Machine learning based structure optimization and transition state search prediction method and system

Abstract

The application discloses a structure optimization and transition state search prediction method based on machine learning, and belongs to the technical field of the cross of computational chemistry and artificial intelligence. The application aims to solve the problems in the prior art, such as high Hessian matrix calculation cost, difficulty in reliably predicting the second derivative by a machine learning potential energy surface, and instability of atomic-lattice joint optimization of a periodic system, and comprises the following steps: predicting energy, atomic force, Hessian matrix and stress tensor by an isometric neural network, wherein the Hessian matrix is decomposed into atomic internal and interatomic components for independent prediction to reduce the calculation cost; calling a geometric optimization algorithm based on the predicted values to perform structure optimization, and synchronously updating atomic coordinates and lattice vectors by using a GEDIIS-PBC full-coupling optimizer for a periodic system; calling a transition state search algorithm based on the atomic force and the Hessian matrix to locate a saddle point; and verifying the transition state by virtual frequency analysis, so that efficient, stable and interpretable structure optimization and transition state search from a molecule to a crystal are finally realized.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of computational chemistry and artificial intelligence, and in particular to a method and system for structure optimization and transition state search prediction based on machine learning. Background Technology

[0002] Structural optimization and transition state search are core fundamental tasks in computational chemistry and materials science. Structural optimization aims to find local minima on the potential energy surface by adjusting atomic coordinates to obtain stable configurations of molecules or materials. A transition state is defined as a first-order saddle point on the potential energy surface connecting reactants and products, possessing a unique negative curvature direction and corresponding to the highest point of the chemical reaction energy barrier. Obtaining accurate transition state structures is crucial for revealing reaction mechanisms, calculating reaction rates, and guiding catalyst design. Solving these tasks heavily relies on the accuracy of potential energy surface information, especially the first derivative of energy with respect to atomic coordinates (i.e., atomic force) and the second derivative (i.e., the Hessian matrix). The Hessian matrix contains local curvature information of the potential energy surface and is a key physical quantity for implementing high-order optimization algorithms such as Newton's method and GDIIS, as well as transition state search algorithms such as eigenvector following (EF) and Sella.

[0003] Existing technologies can be mainly divided into three types. The first type is a computational method based on traditional quantum chemistry, which obtains the energy, atomic force, and even the Hessian matrix of the system by solving equations in density functional theory or wave function theory. Although this type of method has high accuracy in theory, its computational complexity increases to the cubic to fourth degree with the number of atoms. In particular, solving the Hessian matrix involves coupled-perturbation equations, which are extremely costly to compute, severely limiting its application in systems containing dozens of atoms or in high-throughput screening scenarios.

[0004] The second approach is end-to-end structure generation models, such as AlphaFold2 and Uni-Mol. These models attempt to bypass electronic structure calculations and predict 3D structures directly from input information. However, these methods generally lack physical interpretability; their predictions often do not correspond to stationary points on the actual potential energy surface and are prone to unreasonable bond lengths, bond angles, or spatial conflicts. In transition state prediction tasks, the generated structures often fail to meet the mathematical definition of a first-order saddle point, still requiring expensive quantum chemical methods for verification and correction, thus failing to fundamentally resolve the contradiction between efficiency and accuracy.

[0005] The third approach is potential surface modeling based on machine learning. By constructing neural networks or kernel function models to fit quantum chemical data, this method can quickly predict energy and atomic forces, to some extent replacing traditional first-principles calculations. However, existing machine learning potential surfaces still face a significant technical gap in reliably predicting second derivatives (i.e., the Hessian matrix). The lack of accurate Hessian information makes it difficult for efficient geometric optimization algorithms that rely on curvature information, such as Newton's method, quasi-Newton methods, and GDIIS, to fully realize their advantages in accelerating convergence. It also hinders the effective application of transition state search algorithms such as EF and Sella, which require precise saddle point curvature guidance.

