A hybrid evolutionary approach for global optimization of surface catalytic structures accelerated by machine learning

Abstract

A hybrid evolutionary method for global optimization of surface catalytic structures accelerated by machine learning, which introduces a hybrid evolutionary algorithm that collaborates with a genetic algorithm and a differential algorithm. When generating structures, some structures are generated using a genetic algorithm (crossover operation) and some structures are generated using a differential algorithm (differential operation). Compared with the single use of a genetic algorithm or an evolutionary algorithm, the hybrid evolutionary algorithm proposed in the present invention is more effective when processing surface catalytic structures with a large number of atoms. The present invention introduces and uses a Gaussian process regression model in the field of machine learning, and by establishing a corresponding relationship between the atomic coordinates of a structure and its energy, a (Gaussian) posterior distribution is constructed to achieve targeted sampling on the potential energy surface and enhance the efficiency of the optimization process.

Description

Technical Field

[0001] The present invention relates to a method for optimizing a supported surface catalytic structure, and more particularly to a hybrid evolutionary method for global optimization of a surface catalytic structure accelerated by machine learning. Background Art

[0002] The potential energy surface represents the functional relationship between the energy of a chemical system and related parameters (usually atomic coordinates). Matter usually exists in its lowest energy structure, which is the global minimum point on the potential energy surface. Understanding the lowest energy structure (and its atomic coordinates) of the surface catalytic system is crucial for predicting catalyst structure, analyzing adsorption characteristics, studying the mechanism of heterogeneous catalytic reactions, explaining experimental phenomena, and provides a basis for the rational design of catalysts.

[0003] The potential energy surface is highly complex, and the number of minimum points on the potential energy surface increases exponentially with the increase in the number of atoms. Under existing computational conditions, it is almost impossible to search for the global minimum point by traversing all points on the potential energy surface. Therefore, it is necessary to develop a global optimization method to efficiently search for the lowest energy structure of the surface catalytic system within a reasonable computing time.

[0004] Commonly used global optimization methods for chemical systems include basin jumping method and artificial bee colony algorithm. However, these methods are currently mostly used for global optimization of homogeneous systems, such as cluster systems in a vacuum. For surface catalytic systems, the influence of the carrier is often not negligible. The carrier can affect the dispersion of the catalyst on its surface, the particle size, etc., resulting in a significant difference in the structure of the catalyst from the gas phase. Therefore, it is urgent to develop global optimization methods that can be applied to surface catalytic systems, study the lowest energy structure under such systems, and provide a theoretical perspective for analyzing the dynamic process of catalysis. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a hybrid evolution method for global optimization of surface catalytic structures accelerated by machine learning, which can overcome the shortcomings of existing methods in that the prediction ability of complex systems with high-dimensional potential energy surfaces is not strong, and efficiently optimize complex surface catalytic systems and obtain the lowest energy structure of the system.

[0006] The technical solution adopted by the present invention is: a hybrid evolutionary method for global optimization of surface catalytic structures accelerated by machine learning, wherein the atomic coordinates of n surface catalytic structures are respectively q i , i = 1, 2, ... n, the energy function of each surface catalytic structure on the potential energy surface is E i =f(q i ), i = 1, 2, ... n, the energy function solution method includes the first principle density functional method and the neural network potential function method, which specifically includes the following steps:

[0007] Step 1, parameter setting: set the element ratio, the number of new structures generated by crossover operation and difference operation in each generation, the number of sampled structures, and the total number of surface catalytic structures in the structure pool;

[0008] Step 2, initialization: according to the preset element ratio, a number of surface catalytic structures are randomly generated as the initial structure pool, and the number of generated structures is also preset; according to the selected solution method, the energy function of each structure is solved to obtain the energy, and the energy values ​​corresponding to all the structures obtained are used to form the training set of the Gaussian process regression model;

[0009] Step 3: training a Gaussian process regression model to establish the corresponding relationship between the atomic coordinates of the surface catalytic structure and the energy of the surface catalytic structure;

[0010] Step 4: Repeat the crossover operation to generate the first set of new surface catalytic structures q ga ;

[0011] Step 5: Repeat the difference operation to generate a second set of new surface catalytic structures q de ;

[0012] Step 6: mutation operation: merging the first group of new surface catalytic structures and the second group of new surface catalytic structures, randomly selecting some atoms in the merged surface catalytic structures, and moving the coordinates of these atoms to generate new surface catalytic structures;

