Intelligent catalyst design method and system based on multi-objective optimization and deep learning

Abstract

The invention discloses an intelligent catalyst design method and system based on multi-objective optimization and deep learning, and aims to solve the problems of limitation of single-objective optimization, high computing resource consumption and the like in traditional catalyst design. According to the method, graph data are constructed by fusing atomic-scale and macroscopic features, multi-target prediction is carried out by utilizing a multi-task graph neural network (GNN), and collaborative optimization of adsorption energy and stability loss is realized by combining an NSGA-II multi-target optimization algorithm and a dynamic weight adjustment strategy of Bayesian optimization. A closed loop is verified through active learning and virtual experiments, candidate materials are dynamically selected, the model is updated, and the efficiency and precision of material design are remarkably improved. The method is suitable for rapid discovery and optimization of the high-performance catalyst, and has a wide application prospect.

Description

Technical Field

[0001] The present invention belongs to the intersection of materials computing and artificial intelligence, and specifically relates to an intelligent experimental design method that combines graph neural networks (GNNs), multi-objective evolutionary algorithms, and active learning for the optimal design of high-performance catalyst materials. Background Art

[0002] Traditional catalyst design methods typically optimize a single performance metric (such as adsorption energy), but practical applications require balancing multiple objectives, including activity, stability, and cost. For example, random forest-based catalyst screening methods only optimize adsorption energy without considering stability constraints, resulting in material deactivation during actual synthesis.

[0003] Exhaustive searches based on density functional theory (DFT) require extensive computing resources (approximately 10-100 CPU hours per calculation), making it difficult to cover complex material spaces. Furthermore, existing deep learning models lack the ability to dynamically adjust and optimize strategies based on experimental feedback.

[0004] Existing active learning methods lack effective selection criteria in multi-objective scenarios, making it difficult to balance exploration and exploitation. For example, methods that rely solely on predictive uncertainty may ignore the trade-offs between objectives. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: to provide a dynamic closed-loop catalyst intelligent design method, integrating a multi-task graph neural network and a multi-objective optimization algorithm, constructing material graph data through atomic spacing, predicting adsorption energy and stability, and generating a Pareto optimal solution set; using adaptive weight adjustment and hybrid active learning strategies, combined with virtual experiments to verify the closed loop, screen high-potential materials and iteratively optimize the model, solving the problem of collaborative optimization of multiple performance indicators and reducing experimental costs.

[0006] The technical solution of the present invention is: a catalyst intelligent design method based on multi-objective optimization and deep learning, a graph data generation method based on the dynamic construction of the adjacency matrix based on the atomic distance; a multi-task graph neural network loss function that introduces a learnable noise parameter; a dynamic weight adjustment strategy combining NSGA-II and Bayesian optimization; an active learning closed loop based on hybrid scoring and cluster screening; and an interpretable monitoring system that integrates virtual DFT verification and visual decision-making.

[0007] The catalyst intelligent design method based on multi-objective optimization and deep learning has the following specific steps:

[0008] 1) Use DFT calculations to generate an initial data set, including the structural characteristics and performance indicators of the material. Based on the atomic coordinates and chemical bond characteristics in the data, multi-scale feature fusion is used to construct material graph structure data to support model input;

[0009] 2) Based on the dynamic adjacency matrix generation algorithm, the atomic distance threshold is set in the catalyst suitable range (such as ) Determine chemical bond connections and construct non-fully connected graph structures and adjacency matrices;

[0010] 3) Integrate the fused node feature matrix, adjacency matrix, and target vector into a standardized graph data container to support batch input of multi-task graph neural networks;

[0011] 4) Construct a multi-task graph neural network architecture. The input layer receives standardized graph data information including atomic feature matrix, dynamic adjacency matrix and performance target. Local and global features are extracted through two layers of graph convolution (GCN). The attention mechanism is used to realize weight calculation and node feature aggregation. The dynamic loss module for task noise and loss calculation is introduced to optimize the parameters. The feature extraction and enhancement parameters and balance weights are adjusted in the graph convolution layer. The output layer predicts adsorption energy and stability loss in parallel based on global features.