[0006] Furthermore, for crystal systems with periodic boundary conditions, structural optimization involves the joint relaxation of atomic coordinates and lattice parameters. Existing methods typically treat these two aspects separately or employ simple alternating optimization strategies, which can easily lead to zigzag oscillations in the convergence path, lacking a stable and efficient simultaneous optimization scheme.

[0007] In summary, how to efficiently acquire complete potential energy surface information, including the Hessian matrix, while ensuring physical rationality, and to achieve unified, stable, and rapid structure optimization and transition state search from isolated molecules to periodic crystals, has become a technical bottleneck that urgently needs to be overcome in this field. Summary of the Invention

[0008] To address the problems of high cost in calculating the Hessian matrix using quantum chemical methods, unreliable prediction of second derivatives using machine learning potential surfaces, and instability in joint optimization of atoms and lattice in periodic crystal systems, this invention proposes a machine learning-based method for structure optimization and transition state search prediction. It predicts energy, atomic forces, and the Hessian matrix using an equivariant neural network, and decomposes the Hessian matrix into independently predicted intra-atom and inter-atom components, significantly reducing computational costs. For periodic systems, a fully coupled optimizer, GEDIIS-PBC, is developed, constructing a joint DIIS matrix based on atomic forces and stress tensors to achieve synchronous relaxation of atomic coordinates and lattice parameters, avoiding zigzag instability. This invention achieves efficient and stable structure optimization and transition state search from molecules to crystals while ensuring physical interpretability.

[0009] On the one hand, a machine learning-based method for structure optimization and transitional state search prediction is provided, including: Obtain the initial structural information of the target system, wherein the initial structural information includes atom types and atom coordinates; The initial structural information is input into a pre-trained equivariant neural network model to obtain the energy prediction value, atomic force prediction value, and Hessian matrix prediction value of the target system. Based on the predicted atomic force and the predicted Hessian matrix, the atomic coordinates of the target system are iteratively updated using a geometric optimization algorithm until the preset convergence condition is met, thereby obtaining the optimized stable structure. Based on atomic force predictions and Hessian matrix predictions, a transition state search algorithm is used to search and iterate along the negative curvature direction of the saddle point using the precise curvature information provided by the Hessian matrix until the preset convergence condition is met, thereby locating the candidate transition state structure. The candidate transition state structure is analyzed for imaginary frequency. If it has a unique imaginary frequency, it is confirmed as the target transition state structure.

[0010] On the other hand, a machine learning-based method for structure optimization and transition state search prediction is provided, including: Obtain the initial structural information of the target system, wherein the initial structural information includes atom types and atomic coordinates as well as lattice vectors; The initial structural information is input into a pre-trained equivariant neural network model to obtain the energy prediction, atomic force prediction, Hessian matrix prediction, and stress tensor prediction of the target system. Based on the predicted atomic force, the predicted Hessian matrix, and the predicted stress tensor, the atomic coordinates and lattice vectors of the target system are synchronously iteratively updated using a fully coupled optimizer until the preset convergence condition is met, thereby obtaining the optimized stable structure. Based on the atomic force prediction value and the Hessian matrix prediction value, the transition state search algorithm is used to search and iterate along the negative curvature direction of the saddle point using the accurate curvature information provided by the Hessian matrix until the preset convergence condition is met, and the candidate transition state structure is located. The candidate transition state structure is analyzed for imaginary frequency. If it has a unique imaginary frequency, it is confirmed as the target transition state structure.

[0011] On the other hand, a machine learning-based structural optimization and transition state search prediction system is provided, including: The input module is configured to: acquire the initial structural information of the target system, wherein the initial structural information includes atom types and atom coordinates as well as lattice vectors; The physical property prediction module is configured to input the initial structural information into a pre-trained equivariant neural network model to obtain the energy prediction value, atomic force prediction value, Hessian matrix prediction value, and stress tensor prediction value of the target system. The optimization module is configured to: based on the predicted atomic force value, the predicted Hessian matrix value, and the predicted stress tensor value, use a fully coupled optimizer to synchronously iteratively update the atomic coordinates and lattice vectors of the target system until the preset convergence condition is met, thereby obtaining the optimized stable structure. The transition state search module is configured to: based on the atomic force prediction value and the Hessian matrix prediction value, use the transition state search algorithm, utilize the precise curvature information provided by the Hessian matrix, perform search iterations along the negative curvature direction of the saddle point until the preset convergence condition is met, and locate the candidate transition state structure. The transition state verification module is configured to perform imaginary frequency analysis on the candidate transition state structure, and if it has a unique imaginary frequency, it is confirmed as the target transition state structure.

