A machine learning-based method for predicting performance of electrochemical energy storage devices
By introducing a physical information graph neural network model into the performance prediction of electrochemical energy storage devices, the problem of weak generalization ability of existing models is solved, high-precision and stable performance prediction is achieved, physical interpretation is provided, and materials design is guided.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- PANZHIHUA UNIV
- Filing Date
- 2026-03-11
- Publication Date
- 2026-06-12
AI Technical Summary
Existing machine learning models have weak generalization ability in predicting the performance of electrochemical energy storage devices and lack a physical kernel, resulting in decreased prediction accuracy and inability to provide physical explanations when data distribution changes.
A physical information graph neural network model is adopted. By introducing physical constraint operators of the electrochemical diffusion equation into the graph convolutional layer, and combining it with a multilayer perceptron network to dynamically calculate the diffusion coefficient, and introducing a physical consistency penalty term into the loss function, a graph structure is constructed and physical field-guided registration is performed to ensure the physical consistency and interpretability of the model.
It improves the prediction accuracy and stability of the model in new materials and small sample scenarios, provides an explanation of the physical meaning, and guides material design.
Smart Images
Figure CN121809303B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of interdisciplinary technology of electrochemical energy storage and artificial intelligence, specifically to a method for predicting the performance of electrochemical energy storage devices based on machine learning. Background Technology
[0002] The performance of electrochemical energy storage devices, such as lithium-ion batteries and supercapacitors, is essentially determined by the microstructure of the electrode materials. In recent years, using machine learning, especially deep learning models, to directly predict performance from microstructure images has become a highly promising research direction.
[0003] However, existing technical solutions have several fundamental flaws that restrict their application in practical research and development. First, mainstream models, such as convolutional neural networks or standard graph neural networks, rely entirely on statistical regularities in the data for their learning mechanisms, lacking the integration of underlying physical processes such as ion diffusion. This leads to a sharp decline in predictive performance and weak generalization ability when the data distribution changes (e.g., changes in material systems or process conditions). Furthermore, their prediction results are like a "black box," failing to provide physically meaningful explanations and thus unable to guide material design. Summary of the Invention
[0004] To address the aforementioned problems in the prior art, this invention provides a machine learning-based method for predicting the performance of electrochemical energy storage devices, which solves the problems of weak generalization ability and poor interpretability caused by the lack of a physical kernel in existing data-driven models.
[0005] To achieve the above-mentioned objectives, the technical solution adopted by the present invention is as follows:
[0006] A machine learning-based method for predicting the performance of electrochemical energy storage devices includes:
[0007] Obtain microstructure images of electrode materials for electrochemical energy storage devices and construct corresponding graph structures;
[0008] The graph structure is input into a preset physical information graph neural network model, wherein the message passing function of at least one graph convolutional layer in the physical information graph neural network model contains a physical constraint operator based on the electrochemical diffusion equation.
[0009] Output the predicted electrochemical performance of the electrode material.
[0010] Preferably, constructing the corresponding graph structure includes:
[0011] The microstructure image is segmented to obtain multiple superpixel regions;
[0012] A graph structure is constructed based on the superpixel region.
[0013] Preferably, the superpixel region-based graph construction structure includes:
[0014] An initial graph structure is constructed based on the superpixel region. The initial graph structure includes nodes and edges. The nodes represent superpixel regions, and the edges represent the spatial adjacency relationships between superpixel regions.
[0015] Determine the contact area and centroid Euclidean distance between spatially adjacent superpixel regions;
[0016] The intensity of physical interaction between spatially adjacent superpixel regions is determined based on the contact area and the Euclidean distance between their centroids.
[0017] The initial graph structure is optimized based on the strength of the physical interactions to obtain the final graph structure.
[0018] Preferably, optimizing the initial graph structure based on the physical interaction strength to obtain the graph structure includes:
[0019] If the physical interaction strength is lower than a first preset threshold, the two corresponding nodes will be merged into a new node;
[0020] If the physical interaction strength is lower than the second preset threshold, the corresponding edge is removed.
