Methods and related devices for predicting solution field data of dynamic systems

Abstract

This application provides a method and related apparatus for predicting solution field data of a dynamic system, belonging to the field of artificial intelligence. The method includes: calling a context feature learning network to generate initial environmental context features based on prior solution field observation data of the target dynamic system in the environment to be predicted; using these initial environmental context features as the current environmental context features, calling a partial differential equation surrogate model, and generating predicted solution field observation data based on a reference initial state and reference observable conditions, using the current environmental context features as conditions; updating the environmental context features based on the predicted solution field observation data, prior solution field observation data, current environmental context features, and initial environmental context features, and using the updated context features as the new current environmental context features, until a preset number of iterations; calling the surrogate model, and generating target solution field data based on the target initial state and target observable conditions, using the adapted environmental context features of the final iteration as conditions. This can improve the prediction accuracy of unseen operating conditions.

Description

Technical Field

[0001] This application relates to the field of artificial intelligence technology, and in particular to a method and related apparatus for predicting the solution data of a dynamic system. Background Technology

[0002] In the fields of engineering and scientific research, partial differential equations (PDEs) can accurately describe the spatial distribution and temporal evolution mechanisms of physical systems by establishing mathematical constraints between spatial coordinates, time coordinates, and system state variables and their derivatives. For example, they can describe the changes in physical quantities such as heat, fluids, and electromagnetic fields in time and space.

[0003] To avoid the enormous computational overhead of performing high-precision numerical solutions for every operating condition, surrogate modeling techniques for partial differential equations have become an important means of rapidly simulating the spatiotemporal evolution of physical systems. Surrogate models can reuse the common physical laws of the same type of partial differential equation system and adapt to changes in conditions. However, in practical engineering applications, surrogate models can only obtain some controllable or observable explicit conditions (such as set temperature, dimensions, etc.), while the factors that truly determine the physical evolution results (such as slight internal wear of equipment, microscopic inhomogeneities of materials, unrecorded external disturbances, etc.) are often difficult to measure or uncontrollable.

[0004] However, surrogate modeling methods in related technologies assume that system conditions are fully observable. This approach cannot capture and adapt to changes in system response caused by implicit conditions, resulting in low prediction accuracy of surrogate models under unseen new operating conditions. Summary of the Invention

[0005] The main objective of this application is to propose a method and related apparatus for predicting the solution data of a dynamic system, which aims to capture and adapt to changes in system response caused by implicit conditions, and improve the prediction accuracy of the surrogate model under unseen new operating conditions.

[0006] To achieve the above objectives, a first aspect of this application proposes a method for predicting solution field data of a dynamical system, the method comprising: A priori solution field data set of the target dynamic system in the environment to be predicted is obtained. The priori solution field data set includes at least one partial differential equation solution field data sample. Each partial differential equation solution field data sample includes a reference initial state, a reference observable condition, and priori solution field observation data obtained under the reference initial state and the reference observable condition. The pre-trained target context feature learning network is invoked to generate initial environmental context features of the environment to be predicted based on all the prior solution field observation data in the prior solution field dataset; Using the initial environmental context features as the current environmental context features, the pre-trained target partial differential equation surrogate model is invoked. With the current environmental context features as conditional information, the corresponding first predicted solution field observation data is generated based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. The current environmental context features are updated based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features, and the initial environmental context features. The updated environmental context features are used as the new current environmental context features until a preset number of iterations is reached, and the final environmental context features are used as the adapted environmental context features. Obtain the initial state and observable conditions of the target corresponding to the target task in the environment to be predicted; The target partial differential equation proxy model is invoked, and the target solution field data of the target task to be predicted is generated based on the target initial state and the target observable conditions, using the adaptive environment context features as conditional information.

[0007] To achieve the above objectives, a second aspect of this application provides a solution field data prediction device for a dynamic system, the device comprising: The first acquisition unit is used to acquire a priori solution field data set of the target dynamic system in the environment to be predicted. The priori solution field data set includes at least one partial differential equation solution field data sample. Each partial differential equation solution field data sample includes a reference initial state, a reference observable condition, and priori solution field observation data obtained under the reference initial state and the reference observable condition. The first generation unit is used to call a pre-trained target context feature learning network to generate initial environmental context features of the environment to be predicted based on all the prior solution field observation data in the prior solution field dataset. The second generation unit is used to take the initial environmental context features as the current environmental context features, call the pre-trained target partial differential equation proxy model, and use the current environmental context features as conditional information to generate the corresponding first predicted solution field observation data based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. The update unit is used to update the current environmental context features based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features, and the initial environmental context features, and to use the updated environmental context features as the new current environmental context features, until a preset number of iterations is reached, and to use the finally obtained environmental context features as the adapted environmental context features. The second acquisition unit is used to acquire the target initial state and target observable conditions corresponding to the target task to be predicted in the environment to be predicted. The third generation unit is used to call the target partial differential equation proxy model, and generate the target solution field data of the target task to be predicted based on the target initial state and the target observable conditions, using the adaptive environment context features as conditional information.

[0008] To achieve the above objectives, a third aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described in the first aspect.

[0009] To achieve the above objectives, a fourth aspect of the present application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in the first aspect.

[0010] The proposed method and apparatus for predicting solution field data of dynamic systems extract initial environmental context features from a small amount of prior solution field observation data of the environment to be predicted by calling a target context feature learning network, thus achieving a preliminary characterization of the implicit attributes and conditional information of the unknown environment. Then, with the parameters of the surrogate model of the target partial differential equation fixed, forward deduction is performed using the current environmental context features as conditional information to generate the first predicted solution field observation data. Based on the fitting error between the predicted data and the actual prior solution field observation data, and combined with the feature deviation constraint between the current environmental context features and the initial environmental context features, the current environmental context features are iteratively optimized. Thus, compared to related technologies that involve readjusting model parameters to adapt to new environments, resulting in high computational costs, long processing times, and potential collapse of the model's original physical understanding, this application can accurately inject the physical law offset under specific environments into the conditional feature vector. Furthermore, using the adaptive environmental context features matching the environment to be predicted as conditional information, combined with the target's initial state and observable conditions, the surrogate model is driven to solve the problem, effectively capturing and adapting to changes in system response caused by implicit conditions, and improving the prediction accuracy of the surrogate model under unseen new operating conditions. Attached Figure Description

[0011] Figure 1 This is a flowchart of the method for predicting the solution field data of the dynamic system provided in this application; Figure 2A This is a schematic diagram of the target context feature learning network for the spatiotemporal evolution problem provided in this application; Figure 2B This is a schematic diagram of the target context feature learning network for the steady-state problem provided in this application; Figure 3 yes Figure 1 The flowchart of step S103 in the process; Figure 4 This is a schematic diagram of conditional modulation of the surrogate model of the target partial differential equation provided in this application; Figure 5 yes Figure 1 The flowchart of step S104 in the process; Figure 6 yes Figure 5 The flowchart of step S503 in the process; Figure 7 This is another flowchart of the dynamic system solution data prediction method provided in this application; Figure 8 This is a flowchart of the training method for the target context feature learning network and the target partial differential equation surrogate model provided in this application; Figure 9 yes Figure 8 The flowchart of step S804 in the process; Figure 10 This is a schematic diagram of the structure of the power system field data prediction device provided in the embodiments of this application; Figure 11 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0013] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0014] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0015] In the fields of engineering and scientific research, partial differential equations (PDEs) are fundamental mathematical tools used to describe the evolution of spatially distributed systems. By establishing mathematical constraints between spatial coordinates, time coordinates, and system state variables and their derivatives, PDEs can accurately describe the changes in physical quantities such as heat, fluids, and electromagnetic fields in time and space. They are widely used in engineering analysis, design optimization, and control decision-making.