[0012] In another aspect, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, performs the method described in the first or second aspect.

[0013] The above technical solution has the following advantages or beneficial effects: (1) In terms of computational efficiency, this invention replaces expensive first-principles calculations with equivariant neural networks to directly predict energy, atomic force and Hessian matrix. While maintaining a high degree of consistency with density functional theory, it improves computational efficiency and convergence speed. By decomposing the Hessian matrix into diagonal blocks within atoms and off-diagonal blocks between atoms for independent prediction, it significantly reduces computational cost while ensuring the accuracy of the second derivative, enabling efficient optimization algorithms that rely on curvature information, such as Newton's method and GEDIIS, to be practically applied.

[0014] (2) In terms of physical interpretability, the law of conservation of energy is strictly guaranteed by the automatic differentiation mechanism. The predicted energy, force and Hessian matrix all correspond to the physical quantities on the real potential energy surface, avoiding the non-physical structure problems that are common in end-to-end generation models, and ensuring the chemical rationality of optimization and search results.

[0015] (3) For periodic crystal systems, the GEDIIS-PBC fully coupled optimizer developed in this invention achieves synchronous relaxation of atomic coordinates and lattice parameters by simultaneously utilizing atomic force and stress tensor to construct a joint DIIS matrix, which solves the common "zigzag" oscillation problem in traditional alternating optimization methods and greatly improves the convergence stability and efficiency of crystal structure optimization.

[0016] (4) In terms of transition state search, the present invention utilizes the accurate Hessian matrix provided by machine learning, which can accurately identify the negative curvature direction on the potential energy surface. Combined with algorithms such as EF or Sella, the correct transition state structure with a single imaginary frequency can be obtained with a high success rate.

[0017] (5) The method of the present invention supports multiple systems such as molecules, crystals and catalytic surfaces, and can support automated and scalable molecular screening and reaction pathway discovery workflows. It provides new technical means for high-throughput material design, catalyst development and reaction mechanism exploration, and has broad industrial application prospects in the fields of computational chemistry and materials science. Attached Figure Description

[0018] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0019] Figure 1 This is a flowchart of the method according to Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the molecular structure optimization process based on machine learning according to Embodiment 1 of the present invention; Figure 3 This is a flowchart of the method in Embodiment 2 of the present invention; Figure 4 This is a schematic diagram of the crystal structure optimization process based on machine learning in Embodiment 2 of the present invention. Detailed Implementation

[0020] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, 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 invention pertains.

[0021] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0022] All data acquisition in this embodiment is carried out in accordance with laws and regulations and with user consent, and the data is used legally.

[0023] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. Those skilled in the art should understand that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0024] Explanation of relevant terminology in this invention: DetaNet: An equivariant neural network model used to predict physical properties of molecular and material systems, such as energy, atomic forces, Hessian matrices, and stress tensors.

[0025] The Hessian matrix is ​​the second-order partial derivative matrix of energy with respect to atomic coordinates. It contains information about the curvature of the system's potential energy surface and is a key physical quantity for efficient geometric optimization and transition state search.

[0026] Transition state (TS): The first saddle point of the potential energy surface on the chemical reaction path, corresponding to the highest point of the reaction energy barrier, and has a unique imaginary frequency (in the direction of negative curvature).

[0027] GEDIIS: Generalized Energy Direct Inversion Iterative Space Method (GEDIIS), a high-order geometric optimization algorithm based on the Hessian matrix.

[0028] GEDIIS-PBC: A fully coupled GEDIIS optimization scheme for periodic boundary conditions (PBC) that can simultaneously relax atomic coordinates and lattice parameters.