[0012] 5) Design a dynamic loss function module. Based on the multi-task graph neural network trained in step 4, introduce multiple objectives of the trainable tasks, such as adsorption energy and stability noise parameters (σ1, σ2), and automatically optimize the weights of the multi-tasks through backpropagation. The loss function is defined as:

[0013]

[0014] σ1 is the noise parameter of the adsorption energy prediction task, σ2 is the noise parameter of the stability loss prediction task,

[0015] is the loss of the adsorption energy prediction task, the square of the difference between the true value and the model prediction value, The loss of the stability loss prediction task is the square of the difference between the true value and the model prediction value; the network parameters and noise parameters are optimized synchronously through backpropagation, so that σ1 and σ2 dynamically adjust the weights of the two tasks. When the activity prediction error is large, the weight of σ1 is automatically reduced to strengthen the learning intensity of the task; the feature extraction and enhancement parameters are automatically adjusted to balance the weights of different tasks and avoid a single task dominating the training process;

[0016] 6) Define a multi-objective optimization problem: Use the adsorption energy and stability loss rate output from step 4 as optimization objectives, such as maximizing the adsorption energy (maximum absolute value) and minimizing the stability loss, constraining material cost and toxicity score thresholds; use the NSGA-II algorithm to generate the Pareto frontier, use the model prediction results after step 5 optimization as the initial population to generate heuristic rules, integrate Bayesian optimization to construct a proxy model, and calculate the confidence interval based on the σ parameter trained in step 5 to guide the NSGA-II elite selection;

[0017] 7) Implement a dynamic adjustment mechanism for crossover probability and calculate the adaptive probability based on the population crowding (C):

[0018]

[0019] p c is the crossover probability in the genetic algorithm, C is the crowding degree of the current individual, C max is the maximum crowding value of the population, C min Minimize the crowding degree of the population; combine Bayesian optimization to update the target weight, accelerate the optimization convergence, and improve the diversity and quality of the solution set;

[0020] 8) Design a hybrid active learning strategy to generate candidate scores by combining prediction uncertainty (standard deviation) and expected improvement (EI). The formula is:

[0021] S(x)=0.6·Uncertainty(x)+0.4·EI(x)

[0022] S(x) is the comprehensive score of the candidate material, Uncertainty(x) is the standard deviation of the model's prediction results for candidate material X, and EI(x) is the expected improvement. The Pareto solution set is screened using KMeans clustering. The clustering algorithm (KMeans) groups the materials and selects the top 1–10 best materials from each group to avoid concentrating all materials on a single characteristic.

[0023] 9) Construct a virtual DFT verification closed-loop system. The final data after combining the optimal candidate materials from each group screened in step 8 is used for surface adsorption energy calculation and lattice dynamics simulation (to verify thermal stability). When the mean absolute error between the virtual experimental results and the predicted values ​​from step 4 is greater than 5%, the difference data is added to the training set of step 1 to trigger incremental learning. The system then returns to step 5 to re-optimize the multi-task loss weights and update the Bayesian surrogate model. When the error is ≤5%, the preferred material is directly output as the final design solution.

[0024] 10) Integrate full-process monitoring and decision-making, supporting real-time monitoring of graph data generation, model training, multi-objective optimization, and experimental verification, including feature correlation distribution, Pareto frontier, and parameter distribution histogram.

[0025] The dynamic weight adjustment strategy of NSGA-II and Bayesian optimization described above: NSGA-II is a multi-objective optimization algorithm used to generate a Pareto optimal solution set and balance the competition between multiple objectives. Bayesian optimization is used to dynamically adjust the objective weights and prioritize the optimization of sparse areas based on the distribution density of the Pareto frontier.