[0013] Step 7: Use the trained Gaussian process regression model in step 3 to predict the new surface catalytic structure generated in step 6 to obtain a posterior distribution, the average value of the posterior distribution is used as the energy prediction value μ(q) of the newly generated surface catalytic structure, and the variance of the posterior distribution is used as the estimated value σ(q) of the accuracy of the energy prediction value μ(q);

[0014] Step 8: By defining a sampling function f(q), a set number of surface catalytic structures with the lowest sampling function values ​​among all newly generated surface catalytic structures are selected to solve the energy function, and the structures are added to the Gaussian process regression model training set and the structure pool;

[0015] Step 9: re-arrange all the surface catalytic structures in the structure pool according to their energy levels, and select a set number of surface catalytic structures with the lowest energy to ensure that the total number of the structure pool remains unchanged;

[0016] Step 10: Repeat steps 3 to 9, with each repetition constituting one generation, until the convergence criterion is reached.

[0017] Step 4 includes:

[0018] Randomly select two surface catalytic structures from the structure pool, take half of the two structures respectively, cross and merge them to generate a new structure, and ensure that the number of atoms and stoichiometric ratio before and after generation are consistent, and all atomic distances in the surface catalytic structure are more than 0.8 times the covalent bond length between the two atoms. The probability of each surface catalytic structure being selected for the crossover operation is related to the energy of the surface catalytic structure. The surface catalytic structure with lower energy has a higher probability of being selected; each surface catalytic structure q in the structure pool i The probability of being selected is P(q i ) Follow the roulette wheel selection method:

[0019]

[0020] E i is the energy function of each surface catalytic structure on the potential energy surface, and n is the total number of surface catalytic structures in the structure pool;

[0021] This step is repeated until a set number of first sets of new surface catalytic structures are generated.

[0022] Step five includes:

[0023] The new surface catalytic structure q is generated using the following three difference operations: de :

[0024] q de =q r3 +F*(q r1 -q r2 )

[0025] q de =q best +F*(q r1 -q r2 )

[0026] q de =q r3 +F*(q best -q r3 )+F*(q r1 -q r2 )

[0027] where q r1 ,q r2 and q r3 is a surface catalytic structure randomly selected from the structure pool, q best is the surface catalytic structure with the lowest energy in the structure pool, and F is the scaling factor;

[0028] Repeat step 5 until a set number of second sets of new surface catalytic structures are generated.

[0029] The sampling function f(q) described in step 8 uses a Gaussian confidence lower bound, and the specific expression is as follows:

[0030] f(q)=μ(q)-k*σ(q)

[0031] Among them, k is a control parameter used to adjust the emphasis on uncertainty in the sampling function;

[0032] The convergence criterion in step 10 is one of the following three criteria:

[0033] (1) Set the number of generations to be optimized and stop the optimization after the specified number of iterations is reached;

[0034] (2) setting the expected energy value of the optimal structure, and stopping the optimization when the energy of the surface catalytic structure reaches the expected energy value;

[0035] (3) When the energy of the optimal structure does not change after multiple iterations, stop the optimization.

[0036] The hybrid evolutionary method for global optimization of surface catalytic structure accelerated by machine learning of the present invention is a genetic algorithm and a differential algorithm working together, and can process surface catalytic systems with a large number of atoms. The method of the present invention provides a simple and universal potential energy surface function search method, which can find the structure with the lowest energy on the potential energy surface and its atomic coordinates, efficiently optimize complex surface catalytic systems, and obtain the lowest energy structure of the system, which has the following beneficial effects:

[0037] 1. The present invention introduces a hybrid evolutionary algorithm that combines genetic algorithm and differential algorithm. When generating structures, some structures are generated by genetic algorithm (crossover operation) and some structures are generated by differential algorithm (differential operation). Compared with the single use of genetic algorithm or evolutionary algorithm, the hybrid evolutionary algorithm proposed in the present invention is more effective when processing surface catalytic structures with a large number of atoms.

[0038] 2. The present invention introduces the Gaussian process regression model in the field of machine learning. By establishing the correspondence between the atomic coordinates of the structure and its energy, a (Gaussian) posterior distribution is constructed to achieve targeted sampling on the potential energy surface and enhance the efficiency of the optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of a hybrid evolutionary method for global optimization of surface catalytic structures accelerated by machine learning of the present invention;

[0040] Figure 2 It is a front view of the lowest energy structure of the platinum (111) surface after being covered with a layer of oxygen in the example of the present invention;

[0041] Figure 3It is a side view of the lowest energy structure of the platinum (111) surface after being covered with a layer of oxygen in an example of the present invention. DETAILED DESCRIPTION

[0042] The hybrid evolution method for global optimization of surface catalytic structures accelerated by machine learning of the present invention is described in detail below in conjunction with the embodiments and drawings.