[0021] Preferably, the microstructure image includes a multi-scale microstructure image, and the method further includes:
[0022] Obtain a preliminary model with the same structure as the physical information graph neural network model;
[0023] Input the coarse-scale image into the preliminary model to obtain a physical field reference map;
[0024] Initialize the deformation parameters of the B-spline free deformation model, and perform spatial transformation on the fine-scale image based on the deformation parameters to obtain a temporary registration image;
[0025] The temporary registration image is input into the preliminary model to obtain the physical field distribution;
[0026] Calculate the mutual information between the physical field reference map and the physical field distribution;
[0027] With the goal of maximizing the mutual information, the deformation parameters are updated until the mutual information converges or the preset number of iterations is reached, thus obtaining the optimal deformation parameters.
[0028] Based on the optimal deformation parameters, a spatial transformation is performed on the fine-scale image to obtain a fine-scale image that is physically aligned with the coarse-scale image.
[0029] Based on the registered images, the corresponding graph structure is constructed.
[0030] Preferably, the physical constraint operator is expressed as:
[0031]
[0032] in, , , They are nodes ,node ,side eigenvectors, The diffusion coefficient is related to the material. For nodes and Contact area between corresponding regions For nodes and The Euclidean distance between the centroids.
[0033] Preferably, when training the physical information graph neural network model, a physical consistency penalty term is introduced into the loss function, including:
[0034] Extract the node features output from the intermediate layers of the model as physical quantities;
[0035] Determine the spatial gradient divergence and the rate of change over time of the physical quantity;
[0036] Determine the difference between the gradient divergence and the rate of change;
[0037] A physical consistency penalty is determined based on the aforementioned differences.
[0038] Preferably, the method further includes:
[0039] The diffusion coefficient is parameterized as a random variable, and the value distribution of the random variable is determined by the trainable subnetwork based on node features and edge features.
[0040] When making performance predictions, multiple diffusion coefficient values are independently sampled from the value distribution of the random variable, and each sampled value is treated as an independent physical parameter instance.
[0041] For each physical parameter instance, the forward propagation of the physical information graph neural network is run multiple times by randomly discarding neurons to obtain multiple electrochemical performance prediction sample values, and the average of the multiple sample values is calculated as the conditional prediction mean under the corresponding physical parameter instance.
[0042] Obtain the electrochemical performance prediction sample values for all physical parameter instances, calculate the corresponding total variance, and use it as a measure of total uncertainty.
[0043] Calculate the variance of the conditional prediction mean for all physical parameter instances, and use it as the uncertainty component of the physical parameter.
[0044] Subtracting the physical parameterization uncertainty component from the total uncertainty measure yields the model structure uncertainty component;
[0045] Output the uncertainty components of the physical parameters and the uncertainty components of the model structure.
[0046] The beneficial effects of this invention are as follows: by hard-coding the electrochemical diffusion equation in discrete form as the core message-passing operator of a graph neural network, the model's learning and reasoning processes are based on physical laws. This significantly reduces the model's dependence on the statistical distribution of training data, enabling it to maintain high prediction accuracy and stability even when facing new materials with different compositions and processes or small sample scenarios. Attached Figure Description
[0047] Figure 1 This is a flowchart of a machine learning-based method for predicting the performance of electrochemical energy storage devices according to the present invention. Detailed Implementation
[0048] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0049] Current mainstream prediction models, such as those based on convolutional neural networks or ordinary graph neural networks, rely entirely on mining statistical correlations between input images and output performance from training data. These models are essentially black-box systems lacking a physical kernel. This leads to a sharp drop in prediction accuracy and extremely poor generalization ability when the amount of training data is limited or when the material system to be predicted differs significantly from the training data. Furthermore, their prediction results cannot provide explanations based on physical mechanisms, making it difficult to guide practical material design.
[0050] Based on the above reasons, such as Figure 1As shown, this embodiment of the invention provides a machine learning-based method for predicting the performance of electrochemical energy storage devices, comprising: acquiring microstructure images of electrode materials of electrochemical energy storage devices and constructing corresponding graph structures; inputting the graph structures into a preset physical information graph neural network model, wherein the message passing function of at least one graph convolutional layer in the physical information graph neural network model contains a physical constraint operator based on the electrochemical diffusion equation; and outputting the electrochemical performance prediction results of the electrode materials.