[0029] EF algorithm: Eigenvector Following algorithm, is a transition state search method that uses the eigenvectors of the Hessian matrix to locate the saddle point in the negative curvature direction.

[0030] DFT: Density Functional Theory, a first-principles calculation method based on quantum mechanics, widely used for calculating the electronic structure of molecules and materials.

[0031] Stress tensor: A physical quantity that describes the stress state of a lattice in a periodic crystal system and is used for the optimization and updating of lattice parameters.

[0032] Example 1 This embodiment provides a machine learning-based method for structure optimization and transition state search prediction, applicable to isolated molecular systems. Figure 1 This is a flowchart of a method according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes the following steps: S101: Obtain the initial structural information of the target system, including the types of atoms and their coordinates; S102: Input the initial structural information into the pre-trained equivariant neural network model to obtain the energy prediction value, atomic force prediction value and Hessian matrix prediction value of the target system; S103: Based on the predicted atomic force and Hessian matrix values, the atomic coordinates of the target system are iteratively updated using a geometric optimization algorithm until the preset convergence condition is met, thereby obtaining the optimized stable structure. S104: Based on the atomic force prediction value and the Hessian matrix prediction value, the transition state search algorithm is used to search and iterate along the negative curvature direction of the saddle point using the accurate curvature information provided by the Hessian matrix until the preset convergence condition is met, and the candidate transition state structure is located. S105: Perform imaginary frequency analysis on the candidate transition state structure. If it has a unique imaginary frequency, it is confirmed as the target transition state structure.

[0033] Further, S101: Obtain the initial structural information of the target system, including: To support subsequent model training, this embodiment pre-establishes a high-coverage training database of molecular, crystal, and reaction physical properties. For isolated molecular systems, the initial structural information includes atom types and atomic coordinates. Specifically, it integrates the QMe14S small molecule dataset, the Transition-1x gas-phase reaction dataset recalculated based on B3LYP / TZVP, the large crystal dataset OMat24, and the surface catalysis datasets OC20 / OC22.

[0034] Specifically, the reconstruction process of the Transition-1x dataset includes: extracting 50 interpolation structures between reactants and products and calculating their energies and forces, while simultaneously calculating the Hessian matrices of reactants, products, and transition states, thereby providing targeted sampling in key saddle point regions and significantly enhancing the stability of Hessian matrix-based optimization.

[0035] It should be understood that the above databases are derived from publicly available quantum chemical calculation databases, which can be obtained or generated by those skilled in the art as needed.

[0036] Optionally, in constructing the training dataset, in addition to the dataset combination described in this embodiment, those skilled in the art can also replace or expand the training data according to the specific application field. For example, a specific metal-organic framework (MOF) dataset can be added for porous material design, or a solvation effect dataset can be added for transition state search of solution phase reaction.

[0037] Further, S102: The initial structural information is input into the pre-trained equivariant neural network model to obtain the energy prediction, atomic force prediction, and Hessian matrix prediction of the target system, including: This embodiment uses DetaNet as the isovariant neural network model. Specifically, it obtains the element types of the isolated molecular structure. and Cartesian coordinates The DetaNet model maps and transforms the input spatial features (Cartesian coordinates, element type) into physical features (energy, atomic force, Hessian matrix). The core predictive capabilities of the equivariant neural network model include: a) Energy prediction: The total energy of an isolated molecular system is predicted as the sum of the contributions of all atoms, i.e.: , in, Cartesian coordinates, For element type, The total number of atoms, Energy contribution of a single atom For isolated molecular systems without periodic boundary conditions, the lattice vector does not need to be defined to eliminate the physical interaction between adjacent periodic mirror images.

[0038] b) Atomic force calculation: By automatically differentiating the equivariant neural network, the atomic force is calculated as the negative gradient of energy with respect to atomic coordinates, thereby strengthening the law of conservation of energy. , in, The partial derivative representing the total energy of the system. Let represent the partial differential of the coordinates of the i-th atom. This represents the negative gradient of the total energy with respect to the atomic coordinates.