[0026] The material graph structure data is a graph data representation created by fusing the material's atomic-level structural parameters (such as atomic coordinates, bond lengths, and bond angles) with macroscopic physical properties (such as ionization energy, electron affinity, electronegativity, and vacancy formation energy). It consists of a node feature matrix, an adjacency matrix, and a target vector.

[0027] The dynamic adjacency matrix: based on the atomic distance threshold in the catalyst suitable range such as It can determine chemical bond connections and generate an adjacency matrix representing the connection relationship between atoms, which can accurately represent the structural characteristics of the material and support the input of graph neural networks.

[0028] The adjacency matrix is ​​a sparse matrix representing the connection relationship between atoms, with a dimension of N×N (N is the number of atoms), which is used as the input of the graph neural network and represents the structural characteristics of the material.

[0029] The node feature matrix: each node represents an atom, and the feature vector includes atomic-level features such as atomic coordinates, bond length, bond angle, and macroscopic physical parameters such as ionization energy and electronegativity; the adjacency matrix: represents the connection relationship between atoms, based on the atomic distance threshold (such as ) determines chemical bond connections; target vector: performance indicators between multiple targets including adsorption energy and stability loss.

[0030] The described visual monitoring: dynamic adjacency matrix control: interactive adjustment of atomic distance threshold, real-time rendering of three-dimensional bond connection model, multi-objective decision matrix: interactive screening of Pareto solutions, simultaneous display of multi-objective trade-off curves and material cost distribution, real-time monitoring of system operation status, and support for user interaction and decision-making.

[0031] The hybrid active learning strategy described: comprehensive prediction uncertainty and expected improvement (EI) are used to screen candidate materials, and diversity is ensured through KMeans clustering.

[0032] The attention mechanism described above realizes the dynamic aggregation of node features and introduces the bond length gating factor based on the atomic distance and chemical bond characteristics. Suppress invalid connections and enhance physical interpretability. Quantify atomic contribution differences through multiple sets of attention weights, screen key atomic features to generate a global representation, and simultaneously calculate the active center contribution index (KAI).

[0033] The beneficial effects of the present invention are as follows: multi-objective collaborative optimization: combining NSGA-II global search with Bayesian optimization local refinement to balance the competitive relationship between adsorption energy, stability and cost; closed-loop self-evolution design: virtual DFT verification and incremental learning form a "prediction verification and retraining" feedback loop to continuously improve model accuracy.

[0034] The present invention achieves high efficiency, accuracy and interpretability in catalyst design through the combination of dynamic graph data construction, multi-task collaborative learning, hybrid optimization strategy and closed-loop verification system, providing an innovative tool for the development of new materials and has broad application prospects in the fields of photocatalysis, electrocatalysis and so on. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a system flow chart (including dynamic optimization and experimental verification closed loop);

[0036] Figure 2 The graph neural network architecture (labeled with the attention pooling layer and dynamic loss module);

[0037] Figure 3 This is the NSGA-IIPareto frontier diagram, showing the trade-off between adsorption energy and stability loss;

[0038] Figure 4 To optimize the variable distribution diagram, the characteristic value ranges of electron filling factor (f), electron density (ed), surface energy parameter of low-index crystal plane (γ1), surface energy parameter of high-index crystal plane (γ2), interatomic binding energy (W), ideal atomic distance (r0), actual atomic distance (rd), ionization energy (IE), electron affinity (EA), initial electronegativity (chi0), electronegativity (chi), and vacancy formation energy (Vad2) are displayed;

[0039] Figure 5 Generate a performance comparison chart between the optimized solution and the original material through the plot_enhanced_comparison function. DETAILED DESCRIPTION

[0040] The implementation process of the catalyst prediction method for the CO2 adsorption energy and stability of the catalyst is as follows:

[0041] 1. Data preparation and graph structure generation: The CO2 catalytic material data loaded with DFT calculations contain 298 sets of CO2 catalytic material data sets with 12 characteristics, including electron filling factor (f), electron density (ed), low-index crystal surface energy parameter (γ1), high-index crystal surface energy parameter (γ2), interatomic binding energy (W), ideal atomic spacing (r0), actual atomic spacing (rd), ionization energy (IE), electron affinity (EA), initial electronegativity (chi0), electronegativity (chi), vacancy formation energy (Vad2), etc., forming a 15-dimensional feature vector for each atom.