[0051] First, microscopic images of the electrode material are acquired, such as scanning electron microscope (SEM) images, transmission electron microscope (TEM) images, or one or more other methods, and their corresponding graph structures are constructed. This graph structure uses segmented regions of the image as nodes and spatial adjacency relationships between regions as edges. Each node is assigned an initial vector containing its visual and morphological features; the features of each edge include parameters with clear physical meaning directly calculated from the image geometry, primarily the contact area and centroid distance between adjacent regions. Next, the above graph structure is input into a pre-defined physical information graph neural network model. This model typically contains multiple stacked graph convolutional layers and a performance prediction layer at the end of the network; optionally, when processing multi-scale graphs, the model may also include a cross-scale attention fusion layer. The key difference between this physical information graph neural network model and ordinary graph neural networks lies in the fact that the message passing function of at least one graph convolutional layer is dominated by a physically constrained operator obtained by discretization based on the electrochemical diffusion equation. This physical constraint operator stipulates that the amount of information transmitted from node j to node i is proportional to the difference between the eigenvectors of the two nodes, the diffusion coefficient, and the geometric factor consisting of the contact area divided by the square of the centroid distance, thereby forcing the information propagation process of the model to strictly simulate the physical process of ion diffusion.
[0052] Specifically, the message passing function includes: ,in, Represents a node exist The feature vector of the layer, Represents a node exist The feature vector of the layer, Represents a node In the feature vector of the layer, Represents a node The neighborhood group, Indicates the attention coefficient. Representing an edge Features This represents the activation function. This represents a trainable weight matrix. , Represents the physical constraint operator. Indicates the diffusion coefficient. Nodes representing image analysis computation With nodes Contact area between corresponding regions Represents a node With nodes The Euclidean distance of the center of mass.
[0053] In summary, this invention constructs a novel physical information graph neural network model through the design and application of the aforementioned physical constraint operators. This model deeply embeds Fick's law, which describes ion diffusion, into the message passing mechanism of graph convolution, making the model's forward computation process itself a simulation of physical laws. This ensures the model's physical consistency and interpretability at the architectural level, laying a solid foundation for high-performance, highly generalizable material property prediction.
[0054] As a preferred implementation, to characterize the complexity of diffusion capability being influenced by the local microenvironment within a unified physical framework, this embodiment of the invention configures the diffusion coefficient as a learnable function related to the local microenvironment. Specifically, the diffusion coefficient is preferably dynamically calculated by a trainable sub-network (such as a multilayer perceptron). This multilayer perceptron network takes the current feature vectors of two interacting nodes and the feature vectors of the edges between them as input, undergoes nonlinear transformation through several hidden layers, and finally outputs a scalar value as the current local diffusion coefficient between the node pair. During model training, the parameters of this multilayer perceptron network, along with other parameters in the physical information graph neural network model, are optimized through a backpropagation algorithm, enabling the model to adaptively learn and express the differences in diffusion characteristics at different locations within the material.
[0055] As a preferred implementation, to further enhance the model's adaptability and robustness, the message passing function can also employ a gated fusion mechanism. This mechanism, when calculating the final message, does not rely entirely on the aforementioned physical constraint operators, but introduces a learnable gating coefficient. This gating coefficient is dynamically calculated from the features of the current node pair and its edges, and its value ranges from zero to one. The final message is a weighted sum of the message generated by the physical constraint operators and a purely data-driven attention message, with the weights controlled by the gating coefficient. This allows the model to adaptively adjust the dependence ratio on prior physical laws and data-driven features based on the confidence level of local information. After processing through multiple physical information graph convolutional layers, the low-level features of the original image region are gradually refined, fused, and transformed into high-level node features containing rich physical state information. Then, through a global pooling operation, the features of all nodes are aggregated into a fixed-length graph-level feature vector, which represents the global state of the entire material sample. Finally, the graph-level feature vector is input into a performance prediction layer, which typically consists of one or more fully connected layers. This layer is responsible for mapping the high-dimensional features to specific electrochemical performance metrics, such as capacity, rate performance, or cycle life, thereby outputting the final electrochemical performance prediction result.
[0056] In this embodiment of the invention, constructing the graph structure includes: segmenting the microstructure image to obtain multiple superpixel regions; and constructing a graph structure based on the superpixel regions.
[0057] In one possible implementation, pixel regions in an image are connected based on fixed spatial proximity rules. The resulting graph structure only reflects the geometric proximity of image regions and cannot characterize the actual strength of electrochemical physical processes such as ion diffusion between regions. This leads to a graph containing numerous redundant or even erroneous connections, causing information to flow between physically disconnected regions during message passing in subsequent graph neural networks, introducing noise and reducing the model's accuracy and efficiency.