[0039] c) Hessian matrix prediction: Considering the high computational cost of second-order automatic differentiation, this embodiment proposes to decompose the Hessian matrix into diagonal block components within atoms. and interatomic off-diagonal block components Independent predictions are performed. Among them, the diagonal block components within the atom... Off-diagonal components between atoms In the formula It is used to predict the atomic scalar output of the Hessian matrix. , T represents the transpose. By using an equivariant neural network to predict the above components separately and then combining them to output the complete Hessian matrix, the computational cost is significantly reduced.

[0040] Optionally, this embodiment uses DetaNet as the equivariant neural network model. In other implementations, those skilled in the art may also use other equivariant graph neural network architectures such as NequIP, MACE, and PaiNN as the basic model for property prediction, as long as they can output atomic scalar and tensor features and support automatic differentiation to obtain atomic forces.

[0041] Further, S103: Based on the predicted atomic force and Hessian matrix values, the atomic coordinates of the target system are iteratively updated using a geometric optimization algorithm until the preset convergence condition is met, resulting in an optimized stable structure, including: like Figure 3 As shown, in this embodiment, for an isolated molecular system, the predicted energy, atomic force, and Hessian matrix are input into the GEDIIS geometry optimizer for iterative updates. The specific steps are as follows: In the During each iteration, extract and store the atomic coordinates of the current step and several previous steps (e.g., the first 6 steps). , atomic force and the Hessian matrix Then, based on the stored historical atomic coordinates and atomic forces, an error matrix (DIIS matrix) is constructed, whose matrix elements... The calculation formula is: , in, and These represent the sub-coordinate vectors of the unfolded plain in the nth and mth historical iterations, respectively; and These represent the atomic force vectors in the nth and mth iterations, respectively; the superscript T indicates the transpose of the vector.

[0042] By minimizing the above DIIS matrix, and satisfying the normalization constraint... Under the given conditions, the weighted interpolation coefficients for each historical step are obtained by solving. Using the curvature information provided by the Hessian matrix and the interpolation coefficients obtained by solving... The atomic coordinates are updated using a second-order extrapolation, and the update formula is as follows: , in, The offset parameter for Rational Function Optimization (RFO) It is the identity matrix. This is the atomic force. Repeat the above steps until the root-mean-square force reaches the preset convergence criterion.

[0043] Optionally, this embodiment uses GEDIIS as the optimization algorithm. In other implementations, those skilled in the art can also use optimizers such as Newton's method, quasi-Newton's method (BFGS), GDIIS, FIRE, etc., and select the most suitable optimization strategy according to the characteristics of different systems.

[0044] Furthermore, S104: Based on the predicted values ​​of atomic force and Hessian matrix, a transition state search algorithm is used. Utilizing the precise curvature information provided by the Hessian matrix, the search iteratively proceeds along the negative curvature direction of the saddle point until a preset convergence condition is met, thus locating the candidate transition state structure, including: For reaction path exploration, the predicted precise curvature and force field information are combined with the EF algorithm. The EF algorithm locates candidate transition state structures by searching along the negative curvature direction of the saddle point using the precise curvature information provided by the Hessian matrix.

[0045] Specifically, firstly, the initial candidate structure is input into the pre-trained DetaNet equivariant neural network, and the model predicts the energy, atomic force, and complete Hessian matrix of the current structure in one go, which are then processed by the GDIIS or GEDIIS transition state optimizer.

[0046] Next, the eigenvector following EF algorithm identifies the negative curvature direction on the potential energy surface by analyzing the second-order curvature information of the Hessian matrix; at the same time, the GEDIIS algorithm calls the coordinates and mechanical data from multiple historical iterations for interpolation extrapolation, guiding the atomic coordinates to perform extremely stable and efficient second-order accelerated updates along this negative curvature direction.

[0047] The aforementioned prediction-oriented optimization process will iterate continuously until the forces acting on the system meet the preset convergence conditions.