[0016] In practical engineering applications, PDE solvers are often repeatedly invoked under different boundary conditions, material parameters, external inputs, or control strategies to complete tasks such as parameter scanning, online monitoring, rapid prediction, inversion calibration, or closed-loop control. However, traditional high-precision numerical solutions typically have high computational costs and struggle to meet the real-time and efficiency requirements for large-scale repeated invocations in complex geometries, high-resolution meshes, or multi-scale problems. Therefore, to address these issues, surrogate models have emerged. Surrogate models can reuse the common physical laws of the same type of PDE system and achieve adaptive and rapid solutions as conditions change.

[0017] In real-world engineering scenarios, the conditional information acquired by surrogate models during the inference phase is often incomplete. Typically, only partially controllable or recordable explicit conditional variables (such as set temperature, dimensions, boundary / source term parameters, or control inputs) are available. Other factors that truly determine the physical evolution outcome (such as internal wear of equipment, microscopic inhomogeneities of materials, effective coefficient drift, implicit boundary exchanges, or unrecorded external environmental disturbances) are often difficult to measure, uncontrollable, or exist implicitly. Therefore, although the solution field data and response results of similar PDE systems under different operating conditions, device states, or environmental configurations are constrained by the same fundamental physical laws, significant differences may exist due to variations in model coefficients or the relative strength of different physical interactions.

[0018] Proxy modeling methods in related technologies typically assume that system conditions are fully observable, directly using condition variables available during the inference phase as model inputs to learn a single-valued mapping from conditions to solutions. This surrogate modeling approach suffers from the following technical drawbacks: First, the surrogate model cannot capture and adapt to changes in system response caused by implicit conditions. When the predicted results of the solution data still depend on unobserved implicit conditions, different solution results can easily occur under the same observable conditions. Simply fitting the single-valued mapping absorbs the differences caused by implicit conditions into the model parameters or noise, leading to averaging or poor stability of the prediction results. This makes surrogate models in related technologies unable to capture and adapt to changes in system response caused by implicit conditions, resulting in a significant decrease in prediction accuracy when encountering unfamiliar operating conditions or environments.

[0019] Based on this, embodiments of this application provide a method and related apparatus for predicting solution field data of a dynamic system, which aims to capture and adapt to changes in system response caused by implicit conditions, and improve the prediction accuracy of the surrogate model under unseen new operating conditions.

[0020] The method and related apparatus for predicting the solution field data of a power system provided in this application are specifically described through the following embodiments. First, the method for predicting the solution field data of a power system in this application is described.

[0021] The dynamic system solution data prediction method provided in this application relates to the field of artificial intelligence technology. This method can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, etc.; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms; the software can be an application implementing the dynamic system solution data prediction method, but is not limited to the above forms.

[0022] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0023] Figure 1 This is an optional flowchart of the dynamic system solution data prediction method provided in the embodiments of this application. Figure 1 The method may include, but is not limited to, steps S101 to S106.

[0024] Step S101: Obtain the set of prior solution field data of the target dynamic system in the environment to be predicted; Step S102: Invoke the pre-trained target context feature learning network to generate the initial environment context features of the environment to be predicted based on all the prior solution field observation data in the prior solution field dataset; Step S103: Using the initial environmental context features as the current environmental context features, the pre-trained target partial differential equation surrogate model is called. Using the current environmental context features as conditional information, the corresponding first predicted solution field observation data is generated based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. Step S104: Update the current environmental context features based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features, and the initial environmental context features. Use the updated environmental context features as the new current environmental context features until the preset number of iterations is reached, and use the final environmental context features as the adapted environmental context features. Step S105: Obtain the initial state and observable conditions of the target corresponding to the target task in the environment to be predicted; Step S106: Call the target partial differential equation proxy model, and use the environmental context features as conditional information to generate target solution field data for the target task to be predicted based on the target initial state and target observable conditions.

[0025] Steps S101 to S106 of this embodiment involve extracting initial environmental context features from a small amount of prior solution field observation data of the environment to be predicted by calling a target context feature learning network, thereby achieving a preliminary characterization of the implicit attributes and conditional information of the unknown environment. Then, with the parameters of the target partial differential equation surrogate model fixed, forward deduction is performed using the current environmental context features as conditional information to generate the first predicted solution field observation data. Based on the fitting error between the predicted data and the actual prior solution field observation data, and in conjunction with the feature deviation constraint between the current environmental context features and the initial environmental context features, iterative optimization of the current environmental context features is performed. Thus, compared with related technologies that readjust model parameters to adapt to new environments, resulting in high computational overhead, long processing time, and collapse of the original physical cognition of the model, this application can accurately inject the physical law offset of a specific environment into the conditional feature vector. Furthermore, by using the adaptive environmental context features that match the environment to be predicted as conditional information, and combining the initial state of the target and the observable conditions of the target to drive the surrogate model to solve the problem, the system response changes caused by implicit conditions are effectively captured and adapted, thereby improving the prediction accuracy of the surrogate model under new and unseen operating conditions.

[0026] In step S101, a set of prior solution field data for the target dynamic system in the environment to be predicted is obtained. The target dynamic system refers to a system that is studied or modeled in scientific computing or engineering prediction, whose internal state evolves over time or space according to specific physical laws. The target dynamic system is usually constrained by a set of partial differential equations or ordinary differential equations. These equations describe the evolution process of various physical quantities (such as temperature, velocity, pressure, concentration, etc.) within the target dynamic system from the initial state under specific boundary conditions and external driving forces. For example, in the aerospace field, when it is necessary to predict the forces and drag on an aircraft wing during flight, the evolution process of the airflow around the wing (fluid dynamics system) is a target dynamic system; in the field of new energy vehicles, when detecting the risk of battery thermal runaway, the temperature conduction and heat distribution process inside the battery pack (thermodynamics system) is also a target dynamic system. The environment to be predicted refers to the specific operating conditions, physical configuration (e.g., the presence of unrecorded device wear or boundary disturbances), device status, material batch, or operating stage of the same type of target dynamic system.

[0027] In order for the surrogate model of partial differential equations to be able to perceive the implicit conditions in the environment to be predicted, it is first necessary to collect a small number of historical observation records in the environment to be predicted, that is, to collect a set of prior solution field data. The prior solution field data set includes at least one partial differential equation solution field data sample. Each partial differential equation solution field data sample includes a reference initial state, reference observable conditions, and prior solution field observation data obtained under the reference initial state and reference observable conditions. Specifically, the reference initial state represents the spatial distribution of the internal physical field of the target dynamic system at the initial moment of evolution (or the starting moment of entering the observation window); while the reference observable conditions represent explicit physical parameters (such as system boundary constraints, external driving sources, macroscopic control commands, or geometric dimensions) that can be clearly read, directly measured, or artificially set during the evolution process, constituting the visible environmental constraints that dominate the system evolution. For example, when predicting the heat diffusion and fluid evolution process inside the combustion chamber of an automobile engine, the reference initial state represents the temperature distribution and fuel concentration distribution inside the cylinder just before spark plug ignition, the fuel injection command issued by the engine control unit, the opening degree of the intake valve, and the physical dimensions of the cylinder, which are all considered reference observable conditions.