[0058] To address the aforementioned problems, this invention provides a physically driven graph structure construction method. In this embodiment, the graph structure construction based on superpixel regions includes: constructing an initial graph structure based on the superpixel regions, the initial graph structure including nodes and edges, where nodes represent superpixel regions and edges represent spatial adjacency relationships between superpixel regions; determining the contact area and centroid Euclidean distance between spatially adjacent superpixel regions; determining the physical interaction strength between spatially adjacent superpixel regions based on the contact area and centroid Euclidean distance; and optimizing the initial graph structure based on the physical interaction strength to obtain a graph structure. Specifically, optimizing the initial graph structure based on the physical interaction strength to obtain a graph structure includes: if the physical interaction strength is lower than a first preset threshold, merging corresponding two nodes into a new node; if the physical interaction strength is lower than a second preset threshold, removing the corresponding edge.
[0059] Specifically, firstly, a superpixel segmentation algorithm (such as simple linear iterative clustering) is used to segment the microstructure image into multiple superpixel regions, with each superpixel region serving as a candidate node. For each candidate node, initial node features are calculated. These features are multi-dimensional vectors, and their dimensions may include: the average gray value and gray variance of the superpixel region in the image, as well as morphological features extracted through the local binary pattern operator, such as texture histogram, area, perimeter, and circularity. These initial features characterize the low-level visual and geometric properties of the region, providing a foundation for subsequent physical analysis. Next, initial adjacency relationships between nodes are defined: two candidate nodes are considered spatially adjacent if and only if they share a non-zero-length common boundary in the image space. For each pair of such adjacent nodes, an initial edge is constructed, and initial edge features are calculated for this edge. The initial edge feature is a vector whose core dimensions include geometric parameters with clear physical meaning directly calculated from the image segmentation results, including the contact area between corresponding regions of nodes and the Euclidean distance between the centroids of nodes, thus obtaining the initial graph (containing candidate nodes, initial edges, and corresponding features). The physical interaction strength corresponding to each initial edge is calculated; this strength is a scalar used to quantify the potential coupling strength between the regions represented by the nodes, such as diffusion. In one specific implementation, the calculation formula is: ,in, These represent the local elemental concentrations corresponding to nodes i and j, such as the atomic percentages of elements like lithium, nickel, manganese, and cobalt. These concentration values are not learned by a neural network, but are obtained in the preprocessing stage by registering and mapping scanning electron microscope images with simultaneously acquired X-ray energy dispersive spectroscopy (EDS) distribution maps, averaging the EDS data within each superpixel region. Finally, the initial graph is cropped and simplified based on the physical interaction strength to generate the final graph structure for input. Specifically, this involves retaining the top K edges with the highest physical interaction strength from all initial edges to form a candidate set of edges, using physical interaction strength as one dimension of the edge features; for all candidate nodes, if their physical interaction strength is below a preset merging threshold, these two regions are considered physically highly homogeneous and strongly connected, and should be merged into a new node. After merging, the features of the new node are taken as the average of the features of all candidate nodes it contains, and its geometric parameters (such as centroid and area) are recalculated accordingly, thus obtaining the final graph structure.
[0060] Through the above method, the embodiments of the present invention dynamically form a graph structure with a moderate number of nodes, sparse connecting edges, and each edge having significant physical meaning.
[0061] It should be noted that the topology of this graph, i.e. the connection relationship between the nodes, is completely determined before the subsequent training of the physical information graph neural network model begins, and remains fixed throughout the training and inference process of the entire model. Thus, the prior knowledge about the microstructure of materials and their physical interaction modes is hard-coded into the entire machine learning process in a deterministic and immutable graph structure.
[0062] When microstructure images are multi-scale, registration of these multi-scale images is necessary. Traditional registration techniques (such as those based on scale-invariant feature transformation or gray-level mutual information) aim for spatial alignment of appearance features such as pixel grayscale and texture. However, for the specific task of predicting material properties, the continuity of the internal physical states (such as lithium-ion concentration distribution and phase distribution) reflected by images at different scales is far more important than appearance alignment. Appearance features may vary significantly due to differences in imaging principles, contrast mechanisms, and noise patterns, causing appearance-based registration results to fail to guarantee the continuity of the physical state field. This introduces systematic errors into subsequent cross-scale calculations and transfer of physical quantities.