[0042] Generate a standardized graph data container: The original 12-dimensional features (including atomic-level parameters such as atomic coordinates, bond lengths, and bond angles, as well as macroscopic physical properties such as ionization energy and electronegativity) are merged with three-dimensional spatial coordinates. A 15-dimensional feature vector (3-dimensional coordinates + 12-dimensional physical parameters) is generated for each atomic node, forming an N×15 node feature matrix. Target vector: Defines the maximum adsorption energy (absolute value) and minimum stability loss as the optimization target (2×1 dimension). Node features and target values ​​are standardized to eliminate dimensional differences.

[0043] 2. Multi-task graph neural network modeling: Constructing a neural network with two layers of graph convolution (GCN): The first layer focuses on The local chemical bond interactions within the polymer are extracted by limiting the neighboring atoms to Within the spatial range The second layer captures the global characteristics of long-range lattice periodicity. The attention mechanism is used to introduce the bond length gating factor. Suppress invalid connections, Weight decay is applied to the above atomic connections to reduce the weight of connections exceeding the threshold to below 0.2, enabling weight calculation and node feature aggregation. A dynamic loss module for task noise and loss calculation is introduced to optimize parameters. Feature extraction and enhancement parameters and balance weights are adjusted in the graph convolution layer. The output layer predicts adsorption energy and stability loss in parallel based on global features.

[0044] 3. Dynamic loss weight optimization: Based on the multi-task graph neural network trained in the above steps, multiple objectives of the trainable tasks are introduced, such as adsorption energy and stability noise parameters (σ1, σ2). The weights of multiple tasks are automatically optimized through backpropagation, and an adaptive loss function is designed. The noise parameters σ1 and σ2 are automatically adjusted through Bayesian optimization to balance the weights of different tasks and avoid a single task dominating the training process; when the increase in the adsorption energy or stability prediction error exceeds 5%, the parameter update of the stability task is frozen to strengthen the learning of key tasks.

[0045] 4. Multi-objective optimization and active learning: NSGA-II algorithm is used to generate the Pareto frontier, and the optimization objectives are defined as maximizing adsorption energy (large absolute value) and minimizing stability loss, while constraining material cost. < $50 / g and toxicity score ≤ 3. The NSGA-II algorithm was used to generate the Pareto frontier ( Figure 4 ), the model prediction results after step 5 optimization are used as the initial population generation heuristic rules, Bayesian optimization is integrated to build the proxy model, and a dynamic adjustment crossover probability function is introduced The crossover probability is dynamically adjusted to preserve diversity in sparse regions (crossover probability 0.4) and enhance local search in dense regions (crossover probability 0.9). Candidate materials are screened using a hybrid scoring function (S(X) = 0.6σ(X) + 0.4EI(X)). Pareto solutions are then selected using KMeans clustering. The KMeans clustering algorithm groups the materials and selects the top 1–10 best materials from each group, preventing all materials from concentrating on a single characteristic.

[0046] 5. Virtual verification and visualization: Select representative materials for each category to conduct virtual DFT verification, calculate surface adsorption energy (adsorption energy) and lattice dynamics stability. When the prediction error exceeds 5%, the incremental learning mechanism is triggered: the difference data is added to the training set, the underlying network parameters are frozen, the multi-task loss weights are re-optimized, and the Bayesian proxy model is updated. The key parameter distribution is obtained through Figure 4 The histogram clearly shows the range of characteristics such as the target material filling factor (f), electron density (ed), and low-index crystal plane surface energy parameter (γ1), providing a reference for the design of the target catalyst.