[0028] Prior solution field observation data represents the physical field state data (such as contour maps or sequences) recorded during the evolution of a target dynamic system, based on a reference initial state and reference observable conditions, after actual operation, real sensor measurements, or simulation. For example, it could be a fluid velocity field map at a specific moment. The form and emphasis of prior solution field observation data vary depending on the type of physical problem described by the partial differential equations. For spatiotemporal evolution problems, prior solution field observation data represents a dynamic spatiotemporal sequence, where differences between different samples under the same implicit conditions mainly lie in the initial physical field. For steady-state problems, prior solution field observation data represents a spatial steady-state field distribution, where differences between different samples under the same environment mainly lie in geometric parameters, boundary parameters, or environmental parameters. Prior solution field observation data can be pre-calculated using a high-precision numerical simulation solver or directly measured by sensors in real physical entities. For example, in a lithium battery thermal management scenario, the temperature field distribution data actually collected by a temperature sensor array on the surface of the battery pack is prior solution field observation data.

[0029] In step S102, the pre-trained target context feature learning network is invoked to generate initial environmental context features of the environment to be predicted based on all prior solution field observation data in the prior solution field dataset. Specifically, the target context feature learning network is a deep neural network with feature extraction and information fusion capabilities, and can be implemented using convolutional neural networks, neural operator networks, Transformer neural networks, or combinations thereof; no restrictions are placed here. Specifically, the target context feature learning network maps the prior solution field observation data of all samples in the prior solution field dataset to a high-dimensional latent space, and extracts mathematical vectors reflecting the common physical laws of this set of samples through global information aggregation, i.e., the initial environmental context features (denoted as...). ).

[0030] In some embodiments, a pre-trained target context feature learning network is invoked to generate initial context features of the environment to be predicted based on all prior solution field observations in the prior solution field dataset, including: The pre-trained target context feature learning network is invoked to generate corresponding sample context features based on the prior solution field observation data of each partial differential equation solution field data sample in the prior solution field dataset. Feature information fusion is performed on all sample context features to obtain the initial context features of the environment to be predicted.

[0031] In this embodiment, a pre-trained target context feature learning network is invoked to generate corresponding sample context features based on the prior solution field observation data of each partial differential equation solution field data sample in the prior solution field dataset. Specifically, this embodiment extracts the implicit laws reflecting the evolution state of the target dynamical system at the individual sample level. The target context feature learning network includes a feature encoder (such as a convolutional neural network or a Transformer encoding layer), which extracts features from the prior solution field observation data of each sample to obtain the sample context features. .

[0032] Then, feature information fusion is performed on all sample context features to obtain the initial environment context features of the environment to be predicted. Specifically, since a single sample context feature is limited by a specific reference initial state or local observation conditions, it cannot fully mine and characterize the latent conditions in the environment to be predicted. Therefore, the feature aggregation operator in the target context feature learning network is invoked to fuse the context features of all samples. (in Feature information fusion is performed on the total number of samples in the prior solution field dataset. Specifically, it can be achieved through aggregation operators such as cross-attention or self-attention mechanisms. Alternatively, aggregation methods such as average pooling and weighted average can be used to calculate the correlation and information weights between the contextual features of each sample, thereby obtaining the initial contextual features of the environment to be predicted. The initial environmental context features are used to comprehensively describe the overall impact of the environment to be predicted on the PDE solution field. They remove the specific noise of individual samples and accurately characterize the hidden environmental conditions that are unique to the environment to be predicted, which are difficult to measure directly or are not explicitly recorded (such as hidden equipment wear, material aging or changes in internal boundaries).

[0033] Specifically, please refer to Figure 2A and Figure 2B This application flexibly employs different target context feature learning network processing architectures based on the type of physical problem being solved. For example... Figure 2A As shown, for spatiotemporal evolution problems (i.e., physical fields change dynamically over time), the target context feature learning network adopts a spatiotemporal coding structure that combines a spatial encoder with a temporal encoder. Specifically, the target context feature learning network extracts spatial features for each time frame of each partial differential equation solution data sample in the prior solution data set through the spatial encoder. Then, it performs pooling operations on the extracted spatial features of each time frame to reduce dimensions and compress them into time series features (time series tokens) of the partial differential equation solution data samples. Finally, it encodes the temporal relationship of the time series features through a time projection aggregation layer to obtain the sample context features of the partial differential equation solution data samples. For steady-state problems (i.e., physical fields are spatially static and do not evolve over time, with field variables changing only with spatial location, such as inconsistent wear and scaling in different sections of a pipe) or situations where the system possesses spatially heterogeneous potential mechanisms (i.e., the physical properties or implicit laws of the target dynamic system are not uniform across different spatial regions), the target context feature learning network no longer compresses and averages the implicit laws of the physical environment into a globally unified vector without spatial dimensions. Instead, it generates a mechanism field representation, which is a feature tensor with spatial coordinate dimensions. Its data structure corresponds to the real spatial grid, enabling the allocation of independent feature values ​​to different spatial locations within the target dynamic system. This records the system's operating conditions, i.e., global environmental summary information, while simultaneously accurately locating and recording local attribute deviations at specific coordinate points, i.e., spatial local difference information. Figure 2B As shown, the target context learning receives prior solution field observation data as input context samples. Since this type of steady-state problem does not have a time evolution dimension, the input data does not need to be subjected to temporal compression or pooling operations. Instead, it is input to the spatial encoder. The spatial encoder mines information such as geometric structure features, boundary constraint effects, and potential spatial non-uniformity in the samples in a multi-dimensional spatial coordinate system, and outputs a mechanism field representation that retains the spatial distribution form as the sample context features.

[0034] This embodiment first independently extracts the sample context features of a single observation sample, and then uses an aggregation algorithm to fuse the discrete feature sets into initial environmental context features that characterize the global laws of the environment. This effectively filters out local biases and random noise caused by specific initial states or explicit environmental observation conditions in individual samples. Thus, this embodiment not only ensures that the model can stably and accurately capture the true hidden physical laws of the environment to be predicted from a very small amount of prior data with varying operating conditions, but also improves the model's robustness in representing non-stationary physical field data.

[0035] In step S103, the initial environmental context features are... As a feature of the current environmental context, a pre-trained surrogate model for the objective partial differential equation is invoked. Using the current environmental context as conditional information, and based on the reference initial state of each partial differential equation solution field data sample in the prior solution field data set. Reference observable conditions Generate the corresponding first predicted solution field observation data .

[0036] The specific execution form of calling the target partial differential equation surrogate model to generate the first predicted solution field observation data is not fixed, but will flexibly adopt three different implementation architectures according to the actual physical problem type and the network structure of the target partial differential equation surrogate model: the spatiotemporal evolution derivative network type, which is for dynamically evolving transient physical problems. In this mode, the surrogate model will refer to the initial state. As input, Take as the initial physical field The model itself does not directly output the final complete physical field, but rather predicts the evolution derivative (i.e., rate of change) of the target physical field quantity with respect to time, giving the derivative of the field quantity with respect to time. Subsequently, an Ordinary Differential Equation (ODE) numerical integrator is invoked, utilizing derivatives to perform multi-step rolling integration on a preset time grid, ultimately generating a complete time series as the first predicted solution field observation data. This steady-state point-by-point solution type is designed for static physical field problems that do not change with time. In this mode, the surrogate model uses the initial state as a reference. As input, the reference initial state of this application is represented as the initial physical field in the spatiotemporal evolution problem, and as discrete query input coordinates in the steady-state problem. It can be the query location (spatial coordinates) or the starting physics field, when When spatial coordinates (or additional time coordinates as needed) are used as discrete query inputs, the model performs forward computation and provides the solution field values ​​at specific coordinate points. This enables point-by-point reconstruction of the target physical field. The steady-state full-field solution type also addresses steady-state problems but offers a higher macroscopic perspective. In this mode, the surrogate model omits specific spatial coordinates and other inputs. ,Right now Through an end-to-end feature mapping architecture, the steady-state distribution map of the physical space is directly decoded and output as the first prediction solution field observation data.