[0048] Optionally, this embodiment uses the EF algorithm as the transition state search algorithm. In other implementations, those skilled in the art can also combine Sella, CI-NEB, GSM, Dimer and other methods to perform transition state search. In particular, when the initial guess structure is not accurate enough, CI-NEB and GSM methods can be used as pre-screening methods.

[0049] Further, S105: Perform imaginary frequency analysis on the candidate transition state structure. If it has a unique imaginary frequency, it is confirmed as the target transition state structure, including: The candidate transition state structures obtained in step S104 are verified by imaginary frequency analysis. The number of imaginary frequencies is calculated. By checking whether each imaginary frequency has a unique single imaginary frequency, it is determined whether the predicted transition state structure meets the first-order saddle point criterion, and the reaction energy barrier is predicted.

[0050] Specifically, the complete Hessian matrix corresponding to the candidate transition state structure is predicted using an equivariant neural network model. The Hessian matrix contains local curvature information of the potential energy surface. The Hessian matrix is ​​diagonalized, and all its eigenvalues ​​are calculated. The curvature direction of the potential energy surface is determined based on the obtained eigenvalues. If there is one and only one negative eigenvalue in the eigenvalue set, i.e., it has a unique imaginary frequency, it proves that the candidate structure satisfies the strict mathematical definition of a first-order saddle point, thus confirming it as the target transition state structure. If there is no imaginary frequency or there are two or more imaginary frequencies, it indicates that the candidate structure has fallen back to a local minimum point or belongs to a non-physical higher-order saddle point, and the initial guess needs to be readjusted based on gradient information or the iterative search needs to continue.

[0051] Example 2 Embodiment 2 of the present invention provides a machine learning-based method for structure optimization and transition state search prediction, such as... Figure 2 As shown, Figure 2 This is a flowchart of a method according to Embodiment 2 of the present invention, applicable to periodic crystal systems, and includes the following steps: S201: Obtain the initial structural information of the target system, which includes the types of atoms, atomic coordinates, and lattice vectors; S202: Input the initial structural information into the pre-trained equivariant neural network model to obtain the energy prediction, atomic force prediction, Hessian matrix prediction, and stress tensor prediction of the target system. S203: Based on the predicted values ​​of atomic force, Hessian matrix, and stress tensor, a fully coupled optimizer is used to synchronously iterate and update the atomic coordinates and lattice vectors of the target system until the preset convergence condition is met, thereby obtaining the optimized stable structure. S204: Based on the atomic force prediction value and the Hessian matrix prediction value, the transition state search algorithm is used to search and iterate along the negative curvature direction of the saddle point using the accurate curvature information provided by the Hessian matrix until the preset convergence condition is met, and the candidate transition state structure is located. S205: Perform imaginary frequency analysis on the candidate transition state structure. If it has a unique imaginary frequency, it is confirmed as the target transition state structure.

[0052] The difference between this second embodiment and the first embodiment is that the initial structural information further includes lattice vectors, and the model output further includes predicted stress tensor values; in the geometric optimization step, a fully coupled optimizer is used to synchronously iterate and update the atomic coordinates and lattice vectors.

[0053] like Figure 3 As shown, when the initial structural information input to the isotropic neural network includes lattice vectors... At this time, the DetaNet model, in addition to predicting energy E and atomic force, also predicts... In addition to the Hessian matrix, it also predicts the stress tensor. .

[0054] Specifically, the prediction of the stress tensor is achieved in the following way: First, the cell center is defined based on the lattice vectors, and the relative position of each atom with respect to the cell center is calculated. Then the stress tensor is calculated as follows: , in, Represents direct sums, learnable scalars Representing the isotropic (trace) components of the stress tensor, a second-order irreducible representation. It captures the local contribution of atoms to the unscented components, while additional learnable terms... Combining spherical harmonics This includes nonlocal, unscented contributions. Let be the volume of the unit cell.

[0055] For periodic crystal systems, this embodiment employs a fully coupled GEDIIS-PBC optimization algorithm to synchronously iteratively update atomic coordinates and lattice vectors. This avoids the zig-zag instability caused by individually optimizing atomic positions and lattice parameters. The algorithm stores not only atomic coordinates and forces but also the stress tensor from previous steps. .

