7. The method of claim 1 , wherein determining the state of the target physical system at a second time comprises: Determine a position of each of the plurality of physical units in the target physical system at the second time.

8. The method of claim 7, wherein the plurality of physical units include at least one boundary physical unit located at a boundary of the physical system, wherein when determining the positions of the plurality of physical units at the second time, the position of the at least one boundary physical unit remains unchanged.

9. The method according to claim 1, wherein the graph data comprises a plurality of nodes and a plurality of directed edges between the plurality of nodes, the plurality of nodes respectively represent the plurality of physical units in the target physical system, and the plurality of edges respectively represent the interaction relationships between the plurality of physical units.

10. An electronic device comprising: at least one processing unit; as well as at least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, the instructions, when executed by the at least one processing unit, causing the apparatus to: obtaining a neural network that has been trained to determine a change in state of a physical system over time, wherein training data for the neural network indicates states of a plurality of physical systems at a plurality of times; Obtaining state data corresponding to a state of a target physical system at a first time, the state data indicating a plurality of physical units included in the target physical system, material properties of the plurality of physical units, and interaction relationships between the plurality of physical units, the state data including graph data; determining a cell characteristic representation for each of the plurality of physical cells in the target physical system based at least on a target value of a material property for each of the plurality of physical cells; as well as The state of the target physical system at a second time is determined based on the state data by inputting at least the unit feature representation into the neural network, wherein, Based on determining that the neural network is trained for a particle-based discretized physical system, the graph data includes data based on a dynamic nearest neighbor graph, and based on determining that the neural network is trained for a grid-based discretized physical system, the graph data includes data based on a static multi-scale grid graph.

11. The apparatus of claim 10, wherein determining a cell characteristic representation of each of the plurality of physical cells comprises: For a given physical unit among the plurality of physical units, determining a plurality of values of physical units in the plurality of physical systems that have the same material property as the physical unit; as well as If the target value of the material property of the given physical unit is between a first value and a second value among the multiple values, the unit characteristic representation of the given physical unit is determined based on at least a first characteristic representation corresponding to the first value of the material property and a second characteristic representation corresponding to the second value.

12. The apparatus of claim 11 , wherein determining the cell characteristic representation of the given physical cell comprises: determining a first interpolation weight for the first value and a second interpolation weight for the second value based on differences between the target value and the first value and the second value, respectively; as well as The interpolation of the first feature representation and the second feature representation is performed using the first interpolation weights and the second interpolation weights.

13. The apparatus of claim 10 , wherein determining a cell characteristic representation of each of the plurality of physical cells further comprises: The unit characteristic representations of each of the plurality of physical units are also determined based on at least one of: a velocity of each of the plurality of physical units at the first time, and an external force applied to each of the plurality of physical units at the first time.

14. The apparatus of claim 11, wherein the actions further comprise: Relationship feature representations of the interaction relationships between the plurality of physical units are determined, each relationship feature representation being determined based at least on relative positions of a pair of physical units having the interaction relationship at the first time.

15. The apparatus of claim 10, wherein determining the state of the target physical system at the second time comprises: determining, by the neural network, a first message feature representation from a first physical unit to a second physical unit among the plurality of physical units, wherein the first message feature representation represents an influence of the first physical unit on the second physical unit; determining a negative value of the first message characteristic representation as a second message characteristic representation from the second physical unit to the first physical unit, wherein the first message characteristic representation represents an influence of the second physical unit on the first physical unit; and A state of the target physical system at a second time is determined by the neural network based on at least the first message feature representation and the second message feature representation.

16. The apparatus of claim 10, wherein determining the state of the target physical system at the second time comprises: Determine a position of each of the plurality of physical units in the target physical system at the second time.

17. The apparatus of claim 16, wherein the plurality of physical units include at least one boundary physical unit located at a boundary of the physical system, wherein a position of the at least one boundary physical unit remains unchanged when determining the positions of the plurality of physical units at the second time.

18. The device according to claim 10, wherein the graph data comprises a plurality of nodes and a plurality of directed edges between the plurality of nodes, the plurality of nodes respectively represent the plurality of physical units in the target physical system, and the plurality of edges respectively represent the interaction relationships between the plurality of physical units.

19. A device for state prediction, comprising a network obtaining unit configured to obtain a neural network, wherein the neural network has been trained to determine a state change of a physical system over time, wherein training data of the neural network indicates states of a plurality of physical systems at a plurality of times; a state obtaining unit configured to obtain state data corresponding to a state of a target physical system at a first time, the state data indicating a plurality of physical units included in the target physical system, material properties of the plurality of physical units, and interaction relationships between the plurality of physical units, the state data including graph data; a characteristic representation determining unit configured to determine a cell characteristic representation of each of the plurality of physical cells in the target physical system based at least on a target value of a material property of each of the plurality of physical cells; as well as a state determination unit configured to determine a state of the target physical system at a second time based on the state data by inputting at least the unit feature representation into the neural network, wherein Based on determining that the neural network is trained for a particle-based discretized physical system, the graph data includes data based on a dynamic nearest neighbor graph, and based on determining that the neural network is trained for a grid-based discretized physical system, the graph data includes data based on a static multi-scale grid graph.

20. A computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the method according to any one of claims 1 to 9 when executed by a processing unit.

21. A computer program product comprising a computer program executable by a processing unit, the computer program comprising instructions for performing the method of any one of claims 1 to 9.

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