[0037] Step S103 characterizes the initialization and first forward propagation of the finite-step iterative process in the fast adaptation inference phase. Specifically, it assigns the initial environmental context features to the iteration variables, i.e., the current environmental context features. (Initial iteration steps) The objective partial differential equation surrogate model is a deep learning solver used to learn and reuse common dynamic evolution laws or solution field response structures between different environments. Its model parameters are fixed in the inference stage. The objective partial differential equation surrogate model can be implemented using convolutional neural networks, neural operator networks, U-Net structures, fully connected neural networks, Transformer neural networks or combinations thereof, without any restrictions here.

[0038] Specifically, the target partial differential equation surrogate model performs forward decoding calculations based on the reference initial state and reference observable conditions of the partial differential equation solution field data samples. The target partial differential equation surrogate model uses the current environmental context features. This embodiment uses a feature-conditional modulation mechanism to inject the current environmental context features into the computation process. This mechanism conditionally modulates the model's internal feature representations, operator layer outputs, or intermediate latent variables. The modulation process can be implemented at any point in the encoder, latent variable layer, operator layer, decoder, or time-progression module. The result is then an intermediate simulation result under the current environmental perception, i.e., the first predicted solution field observation data. The initial environmental context features can be utilized through features linear modulation, gated modulation, bias injection, latent variable replacement, or hypernetwork parameter generation. When the initial environmental context features are in vector form, the conditional modulation applies to the channel dimension or feature dimension; when the initial environmental context features are in spatial mechanism field form, the conditional modulation applies to the joint dimension of the spatial location dimension and the channel dimension. Both forms characterize differences in environmental conditions and enable the target partial differential equation surrogate model to adaptively adjust its internal feature representations and prediction process according to different environmental condition differences.

[0039] In some embodiments, please refer to Figure 3The pre-trained target partial differential equation surrogate model is invoked. Using the current environmental context features as conditional information, and based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field dataset, the corresponding first predicted solution field observation data is generated, including: Step S301: Call the pre-trained target partial differential equation surrogate model and generate intermediate features of the model based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. Step S302: Invoke the preset feature conditional modulation network to generate the scaling coefficient vector and offset coefficient vector corresponding to the intermediate features of the model based on the current environmental context features; Step S303: Conditionally modulate the intermediate features of the model based on the scaling coefficient vector and the offset coefficient vector to obtain the modulated features; Step S304: Call the target partial differential equation proxy model to generate the corresponding first predicted solution field observation data based on modulation feature decoding.

[0040] In step S301, a pre-trained surrogate model for the target partial differential equation is invoked, and intermediate features of the model are generated based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. Specifically, for the first partial differential equation solution field data sample in the prior solution field data set... For each partial differential equation solution field data sample, a shallow encoder (or mapping layer) within the surrogate model of the target partial differential equation receives its corresponding reference initial state and reference observable conditions. Subsequently, the shallow encoder maps and projects this data into a high-dimensional hidden channel space, extracting the initial implicit representation based on known explicit observation conditions, i.e., the model's intermediate features (which can be denoted as...). ).

[0041] In step S302, a preset feature conditional modulation network is invoked to generate scaling coefficient vectors and offset coefficient vectors corresponding to the intermediate features of the model based on the current environmental context features. Specifically, in order to enable the fixed proxy model to perceive and adapt to the current specific physical environment deviation, this embodiment introduces a feature conditional modulation network, which may include a multilayer perceptron or a fully connected layer. The feature conditional modulation network receives the current environmental context features, decodes and splits the current environmental context features into two sets corresponding to the aforementioned intermediate features of the model through linear or nonlinear transformations. The feature channel dimension aligned parameter vector, specifically including the scaling factor vector (denoted as...). ) and offset coefficient vector (denoted as The scaling factor vector and the offset factor vector are control parameters used to dynamically reshape the feature flow within the model during feature condition modulation. The scaling factor vector acts on the intermediate features of the model through element-wise multiplication to proportionally amplify or reduce the response intensity of specific feature channels, thereby determining the model's sensitivity to certain environmental signals or weight allocation. The offset factor vector acts on the intermediate features of the model through element-wise addition to shift the reference value of a specific channel as a whole.

[0042] Thus, this embodiment can perform channel-wise affine transformations on features in the high-dimensional latent space, thereby guiding and adaptively adjusting the physical deduction logic without changing the original parameters of the backbone network, enabling the model to accurately adapt to the hidden constraints of the current environment.

[0043] In step S303, specifically, after obtaining the above modulation parameters, feature-wise linear modulation (FiLM) is performed on the intermediate features of the model. Specifically, the intermediate features of the model are multiplied element-wise channel by channel using the scaling coefficient vector, and then shifted channel by channel using the offset coefficient vector. The specific expression is as follows: The features output after the above affine transformation operation are the modulation features. .

[0044] Thus, this embodiment can change the numerical distribution of physical features from the dimension of feature channels without changing the original weight parameters of the target partial differential equation surrogate model, thereby achieving conditional modulation of the physical evolution logic of the target dynamic system in the environment to be predicted.

[0045] In step S304, the target partial differential equation surrogate model is invoked to generate the corresponding first predicted solution field observation data based on the modulation feature decoding. Specifically, the modulation features, after environmental information injection, are input into the neural operator layer (such as a Fourier neural operator layer or a graph neural operator layer) of the target partial differential equation surrogate model to perform multiple nonlinear integral and partial derivative approximation calculations in high-dimensional space to deduce the evolution trend of the physical field in time or space. After completing the deep calculation, the decoder of the target partial differential equation surrogate model receives the evolution features and projects them back from the high-dimensional latent space to the real coordinate grid. Depending on the type of problem being solved, the decoder ultimately reconstructs and outputs the corresponding first predicted solution field observation data, such as the predicted time series in a spatiotemporal evolution problem, or the predicted steady-state distribution field in a steady-state problem.

[0046] In this embodiment, with the parameters of the partial differential equation surrogate model completely frozen, the target context feature learning network first extracts environment-level context representations from at least one partial differential equation solution field data sample within the same environment to be predicted. Then, the environment-level context representations are introduced into the target partial differential equation surrogate model to conditionally modulate the model's internal features, intermediate latent variables, or operator outputs. This allows the target partial differential equation surrogate model to reuse common laws across environments while responding sensitively and smoothly to subtle changes in environment context features. It adaptively adjusts its prediction behavior based on potential differences in different environments, thereby outputting high-precision prediction results under unknown environmental conditions with extremely low computational cost, thus improving the engineering generalization capability of the partial differential equation surrogate model.

[0047] In some embodiments, please refer to Figure 4 , Figure 4 This is a schematic diagram of conditional modulation of the surrogate model of the target partial differential equation provided in this application, as shown below. Figure 4 As shown, the target partial differential equation surrogate model receives the reference initial state and reference observable conditions as explicit inputs. After being mapped to a high-dimensional latent space by the input lifting layer, it sequentially passes through a multi-level cascaded neural operator from the first layer to the Lth layer, and finally the output projection layer decodes to generate the first predicted solution field observation data. Simultaneously with the forward derivation of the target partial differential equation surrogate model, a parallel feature condition modulation network uses the current environmental context features as its sole input and decodes them using a multilayer perceptron, dynamically generating corresponding scaling coefficient vectors and offset coefficient vectors specifically for each neural operator layer within the target partial differential equation surrogate model. For example... Figure 4 As shown by the dashed path, the extracted environmental context features are precisely injected into each layer of the neural operator in the target partial differential equation surrogate model. Feature-level linear modulation is applied to the output features of each layer's neural operator. Specifically, an affine transformation of multiplication (scaling) followed by addition (translation) is performed layer by layer on the intermediate output features of each layer to obtain the corresponding feature-level linearly modulated output features (e.g., feature-level linear modulation of the first layer's output features). Thus, this embodiment can receive intervention and guidance from external hidden environmental features, achieving adaptation to the current specific working condition and accurate prediction of the solution results without changing the parameters of the main operator.