[0056] Specifically, based on the previous The updated atomic coordinates and lattice variables for: , , In the formula and These represent the flattened atomic coordinates and lattice parameters, respectively. For atomic forces, For lattice gradient, Cell matrix, scalar Controlling the step size of lattice updates, Offset parameters for rational function optimization (RFO) for, The identity matrix. Interpolation coefficients. The DIIS matrix is ​​obtained by solving the generalized DIIS problem and constructed as follows:

[0057] in:

[0058]

[0059] parameter The relative weights of the controlled lattice optimization are such that these coefficients satisfy the normalization constraint condition, i.e.

[0060] Through the above-described fully coupled optimization, this embodiment achieves synchronous relaxation of atomic positions and lattice features, effectively avoiding the "zigzag" oscillation behavior commonly found in traditional alternating optimization methods.

[0061] Steps S204 and S205 are the same as steps S104 and S105 in Example 1. Under the condition of fixed lattice vector, transition state search and imaginary frequency verification are performed based on atomic force prediction value and Hessian matrix prediction value, which will not be described in detail here.

[0062] Example 3 This embodiment provides a machine learning-based structure optimization and transition state search prediction system, including: The input module is configured to: acquire the initial structural information of the target system, wherein the initial structural information includes the types of atoms, atomic coordinates, and lattice vectors; The physical property prediction module is configured to input the initial structural information into a pre-trained equivariant neural network model to obtain the energy prediction value, atomic force prediction value, Hessian matrix prediction value, and stress tensor prediction value of the target system. The optimization module is configured to: based on the predicted atomic force, Hessian matrix, and stress tensor values, use a fully coupled optimizer to synchronously iteratively update the atomic coordinates and lattice vectors of the target system until the preset convergence conditions are met, thereby obtaining the optimized stable structure. The transition state search module is configured to: based on the atomic force prediction value and the Hessian matrix prediction value, use the transition state search algorithm to search along the negative curvature direction of the saddle point using the accurate curvature information provided by the Hessian matrix, and locate the candidate transition state structure. The transition state verification module is configured to perform imaginary frequency analysis on candidate transition state structures, and if a structure has a unique imaginary frequency, it is confirmed as the target transition state structure.

[0063] It should be noted that the input module, property prediction module, optimization module, transition state search module, and transition state verification module mentioned above correspond to steps S101 to S105 in Embodiment 1. The examples and application scenarios implemented by these modules and their corresponding steps are the same, but they are not limited to the content disclosed in Embodiment 1. It should be noted that these modules, as part of the system, can be executed in a computer system such as a set of computer-executable instructions.

[0064] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0065] The proposed system can be implemented in other ways. For example, the system embodiments described above are merely illustrative, and the division of modules described above is only a logical functional division. In actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed.

[0066] Example 4 This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the method described in Embodiment 1.

[0067] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A machine learning-based structural optimization and transition state search prediction method, characterized in that, include: Obtain the initial structural information of the target system, wherein the initial structural information includes atom types and atom coordinates; The initial structural information is input into a pre-trained equivariant neural network model to obtain the energy prediction value, atomic force prediction value, and Hessian matrix prediction value of the target system. Based on the predicted atomic force and the predicted Hessian matrix, the atomic coordinates of the target system are iteratively updated using a geometric optimization algorithm until the preset convergence condition is met, thereby obtaining the optimized stable structure. Based on the atomic force prediction value and the Hessian matrix prediction value, the transition state search algorithm is used to search and iterate along the negative curvature direction of the saddle point using the accurate curvature information provided by the Hessian matrix until the preset convergence condition is met, and the candidate transition state structure is located. The candidate transition state structure is analyzed for imaginary frequency. If it has a unique imaginary frequency, it is confirmed as the target transition state structure.

2. The method according to claim 1, characterized in that, The geometric optimization algorithm is any one of Newton's method, quasi-Newton's method, GDIIS, or GEDIIS.