[0047] 6. Visualized decision-making and closed-loop feedback: An explainable monitoring system that integrates full-process monitoring and decision-making, and user interactive adjustment Figure 2 The interatomic distance threshold in ( Adjustable range), and observe the impact of different thresholds on active centers in real time. Figure 3 The Pareto front provides a multi-objective trade-off curve. When the extreme solution of adsorption energy is selected, the system simultaneously shows that the material Figure 4 Performance parameter position in box plot. Visual feedback: Figure 5 The comparison shows that the optimized CO2 adsorption energy is improved by an average of 60.1%, the stability is improved by 28.8%, and the coverage is 1.7%. The diversity of the solution set is ensured by KMeans.

Claims

1. A catalyst intelligent design method based on multi-objective optimization and deep learning, characterized by: A graph data generation method based on dynamically constructing an adjacency matrix based on atomic distances; a multi-task graph neural network loss function that introduces learnable noise parameters; a dynamic weight adjustment strategy combining NSGA-II and Bayesian optimization; an active learning closed loop based on hybrid scoring and clustering screening; and an interpretable monitoring system that integrates virtual DFT verification and visual decision-making.

2. The catalyst intelligent design method based on multi-objective optimization and deep learning according to claim 1, characterized in that: The specific steps are as follows: 1) Use DFT calculations to generate an initial data set, including the structural characteristics and performance indicators of the material. Based on the atomic coordinates and chemical bond characteristics in the data, multi-scale feature fusion is used to construct material graph structure data to support model input; 2) Based on the dynamic adjacency matrix generation algorithm, the atomic distance threshold is set in the catalyst suitable range (such as ) Determine chemical bond connections and construct non-fully connected graph structures and adjacency matrices; 3) Integrate the fused node feature matrix, adjacency matrix, and target vector into a standardized graph data container to support batch input of multi-task graph neural networks; 4) Construct a multi-task graph neural network architecture. The input layer receives standardized graph data information including atomic feature matrix, dynamic adjacency matrix and performance target. It extracts local and global features through two layers of graph convolution (GCN), adopts attention mechanism to achieve node feature aggregation, and the output layer predicts adsorption energy and stability loss in parallel. 5) Design a dynamic loss function module. Based on the multi-task graph neural network trained in step 4, introduce multiple objectives of the trainable tasks, such as adsorption energy and stability noise parameters (σ1, σ2), and automatically optimize the weights of the multi-tasks through backpropagation. The loss function is defined as: σ1 is the noise parameter of the adsorption energy prediction task, σ2 is the noise parameter of the stability loss prediction task, is the loss of the adsorption energy prediction task, the square of the difference between the true value and the model prediction value, The loss of the stability loss prediction task is the square of the difference between the true value and the model prediction value; the network parameters and noise parameters are optimized synchronously through backpropagation, so that σ1 and σ2 dynamically adjust the dual-task weights. When the activity prediction error is large, the σ1 weight is automatically reduced to strengthen the learning intensity of the task; Automatically balance the weights of different tasks to avoid a single task dominating the training process; 6) Define a multi-objective optimization problem: Use the adsorption energy and stability loss rate output from step 4 as optimization objectives, such as maximizing the adsorption energy (maximum absolute value) and minimizing the stability loss, constraining material cost and toxicity score thresholds; use the NSGA-II algorithm to generate the Pareto frontier, use the model prediction results after step 5 optimization as the initial population to generate heuristic rules, integrate Bayesian optimization to construct a proxy model, and calculate the confidence interval based on the σ parameter trained in step 5 to guide the NSGA-II elite selection; 7) Implement a dynamic adjustment mechanism for crossover probability and calculate the adaptive probability based on the population crowding (C): p c is the crossover probability in the genetic algorithm, C is the crowding degree of the current individual, C max is the maximum crowding value of the population, C min Minimize the crowding degree of the population; combine Bayesian optimization to update the target weight, accelerate the optimization convergence, and improve the diversity and quality of the solution set; 8) Design a hybrid active learning strategy to generate candidate scores by combining prediction uncertainty (standard deviation) and expected improvement (EI). The formula is: S(x)=0.6·Uncertainty(x)+0.4·EI(x) S(x) is the comprehensive score of the candidate material, Uncertainty(x) is the standard deviation of the model's prediction results for candidate material X, and EI(x) is the expected improvement. KMeans clustering is used to screen the Pareto solution set and select the top 1–10 candidate materials by category to ensure diversity. 9) Construct a virtual DFT verification closed-loop system, and perform surface adsorption energy calculations and lattice dynamics simulations (to verify thermal stability) on each group of optimal candidate materials screened in step 8. When the mean absolute error between the virtual experimental results and the predicted values ​​in step 4 is greater than 5%, the difference data is added to the training set in step 1, triggering incremental learning. Return to step 5 to re-optimize the multi-task loss weights and update the Bayesian surrogate model. When the error is ≤5%, the preferred material is directly output as the final design solution. 10) Integrate full-process monitoring and decision-making, supporting real-time monitoring of graph data generation, model training, multi-objective optimization, and experimental verification, including correlation, loss curves, Pareto frontiers, and parameter distribution histograms.