[0063] To address the aforementioned problems, this invention proposes a physical field-guided elastic registration method. In this embodiment, the microstructure image includes multi-scale microstructure images, and the method further includes: acquiring a preliminary model with the same structure as the physical information graph neural network model; inputting a coarse-scale image into the preliminary model to obtain a physical field reference image; initializing the deformation parameters of the B-spline free deformation model, and performing a spatial transformation on the fine-scale image based on the deformation parameters to obtain a temporary registration image; inputting the temporary registration image into the preliminary model to obtain a physical field distribution; calculating the mutual information between the physical field reference image and the physical field distribution; updating the deformation parameters with the goal of maximizing the mutual information until the mutual information converges or reaches a preset number of iterations to obtain the optimal deformation parameters; performing a spatial transformation on the fine-scale image based on the optimal deformation parameters to obtain a fine-scale image aligned with the coarse-scale image at the physical state level; and constructing a corresponding graph structure based on the registered image.
[0064] In one possible implementation, a preliminary model with the same structure as the physical information graph neural network model needs to be obtained and pre-trained on a coarse-scale image dataset to enable it to interpret physical states from images. During the registration stage, the parameters of this preliminary model are fixed; the coarse-scale image is input into this model, and feature maps are extracted from its intermediate layers. These feature maps are considered as reference maps encoding the physical field distribution. Then, a spatial transformation described by a B-spline free deformation model is applied to the fine-scale image, and the transformed image is input into the same preliminary model to obtain its physical field distribution map. Next, a statistical similarity measure, such as normalized mutual information, between the physical field reference map and the distribution map is calculated. The optimization goal of the registration algorithm is to continuously adjust the B-spline deformation parameters to maximize the normalized mutual information between the two physical field maps. Through iterative optimization using gradient descent, the optimal deformation parameters are finally obtained and used to resample the fine-scale image, outputting a final image that is physically aligned with the coarse-scale image.
[0065] Compared to traditional registration, the method of this invention is insensitive to differences in imaging conditions, ensuring the continuity and consistency of the registered images in terms of physical semantics, and significantly improving its friendliness to the final performance prediction task.
[0066] In this embodiment of the invention, when training the physical information graph neural network model, a physical consistency penalty term is introduced into the loss function, including: extracting node features output from the intermediate layers of the model as physical quantities; determining the gradient divergence of the physical quantities in space and the rate of change in time; determining the difference between the gradient divergence and the rate of change in time; and determining the physical consistency penalty term based on the difference.
[0067] In practical applications, although physical constraint operators are rigidly embedded in the physical information graph neural network model architecture, the feature representations learned by the intermediate layers of the network may still deviate from their intended physical meaning during training. A mechanism is needed to continuously guide and correct them during training.
[0068] To address this, this invention introduces an additional physical consistency penalty term during the model training phase, in addition to the conventional prediction error loss function. This loss is not part of the model's forward computation but serves as a supervisory signal during training, forcing the feature evolution of the network's intermediate layers to obey physical laws.
[0069] Specifically, during training, the output node features of a convolutional layer at an intermediate graph in the network are selected as the current physical quantity. According to the diffusion law, the rate of change of this physical quantity over time should be equal to its spatial gradient divergence. In practice, the rate of change over time... The gradient divergence in space can be approximated by the difference of eigenvectors from adjacent cycles. The spatial gradient divergence is then approximated by discretization using the graph Laplacian matrix from graph theory, and can be calculated as follows: The physical consistency penalty term is defined as the sum of the squares of the differences between the time derivative and the spatial divergence at all nodes, i.e. ,in, , , Indicates the number of loops. Indicates the difference in the number of iterations. Indicates the first The node in the next loop The eigenvector of represents the eigenvalue of . The node in the next loop eigenvectors, This represents the total number of nodes. This term, along with the weighted sum of the regular prediction error term, constitutes the overall training objective of the model.
[0070] This invention, through the design of a physical consistency penalty loss, ensures dual protection of the physical consistency of the Physical Information Graph Neural Network (PIPN) model across the entire chain, from computation to internal state. Furthermore, it enables the PIPN model to utilize a large amount of microstructure image data lacking final performance labels but possessing time-series characteristics for self-supervised pre-training, learning general diffusion dynamics. This significantly reduces reliance on expensive performance label data, improving the method's data utilization efficiency and practicality.