3. A machine learning-based structure optimization and transition state search prediction method, characterized in that, include: Obtain the initial structural information of the target system, wherein the initial structural information includes atom types and atomic coordinates as well as lattice vectors; The initial structural information is input into a pre-trained equivariant neural network model to obtain the energy prediction, atomic force prediction, Hessian matrix prediction, and stress tensor prediction of the target system. Based on the predicted atomic force, the predicted Hessian matrix, and the predicted stress tensor, the atomic coordinates and lattice vectors of the target system are synchronously iteratively updated using a fully coupled optimizer until the preset convergence condition is met, thereby obtaining the optimized stable structure. Based on the atomic force prediction value and the Hessian matrix prediction value, the transition state search algorithm is used to search and iterate along the negative curvature direction of the saddle point using the accurate curvature information provided by the Hessian matrix until the preset convergence condition is met, and the candidate transition state structure is located. The candidate transition state structure is analyzed for imaginary frequency. If it has a unique imaginary frequency, it is confirmed as the target transition state structure.

4. The method according to claim 3, characterized in that, The geometry optimization algorithm is a fully coupled GEDIIS-PBC optimization algorithm, including: Stores atomic coordinates, atomic forces, and stress tensors from historical iteration steps; Atomic component DIIS matrices are constructed based on atomic coordinates and atomic forces of the current step and historical steps; The lattice component DIIS matrix is ​​constructed based on the lattice vectors and stress tensors of the current and historical steps; A joint DIIS matrix is ​​constructed by weighting the atomic component DIIS matrix and the lattice component DIIS matrix; Solve the minimization problem of the joint DIIS matrix to obtain the interpolation coefficients; Based on the interpolation coefficients, the historical atomic coordinates and lattice vectors are weighted and combined to synchronously update the atomic coordinates and lattice vectors of the current step.

5. The method according to claim 1 or 3, characterized in that, The specific method for obtaining the predicted value of the Hessian matrix is ​​as follows: the equivariant neural network model decomposes the Hessian matrix into diagonal block components within atoms and off-diagonal block components between atoms for independent prediction, and then combines the components to output the complete Hessian matrix.

6. The method according to claim 1 or 3, characterized in that, The equivariant neural network model is any one of DetaNet, NequIP, MACE, or PaiNN.

7. The method according to claim 1 or 3, characterized in that, The transition state search algorithm is any one of the following algorithms: EF algorithm, Sella algorithm, CI-NEB algorithm, GSM algorithm, or Dimer algorithm.

8. The method according to claim 1, characterized in that, The training database for the pre-trained isotropic neural network model includes: molecular system dataset, crystal system dataset, and reaction system dataset; the reaction system dataset contains Hessian matrix labels for reactants, products, and transition state structures, and the transition state region is enhanced by interpolation.

9. A machine learning-based structural optimization and transition state search prediction system, characterized in that, include: The input module is configured to: acquire the initial structural information of the target system, wherein the initial structural information includes atom types and atom coordinates as well as lattice vectors; The physical property prediction module is configured to input the initial structural information into a pre-trained equivariant neural network model to obtain the energy prediction value, atomic force prediction value, Hessian matrix prediction value, and stress tensor prediction value of the target system. The optimization module is configured to: based on the predicted atomic force value, the predicted Hessian matrix value, and the predicted stress tensor value, use a fully coupled optimizer to synchronously iteratively update the atomic coordinates and lattice vectors of the target system until the preset convergence condition is met, thereby obtaining the optimized stable structure. The transition state search module is configured to: based on the atomic force prediction value and the Hessian matrix prediction value, use the transition state search algorithm, utilize the precise curvature information provided by the Hessian matrix, perform search iterations along the negative curvature direction of the saddle point until the preset convergence condition is met, and locate the candidate transition state structure. The transition state verification module is configured to perform imaginary frequency analysis on the candidate transition state structure, and if it has a unique imaginary frequency, it is confirmed as the target transition state structure.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the machine learning-based structural optimization and transitional search prediction method as described in any one of claims 1 to 8.

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