3. The catalyst intelligent design method based on multi-objective optimization and deep learning according to claim 1, characterized in that: Dynamic weight adjustment strategy of NSGA-II and Bayesian optimization: NSGA-II is a multi-objective optimization algorithm used to generate Pareto optimal solutions and balance the competition between multiple objectives. Bayesian optimization is used to dynamically adjust objective weights, prioritizing optimization of objectives in sparse areas based on the distribution density of the Pareto frontier.

4. The method according to claim 2, wherein: The material graph structure data is represented by a graph data that combines the atomic-level structural parameters of the material, such as atomic coordinates, bond length, bond angle, and macroscopic physical property parameters, such as ionization energy, electron affinity, electronegativity, and vacancy formation energy. The graph data is composed of a node feature matrix, an adjacency matrix, and a target vector.

5. The catalyst intelligent design method based on multi-objective optimization and deep learning according to claim 2, characterized in that: Dynamic adjacency matrix: based on interatomic distance threshold Determining chemical bond connections and generating an adjacency matrix representing the connection relationship between atoms can accurately represent the structural characteristics of the material and support the input of graph neural networks.

6. The method according to claim 2, wherein: Adjacency matrix: A sparse matrix representing the connectivity between atoms, with a dimension of N×N, where N is the number of atoms. It is used as input for graph neural networks and represents the structural characteristics of the material.

7. The method according to claim 2, wherein: The node feature matrix: each node represents an atom, and the feature vector includes atomic-level features such as atomic coordinates, bond length, bond angle, and macroscopic physical parameters such as ionization energy and electronegativity; the adjacency matrix: represents the connection relationship between atoms, based on the atomic spacing threshold Determine chemical bond connections; target vector: performance indicators between multiple targets including adsorption energy and stability loss.

8. The method according to claim 2, wherein: Visual monitoring: Dynamic adjacency matrix control: interactively adjust the atomic distance threshold, real-time rendering of three-dimensional bond connection model, multi-objective decision matrix: interactive screening of Pareto solutions, simultaneous display of multi-objective trade-off curves and material cost distribution, real-time monitoring of system operation status, and support for user interaction and decision-making.

9. The method according to claim 2, wherein: Hybrid active learning strategy: Integrate prediction uncertainty and expectation to improve EI to screen candidate materials and ensure diversity through KMeans clustering.

10. The method according to claim 2, characterized in that: The attention mechanism realizes the dynamic aggregation of node features. Introducing bond length gating factors based on interatomic distances and chemical bond characteristics Suppress invalid connections and enhance physical interpretability; quantify atomic contribution differences through multiple sets of attention weights, screen key atomic features to generate global representation, and simultaneously calculate the active center contribution index KAI.

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