[0071] Those skilled in the art will understand that although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the machine equivalents of the claims, the invention also intends to include these modifications and modifications.
Claims
1. A method for predicting the performance of electrochemical energy storage devices based on machine learning, characterized in that, include: Obtain microstructure images of electrode materials for electrochemical energy storage devices, and construct corresponding graph structures. The graph structures include nodes and edges, where nodes correspond to material regions and edges correspond to the spatial adjacency relationships between material regions. The graph structure is input into a preset physical information graph neural network model, wherein the message passing function of at least one graph convolutional layer in the physical information graph neural network model contains a physical constraint operator based on the electrochemical diffusion equation. Output the predicted electrochemical performance of the electrode material; The physical constraint operator is expressed as follows: in, , , They are nodes ,node ,side eigenvectors, The diffusion coefficient is related to the material. For nodes and Contact area between corresponding regions For nodes and The Euclidean distance between the centroids.
2. The method according to claim 1, characterized in that, The corresponding graph structure to be constructed includes: The microstructure image is segmented to obtain multiple superpixel regions; A graph structure is constructed based on the superpixel region.
3. The method according to claim 2, characterized in that, The superpixel region-based graph construction structure includes: An initial graph structure is constructed based on the superpixel region; Determine the contact area and centroid Euclidean distance between spatially adjacent superpixel regions; The intensity of physical interaction between spatially adjacent superpixel regions is determined based on the contact area and the Euclidean distance between their centroids. The initial graph structure is optimized based on the strength of the physical interactions to obtain the final graph structure.
4. The method according to claim 3, characterized in that, The optimization of the initial graph structure based on the physical interaction strength to obtain the graph structure includes: If the physical interaction strength is lower than a first preset threshold, the two corresponding nodes will be merged into a new node; If the physical interaction strength is lower than the second preset threshold, the corresponding edge is removed.
5. The method according to claim 1, characterized in that, The microstructure image includes multi-scale microstructure images, and the method further includes: Obtain a preliminary model with the same structure as the physical information graph neural network model; Input the coarse-scale image into the preliminary model to obtain a physical field reference map; Initialize the deformation parameters of the B-spline free deformation model, and perform spatial transformation on the fine-scale image based on the deformation parameters to obtain a temporary registration image; The temporary registration image is input into the preliminary model to obtain the physical field distribution; Calculate the mutual information between the physical field reference map and the physical field distribution; With the goal of maximizing the mutual information, the deformation parameters are updated until the mutual information converges or the preset number of iterations is reached, thus obtaining the optimal deformation parameters. Based on the optimal deformation parameters, a spatial transformation is performed on the fine-scale image to obtain a fine-scale image that is physically aligned with the coarse-scale image. Based on the registered images, the corresponding graph structure is constructed.
6. The method according to claim 1, characterized in that, When training the physical information graph neural network model, a physical consistency penalty term is introduced into the loss function, including: Extract the node features output from the intermediate layers of the model as physical quantities; Determine the spatial gradient divergence and the rate of change over time of the physical quantity; Determine the difference between the gradient divergence and the rate of change; A physical consistency penalty is determined based on the aforementioned differences.
7. The method according to claim 1, characterized in that, The method further includes: The diffusion coefficient is parameterized as a random variable, and the value distribution of the random variable is determined by the trainable subnetwork based on node features and edge features. When making performance predictions, multiple diffusion coefficient values are independently sampled from the value distribution of the random variable, and each sampled value is treated as an independent physical parameter instance. For each physical parameter instance, the forward propagation of the physical information graph neural network is run multiple times by randomly discarding neurons to obtain multiple electrochemical performance prediction sample values, and the average of the multiple sample values is calculated as the conditional prediction mean under the corresponding physical parameter instance. Obtain the electrochemical performance prediction sample values for all physical parameter instances, calculate the corresponding total variance, and use it as a measure of total uncertainty. Calculate the variance of the conditional prediction mean for all physical parameter instances, and use it as the uncertainty component of the physical parameter. Subtracting the physical parameterization uncertainty component from the total uncertainty measure yields the model structure uncertainty component; Output the uncertainty components of the physical parameters and the uncertainty components of the model structure.