[0048] In step S104, specifically, in practical applications, this embodiment adopts different adaptation strategies based on the historical visibility of the current working conditions. When the environment to be predicted belongs to an environment that has already been encountered during the training of the surrogate model, the features extracted by the target context feature learning network in a single instance already have high accuracy. At this time, there is no need to introduce additional computational overhead. The initial environment context features are used to conditionally modulate the target partial differential equation surrogate model, that is, they are directly used as the final adapted environment context features.

[0049] When the environment to be predicted is an environment not seen during training, a new operating condition, or an operating condition outside the distribution, the initial features extracted in a single step often have limitations. In order to improve the physical matching degree between the context representation and the current unknown real environment, this embodiment iteratively updates the context features. During the iteration process, the shared conditional partial differential equation surrogate model parameters are fixed, and the environmental context representation is only updated in a finite number of steps.

[0050] Based on the first predicted solution field observation data and the corresponding prior solution field observation data, and combined with the deviation relationship between the current environmental context features and the initial environmental context features, the current environmental context features are numerically updated. The result of each update is used as the new current environmental context features to continue participating in the next iterative calculation until the preset number of iterations is reached (i.e., a finite number of closed-loop optimization steps are completed). Finally, the high-precision environmental context features obtained at the end of the iteration are used as the adaptive environmental context features under unknown operating conditions.

[0051] In some embodiments, please refer to Figure 5 The current environmental context features are updated based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features, and the initial environmental context features, including: Step S501: For each partial differential equation solution field data sample, calculate the first prediction error loss based on the first predicted solution field observation data and the corresponding prior solution field observation data. Step S502: Calculate the corresponding feature deviation constraint terms based on the current environmental context features and the initial environmental context features; Step S503: Update the current environmental context features based on the first prediction error loss and feature deviation constraint terms corresponding to all partial differential equation solution field data samples.

[0052] In step S501, for each partial differential equation solution field data sample, the first prediction error loss is calculated based on the first predicted solution field observation data and the corresponding prior solution field observation data. This loss is applied in the current step of the iterative adaptation (e.g., the first...). In the next iteration, the surrogate model has already output a set of simulated first predicted solution field observation data based on the current environmental context features. Then, the first predicted solution field observation data is aligned and compared with the prior solution field observation data obtained from the real physical environment at the pixel level or grid node level. This embodiment calculates the numerical deviation between the two to obtain the first prediction error loss, which can specifically be achieved using relative... Norm loss, Mean Squared Error (MSE) loss, Log-Cosh loss, or other loss functions suitable for PDE solution prediction, the expression for the first prediction error loss is: ,in, Indicates the first element in the prior solution field data set. Sample data of solution fields for a partial differential equation This represents the reference initial state in the sample of solution field data for partial differential equations. Indicates reference observable conditions. Indicates the reference initial state and reference observable conditions The prior solution field observation data obtained below, Indicates the current environmental context features, This represents the observation data for the first predicted solution field. The first prediction error loss reflects the degree of matching error between the physical field (such as flow velocity and temperature field) currently derived by the surrogate model and the actual physical space evolution results.

[0053] In step S502, the corresponding feature deviation constraint term can be calculated based on the current environmental context features and the initial environmental context features. Specifically, since the number of samples in the prior solution field dataset is extremely small (i.e., a small sample scenario), if the first prediction error loss is simply fitted during iterative optimization, the context features are prone to overfitting, thus losing their original ability to generalize the macroscopic physical laws of the environment (i.e., representation collapse occurs). To avoid the above problems, this embodiment introduces a feature deviation constraint term (i.e., a regularization term). Specifically, the feature deviation constraint term... Initial environmental context features can be calculated Current environment context features corresponding to the current iteration step The geometric distance in the implicit feature space is obtained, specifically, it can be any one or more combinations of the following: offset magnitude constraint. or scale stability constraints These are used to limit the magnitude of feature offset or to maintain the stability of the representation scale, respectively. In this way, the feature offset constraint term can force the target context feature learning network not to deviate too far from the initial context features when fine-tuning the environment features in the subsequent process, thereby ensuring the macroscopic rationality of the context representation while pursuing local fitting accuracy.

[0054] In step S503, the current environmental context features are updated based on the first prediction error loss and feature deviation constraint terms corresponding to all partial differential equation solution field data samples.

[0055] This embodiment constructs an adaptive iterative optimization architecture during the inference period, combining the first prediction error loss representing physical facts with the feature deviation constraint representing global cognition. Without needing to re-fine-tune the backbone network (target partial differential equation surrogate model and target context feature learning network) and saving computational overhead, it can stably and quickly infer the environmental context representation of the current unknown environment on a very small amount of prior sample data. If necessary, only a finite number of optimization updates to the environmental context representation are required to achieve rapid adaptation and generalized prediction for new environments, thereby reducing the cost of retraining or overall fine-tuning. Compared to related technologies that rely on model fine-tuning or retraining when facing new environments, requiring a large amount of data and training time, and having limited effectiveness in scenarios with few samples or rapid adaptation, this embodiment can achieve rapid adaptation and generalized prediction for new environments, improving the generalization ability and engineering practicality of the partial differential equation surrogate model.

[0056] In some embodiments, please refer to Figure 6 The current environmental context features are updated based on the first prediction error loss and feature deviation constraint terms corresponding to all partial differential equation solution field data samples, including: Step S601: Under the condition of fixing the model parameters of the target partial differential equation surrogate model, generate the adaptive target loss corresponding to the current iteration based on the mean of the first prediction error loss corresponding to all partial differential equation solution field data samples and the feature deviation constraint term. Step S602: Determine the gradient of the adaptation target loss with respect to the current environmental context features, and update the current environmental context features based on the gradient.

[0057] In step S601, with the model parameters of the target partial differential equation surrogate model fixed, the adaptive target loss for the current iteration is generated based on the mean of the first prediction error loss corresponding to all partial differential equation solution field data samples and the feature deviation constraint term. Specifically, all weight matrices within the target partial differential equation surrogate model are frozen and no longer participate in subsequent parameter updates. Subsequently, the first prediction error loss calculated for each partial differential equation solution field data sample is extracted, and the entire prior solution field data set is calculated. The mean of the first prediction error loss for all partial differential equation solution field data samples is expressed as follows: ,in, Represents the set of prior solution field data. Represents the set of prior solution field data. The first in Sample data of solution fields for a partial differential equation This represents the reference initial state in the sample of solution field data for partial differential equations. Indicates reference observable conditions. Indicates the reference initial state and reference observable conditions The prior solution field observation data obtained below, Indicates the current environmental context features, This represents the observation data for the first predicted solution field. This represents the total number of partial differential equation solution field data samples in the prior solution field dataset. Using the mean value effectively smooths out extreme noise that might be introduced by a single local sample, thus providing a stable numerical indicator reflecting the overall prediction bias of the model under the current environment. Then, the mean prediction error is weighted and combined with the feature deviation constraint term to generate the adaptation target loss corresponding to the current iteration. The adaptive target loss not only requires the model to fit the observed data of the new environment as closely as possible, but also limits the shift of environmental context features in the latent space to prevent overfitting. The specific expression for the adaptive target loss is as follows: ,in The weighting coefficients for the feature deviation constraint term.

[0058] In step S602, the gradient of the adaptation target loss with respect to the current environmental context features can be determined, and the current environmental context features can be updated based on the gradient. Specifically, the adaptation target loss can be calculated with respect to the current environmental context features. The partial derivatives, i.e., the gradient vector, determine the gradient vector. ,in, Since the parameters of the target context feature learning network and the target partial differential equation surrogate model are frozen, the gradient flow does not act on any network weights or model weights. Instead, it is specifically used to indicate in which direction the current environmental context features should move in the latent feature space in order to minimize prediction errors and satisfy constraints as quickly as possible.

[0059] Then, call numerical optimization algorithms such as gradient descent or Adam, and set an appropriate iteration step size (learning rate). Along the inverse direction of the gradient that decreases the loss function, a numerical update operation is performed on the current environmental context features, specifically expressed as follows: ,in, Indicates the current environmental context features, This represents the environmental context features after gradient update, thereby enabling adaptive iterative calibration of environmental physical laws.

[0060] This embodiment freezes the computationally intensive backbone parameters of the surrogate model during the iteration process, applying only the optimization objective (adaptive target loss) and its gradient to the lightweight environmental context feature vector. In this way, this embodiment can quickly and accurately capture the implicit environmental conditions and physical law shifts with extremely low computational overhead and a very small number of iterations when facing completely unknown operating condition deviations or new environments. While avoiding catastrophic forgetting or representation collapse of the model, it improves the robustness and cross-operating condition generalization prediction ability of the partial differential equation surrogate model.

[0061] In step S105, the target initial state and target observable conditions corresponding to the target task in the environment to be predicted are obtained. Specifically, after completing the implicit context inference and context feature adaptation of the environment to be predicted, this embodiment can begin the prediction phase for a completely new unknown operating condition. The target task to be predicted is a specific partial differential equation evolution task or steady-state solution task in the environment to be predicted (such as an operating condition with hidden wear or unknown material deviations) that requires calling a proxy model to solve, for example, predicting the temperature field change of an aging lithium battery pack in a future charge-discharge cycle. The target initial state refers to the physical field distribution of the target task at the starting point of the time axis (i.e., the initial moment), such as the initial temperature field of each node when the battery pack starts working. The target observable conditions represent the physical boundaries and control parameters that can be directly measured by sensors, explicitly set manually, or used as known explicit inputs when solving the target task to be predicted, such as the coolant flow rate, inlet temperature, or explicit geometric parameters set in the battery thermal management system.

[0062] In step S106, the target partial differential equation proxy model is invoked, and the corresponding prediction branch is constructed for the problem type of the target task to be predicted, using the environmental context features as conditional information, to generate the final target solution field data.

[0063] Specifically, when the target to be predicted is a multi-step prediction of spatiotemporal evolution, a spatiotemporal evolution prediction branch is constructed. This branch uses the current state, initial state, or known historical sequence of the target dynamic system as explicit physical input and adapts the environmental context features as conditional representation. In this branch, the target partial differential equation proxy model is constructed as a derivative network in the form of continuous time progression (i.e., the network itself does not directly output field data, but outputs the derivative of the physical state with respect to time). Then, combined with the preset time grid, an external ordinary differential equation (ODE) numerical integrator is called to use the derivative to perform step-by-step calculation of the physical state, and finally obtains a complete solution field prediction sequence covering the target time range.

[0064] When the task to be predicted is steady-state solution prediction or single-step response prediction, a steady-state solution prediction branch is constructed. Under this branch, for the target task to be predicted, the observable conditional variables obtained in the inference stage are input into the target partial differential equation surrogate model. At the same time, the adaptive environmental context features are introduced as conditional information. The intermediate features of the surrogate model are conditionally corrected and modulated through the above feature modulation mechanism, and then the decoder directly outputs the target steady-state solution field or single-step response field.

[0065] In some embodiments, please refer to Figure 7 , Figure 7 This is another flowchart of the method for predicting the solution field data of the dynamic system provided in this application, as follows: Figure 7 As shown, firstly, training sample data is acquired from multiple different sample environments and divided into context sample data for implicit context feature extraction and target sample data for inference result evaluation. Then, a context feature learning network and a partial differential equation surrogate model are constructed. In the actual forward inference stage, solution paths for steady-state prediction / single-step prediction or multi-time-step prediction are flexibly supported according to different branches of the specific prediction task. Based on the output results of the above prediction branches, end-to-end joint training is performed on the context feature learning network and the partial differential equation surrogate model to achieve bidirectional coupling optimization of feature extraction and operator computation. Finally, the jointly trained model is deployed in practical applications, enabling fast adaptive matching and high-precision solution prediction when facing unknown environmental conditions during the inference stage.

[0066] In some embodiments, please refer to Figure 8 The training methods for the target context feature learning network and the target partial differential equation surrogate model include the following steps: Step S801: Obtain the training set of partial differential equation solution fields for the target dynamical system; Step S802: For each sample environment, select context sample data and target sample data from the corresponding training sample data; Step S803: Generate predicted environment context features based on the first sample solution field observation data of the context sample data through a preset context feature learning network; Step S804: Using the predicted environmental context features as conditional information, the initial state of the sample corresponding to the target sample data and the sample observable conditions as inputs to the preset partial differential equation surrogate model, and using the second sample solution field observation data corresponding to the target sample data as the solution field observation data label, the network parameters of the context feature learning network are updated to obtain the target context feature learning network, and the model parameters of the partial differential equation surrogate model are updated to obtain the target partial differential equation surrogate model.

[0067] In step S801, a training set of partial differential equation solutions for the target dynamic system is obtained. This training set includes training sample data corresponding to multiple sample environments. Specifically, in complex dynamic systems (such as fluid dynamics and thermodynamic systems), the dominant physical mechanisms and macroscopic evolution patterns of the dynamic system often change (or migrate) with variations in environmental parameters (such as different material viscosities or geometric boundaries). To enable the neural network (contextual feature learning network and partial differential equation surrogate model) to generalize across environments, this embodiment collects historical computational data or experimental observation data covering various known operating conditions or environments to construct a training set of partial differential equation solutions. The training set of partial differential equation solutions is classified and organized according to the sample environment (i.e., specific operating conditions or configurations), with each independent sample environment corresponding to a dedicated set of training sample data.

[0068] In step S802, for each sample environment, context sample data and target sample data are selected from the corresponding training sample data. The context sample data includes first sample solution field observation data, and the target sample data includes the initial state of the sample, the observable conditions of the sample, and second sample solution field observation data obtained under the initial state and observable conditions of the sample. Specifically, in each batch iteration of offline training, this embodiment divides the training sample data corresponding to the currently selected sample environment. First, a small number of samples are extracted as context sample data. The context sample data only provides physical field observation results, i.e., the first sample solution field observation data, which is used to allow the model to perceive the hidden condition characteristics of the current sample environment. Subsequently, another batch of samples that do not overlap with the context sample data are extracted from the training sample data corresponding to the sample environment as target sample data. The target sample data serves as a supervision sample (validation set) to test the model's inference ability. The target sample data includes the initial state of the sample and the observable conditions of the sample, and also includes the real physical field distribution obtained by the natural evolution of the target dynamic system under the initial state and observable conditions of the sample, i.e., the second sample solution field observation data used as supervision labels.

[0069] In step S803, a pre-defined context feature learning network generates predictive environment context features based on the first sample solution field observation data of the context sample data. Specifically, the context feature learning network first receives the first sample solution field observation data, performs spatial feature mapping and temporal dimension aggregation (for spatiotemporal problems) or mechanism field extraction (for steady-state problems) on it, and derives predictive environment context features representing the physical laws and implicit constraints of the sample environment.

[0070] In step S804, the initial state and observable conditions of the sample corresponding to the target sample data are used as inputs to a preset partial differential equation surrogate model. The partial differential equation surrogate model receives the prediction environment context features through a feature linear modulation mechanism as implicit environmental condition information, outputs the simulation prediction solution field data, and uses the second sample solution field observation data corresponding to the target sample data as the solution field observation data label to update the network parameters of the context feature learning network to obtain the target context feature learning network. The model parameters of the partial differential equation surrogate model are then updated to obtain the target partial differential equation surrogate model.

[0071] In some embodiments, please refer to Figure 9 Using predicted environmental context features as conditional information, the initial state and observable conditions of the target sample data as inputs to a pre-defined partial differential equation surrogate model, and the second sample solution field observation data corresponding to the target sample data as the solution field observation data label, the network parameters of the context feature learning network are updated to obtain the target context feature learning network. The model parameters of the partial differential equation surrogate model are then updated to obtain the target partial differential equation surrogate model, including: Step S901: Call the preset partial differential equation proxy model to generate intermediate features of the prediction model based on the initial state of the sample and the observable conditions of the sample in each target sample data. Step S902: Conditionally modulate the intermediate features of the prediction model using the predicted environmental context features as conditional information to obtain the predicted modulation features, and generate the second predicted solution field observation data based on the predicted modulation features. Step S903: Calculate the second prediction error loss based on the second predicted solution field observation data and the corresponding second sample solution field observation data of the target sample data; Step S904: Obtain the predicted sample context features generated by the context feature learning network based on the first sample solution field observation data of each context sample data, and calculate the consistency constraint loss based on the predicted sample context features and the predicted environment context features. Step S905: Update the network parameters of the context feature learning network according to the second prediction error loss and the consistency constraint loss to obtain the target context feature learning network, and update the model parameters of the partial differential equation surrogate model according to the second prediction error loss and the consistency constraint loss to obtain the target partial differential equation surrogate model.

[0072] In step S901, a preset partial differential equation surrogate model is invoked to generate intermediate features for the prediction model based on the initial state and observable conditions of each target sample data. Specifically, the target sample data is input into the preset partial differential equation surrogate model. The surrogate model receives the initial state and observable conditions of the sample, and transforms them into a high-dimensional hidden feature space through forward feature extraction and dimensionality upscaling, thereby generating intermediate features for the prediction model. .

[0073] In step S902, the intermediate features of the prediction model are conditionally modulated using the prediction environment context features as conditional information to obtain prediction modulation features. Based on these prediction modulation features, second prediction solution field observation data is generated. Specifically, the feature conditional modulation network generates a scaling coefficient vector based on the prediction environment context features. With offset coefficient vector Subsequently, a feature linear modulation mechanism is used to perform a channel-by-channel affine transformation on the intermediate features of the prediction model. The specific transformation expression is as follows: The predicted modulation features output after this affine modulation operation. The model has already injected unique environmental constraints into the implicit high-dimensional space. Finally, the neural operator layer inside the surrogate model performs complex nonlinear integral calculations based on modulation features, and projects them back to the physical space through a decoder, outputting the second predicted solution field observation data obtained from the simulation.

[0074] In step S903, the second prediction error loss is calculated based on the second predicted solution field observation data and the corresponding second sample solution field observation data of the target sample data. Specifically, this embodiment performs supervised model accuracy evaluation by comparing the second predicted solution field observation data with the second sample solution field observation data in the target sample data at the grid node level, and calculating the spatial distribution numerical difference between the two (usually using mean square error or relative error). The norm is used to quantify the inference bias of the surrogate model under the guidance of the current environmental characteristics, and the second prediction error loss is obtained.

[0075] In step S904, the context features of the predicted samples generated by the context feature learning network based on the first sample solution field observation data of each context sample data are obtained, and the consistency constraint loss is calculated based on the predicted sample context features and the predicted environment context features. In actual physical systems, as long as they are in the same working environment, the underlying mechanisms implied by any local observation sample should be the same. Therefore, the target dynamic system not only extracts the predicted environment context features that fuse global information representing multiple samples, but also extracts the predicted sample context features generated by the context feature learning network when processing each context sample. Subsequently, the consistency constraint loss is constructed by calculating the geometric distance (such as Euclidean distance or cosine similarity distance) between these two features in the implicit high-dimensional space. The expression for the consistency constraint loss is: ,in, Indicates the sample environment. Indicates the sample environment The corresponding training sample data, Represents the contextual features of the predicted sample. This indicates the predicted environmental context features. The consistency constraint loss represents the number of samples in the context sample data. It is used to ensure that the implicit physical laws extracted from a single local sample are consistent with the overall laws of the global environment, effectively preventing the model from overfitting to individual samples with noise.

[0076] In step S905, the network parameters of the context feature learning network are updated based on the second prediction error loss and the consistency constraint loss to obtain the target context feature learning network. Similarly, the model parameters of the partial differential equation surrogate model are updated based on the second prediction error loss and the consistency constraint loss to obtain the target partial differential equation surrogate model. Specifically, the second prediction error loss and the consistency constraint loss are weighted and summed to construct a joint training loss function. Gradients are calculated synchronously end-to-end using backpropagation of the joint loss function, and the weight parameters of both the context feature learning network and the partial differential equation surrogate model are updated simultaneously using an optimization algorithm (such as Adam). Through multiple iterative updates in different sample environments until the loss converges, the target context feature learning network and the target partial differential equation surrogate model are obtained.

[0077] This embodiment uses consistency constraint loss to ensure that the context feature extraction network discards local sample noise and accurately and stably extracts the environmental context. Through end-to-end joint gradient backpropagation, the partial differential equation surrogate model learns how to dynamically adjust its internal derivation rules based on environmental context features. This ensures that the trained model can extract reliable environmental features when facing unknown new working conditions in the future, thereby improving the prediction accuracy and generalization of physical field evolution results without changing the model parameters.

[0078] Please see Figure 10 This application also provides a dynamic system solution data prediction device 1000, which can implement the above-mentioned dynamic system solution data prediction method. The device includes: The first acquisition unit 1001 is used to acquire a priori solution field data set of the target dynamic system in the environment to be predicted. The priori solution field data set includes at least one partial differential equation solution field data sample. Each partial differential equation solution field data sample includes a reference initial state, a reference observable condition, and priori solution field observation data obtained under the reference initial state and the reference observable condition. The first generation unit 1002 is used to call the pre-trained target context feature learning network to generate the initial environment context features of the environment to be predicted based on all the prior solution field observation data in the prior solution field dataset. The second generation unit 1003 is used to take the initial environmental context features as the current environmental context features, call the pre-trained target partial differential equation proxy model, and use the current environmental context features as conditional information to generate the corresponding first predicted solution field observation data based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. The update unit 1004 is used to update the current environmental context features based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features and the initial environmental context features, and to use the updated environmental context features as the new current environmental context features until a preset number of iterations is reached, and to use the final environmental context features as the adapted environmental context features. The second acquisition unit 1005 is used to acquire the target initial state and target observable conditions corresponding to the target task in the environment to be predicted. The third generation unit 1006 is used to call the target partial differential equation proxy model, and generate target solution field data of the target task to be predicted based on the target initial state and target observable conditions, using the environmental context features as conditional information.

[0079] The specific implementation of the power system's solution data prediction device is basically the same as the specific implementation of the power system's solution data prediction method described above, and will not be repeated here.

[0080] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method for predicting the solution data of a power system. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0081] Please see Figure 11 , Figure 11 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes: The processor 1101 can be implemented using a general-purpose central processing unit (CPU), microprocessor, application specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application. The memory 1102 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 1102 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1102 and is called by the processor 1101 to execute the field data prediction method for the power system of the embodiments of this application. Input / output interface 1103 is used to implement information input and output; The communication interface 1104 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 1105 transmits information between various components of the device (e.g., processor 1101, memory 1102, input / output interface 1103, and communication interface 1104); The processor 1101, memory 1102, input / output interface 1103 and communication interface 1104 are connected to each other within the device via bus 1105.

[0082] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for predicting the solution data of a dynamic system.

[0083] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0084] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0085] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0086] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0087] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0088] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0089] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0090] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0091] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0092] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0093] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0094] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for predicting solution field data of a dynamical system, characterized in that, The method includes: A priori solution field data set of the target dynamic system in the environment to be predicted is obtained. The priori solution field data set includes at least one partial differential equation solution field data sample. Each partial differential equation solution field data sample includes a reference initial state, a reference observable condition, and priori solution field observation data obtained under the reference initial state and the reference observable condition. The pre-trained target context feature learning network is invoked to generate initial environmental context features of the environment to be predicted based on all the prior solution field observation data in the prior solution field dataset; Using the initial environmental context features as the current environmental context features, the pre-trained target partial differential equation surrogate model is invoked. With the current environmental context features as conditional information, the corresponding first predicted solution field observation data is generated based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. The current environmental context features are updated based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features, and the initial environmental context features. The updated environmental context features are used as the new current environmental context features until a preset number of iterations is reached, and the final environmental context features are used as the adapted environmental context features. Obtain the initial state and observable conditions of the target corresponding to the target task in the environment to be predicted; The target partial differential equation proxy model is invoked, and the target solution field data of the target task to be predicted is generated based on the target initial state and the target observable conditions, using the adaptive environment context features as conditional information.

2. The method for predicting solution field data of a dynamic system according to claim 1, characterized in that, The step of updating the current environmental context features based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features, and the initial environmental context features includes: For each partial differential equation solution field data sample, a first prediction error loss is calculated based on the first predicted solution field observation data and the corresponding prior solution field observation data. Calculate the corresponding feature deviation constraint terms based on the current environmental context features and the initial environmental context features; The current environmental context features are updated based on the first prediction error loss corresponding to all the partial differential equation solution field data samples and the feature deviation constraint term.

3. The method for predicting solution field data of a dynamic system according to claim 2, characterized in that, The step of updating the current environmental context features based on the first prediction error loss corresponding to all the partial differential equation solution field data samples and the feature deviation constraint term includes: With the model parameters of the target partial differential equation proxy model fixed, the adaptation target loss corresponding to the current iteration round is generated based on the mean of the first prediction error loss corresponding to all the partial differential equation solution field data samples and the feature deviation constraint term. Determine the gradient of the adaptation target loss with respect to the current environmental context features, and update the current environmental context features based on the gradient.

4. The method for predicting solution field data of a dynamic system according to claim 1, characterized in that, The pre-trained target context feature learning network generates initial environmental context features of the environment to be predicted based on all the prior solution field observation data in the prior solution field dataset, including: The pre-trained target context feature learning network is invoked to generate corresponding sample context features based on the prior solution field observation data of each partial differential equation solution field data sample in the prior solution field dataset. Feature information fusion is performed on all the sample context features to obtain the initial environment context features of the environment to be predicted.

5. The method for predicting solution field data of a dynamic system according to claim 1, characterized in that, The step of invoking a pre-trained target partial differential equation proxy model, using the current environmental context features as conditional information, and generating corresponding first predicted solution field observation data based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field dataset, includes: Invoke the pre-trained target partial differential equation surrogate model, and generate intermediate features of the model based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set; The preset feature condition modulation network is invoked to generate scaling coefficient vectors and offset coefficient vectors corresponding to the intermediate features of the model based on the current environmental context features; Based on the scaling coefficient vector and the offset coefficient vector, the intermediate features of the model are conditionally modulated to obtain modulated features; The target partial differential equation proxy model is invoked to generate the corresponding first predicted solution field observation data based on the modulation feature decoding.

6. The method for predicting solution field data of a dynamic system according to claim 1, characterized in that, The training methods for the target context feature learning network and the target partial differential equation surrogate model include the following steps: Obtain the partial differential equation solution field training set of the target dynamical system, wherein the partial differential equation solution field training set includes training sample data corresponding to multiple sample environments; For each of the aforementioned sample environments, context sample data and target sample data are selected from the corresponding training sample data. The context sample data includes first sample solution field observation data, and the target sample data includes sample initial state, sample observable conditions, and second sample solution field observation data obtained under the sample initial state and the sample observable conditions. A pre-defined context feature learning network generates predictive environmental context features based on the first sample solution field observation data of the context sample data; Using the predicted environment context features as conditional information, the initial state of the sample corresponding to the target sample data and the sample observable conditions as inputs to a preset partial differential equation surrogate model, and the second sample solution field observation data corresponding to the target sample data as the solution field observation data label, the network parameters of the context feature learning network are updated to obtain the target context feature learning network, and the model parameters of the partial differential equation surrogate model are updated to obtain the target partial differential equation surrogate model.

7. The method for predicting solution field data of a dynamic system according to claim 6, characterized in that, The process involves using the predicted environment context features as conditional information, the initial state and observable conditions of the target sample data as inputs to a preset partial differential equation surrogate model, and the second sample solution field observation data corresponding to the target sample data as the solution field observation data label. This process updates the network parameters of the context feature learning network to obtain the target context feature learning network, and then updates the model parameters of the partial differential equation surrogate model to obtain the target partial differential equation surrogate model. The process includes: The preset partial differential equation proxy model is invoked to generate intermediate features of the prediction model based on the initial state and observable conditions of the sample corresponding to each target sample data. Using the predicted environment context features as conditional information, the intermediate features of the prediction model are conditionally modulated to obtain the predicted modulation features, and second predicted solution field observation data are generated based on the predicted modulation features. The second prediction error loss is calculated based on the second predicted solution field observation data of the target sample data and the corresponding second sample solution field observation data. The context feature learning network obtains the predicted sample context features generated by the first sample solution field observation data for each context sample data, and calculates the consistency constraint loss based on the predicted sample context features and the predicted environment context features. The network parameters of the context feature learning network are updated based on the second prediction error loss and the consistency constraint loss to obtain the target context feature learning network. The model parameters of the partial differential equation surrogate model are then updated based on the second prediction error loss and the consistency constraint loss to obtain the target partial differential equation surrogate model.

8. A device for predicting the solution field data of a dynamic system, characterized in that, The device includes: The first acquisition unit is used to acquire a priori solution field data set of the target dynamic system in the environment to be predicted. The priori solution field data set includes at least one partial differential equation solution field data sample. Each partial differential equation solution field data sample includes a reference initial state, a reference observable condition, and priori solution field observation data obtained under the reference initial state and the reference observable condition. The first generation unit is used to call a pre-trained target context feature learning network to generate initial environmental context features of the environment to be predicted based on all the prior solution field observation data in the prior solution field dataset. The second generation unit is used to take the initial environmental context features as the current environmental context features, call the pre-trained target partial differential equation proxy model, and use the current environmental context features as conditional information to generate the corresponding first predicted solution field observation data based on the reference initial state and reference observable conditions of each partial differential equation solution field data sample in the prior solution field data set. The update unit is used to update the current environmental context features based on the first predicted solution field observation data, the corresponding prior solution field observation data, the current environmental context features, and the initial environmental context features, and to use the updated environmental context features as the new current environmental context features, until a preset number of iterations is reached, and to use the finally obtained environmental context features as the adapted environmental context features. The second acquisition unit is used to acquire the target initial state and target observable conditions corresponding to the target task to be predicted in the environment to be predicted. The third generation unit is used to call the target partial differential equation proxy model, and generate the target solution field data of the target task to be predicted based on the target initial state and the target observable conditions, using the adaptive environment context features as conditional information.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the solution data prediction method for the dynamic system according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for predicting the solution data of the dynamic system as described in any one of claims 1 to 7.

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