[0043] The hybrid evolutionary method for global optimization of surface catalytic structures accelerated by machine learning of the present invention is known that the atomic coordinates of n surface catalytic structures are q i , i = 1, 2, ... n, the energy function of each surface catalytic structure on the potential energy surface is E i =f(q i ),i=1,2,…n, as Figure 1 As shown, the following steps are included:

[0044] Step 1: Parameter setting: set the element ratio, the number of new structures generated by crossover operation and difference operation in each generation, the number of sampled structures, and the total number of surface catalytic structures in the structure pool.

[0045] Step 2: Initialization: According to the preset element ratio, a number of surface catalytic structures are randomly generated as the initial structure pool, and the number of generated structures is also preset; according to the selected solution method, the energy function of each structure is solved to obtain the energy, and the energy values ​​corresponding to all the structures obtained constitute the training set of the Gaussian process regression model.

[0046] Step 3: Train the Gaussian process regression model to establish the corresponding relationship between the atomic coordinates of the surface catalytic structure and the energy of the surface catalytic structure.

[0047] Step 4: Repeat the crossover operation to generate the first set of new surface catalytic structures q ga ;include:

[0048] Randomly select two surface catalytic structures from the structure pool, take half of the two structures respectively, cross and merge them to generate a new structure, and ensure that the number of atoms and stoichiometric ratio before and after generation are consistent, and all atomic distances in the surface catalytic structure are more than 0.8 times the covalent bond length between the two atoms. The probability of each surface catalytic structure being selected for the crossover operation is related to the energy of the surface catalytic structure. The surface catalytic structure with lower energy has a higher probability of being selected; each surface catalytic structure q in the structure pool i The probability of being selected is P(q i ) Follow the roulette wheel selection method:

[0049]

[0050] E iis the energy function of each surface catalytic structure on the potential energy surface, and n is the total number of surface catalytic structures in the structure pool;

[0051] This step is repeated until a set number of first sets of new surface catalytic structures are generated.

[0052] Step 5: Repeat the differential operation to generate a second set of new surface catalytic structures; including:

[0053] The new surface catalytic structure q is generated using the following three difference operations: de :

[0054] q de =q r3 +F*(q r1 -q r2 )

[0055] q de =q best +F*(q r1 -q r2 )

[0056] q de =q r3 +F*(q best -q r3 )+F*(q r1 -q r2 )

[0057] where q r1 ,q r2 and q r3 is a surface catalytic structure randomly selected from the structure pool, q best is the surface catalytic structure with the lowest energy in the structure pool, and F is the scaling factor;

[0058] Repeat step 5 until a set number of second sets of new surface catalytic structures are generated.

[0059] Step 6: mutation operation: merging the first group of new surface catalytic structures and the second group of new surface catalytic structures, randomly selecting some atoms in the merged surface catalytic structures, and moving the coordinates of these atoms to generate new surface catalytic structures;

[0060] Step 7: Use the trained Gaussian process regression model in step 3 to predict the new surface catalytic structure generated in step 6 to obtain a posterior distribution, the average value of the posterior distribution is used as the energy prediction value μ(q) of the newly generated surface catalytic structure, and the variance of the posterior distribution is used as the estimated value σ(q) of the accuracy of the energy prediction value μ(q);

[0061] Step 8: By defining a sampling function f(q), a set number of surface catalytic structures with the lowest sampling function values ​​among all newly generated surface catalytic structures are selected to solve the energy function, and the structures are added to the Gaussian process regression model training set and the structure pool;

[0062] The sampling function f(q) uses a Gaussian confidence lower bound, and the specific expression is as follows:

[0063] f(q)=μ(q)-k*σ(q)

[0064] Among them, k is a control parameter used to adjust the emphasis on uncertainty in the sampling function;

[0065] Step 9: Rearrange all surface catalytic structures in the structure pool according to their energy levels, and select a set number of surface catalytic structures with the lowest energy to ensure that the total number of the structure pool remains unchanged.

[0066] Step 10: Repeat steps 3 to 9, each repetition forming a generation, until a convergence criterion is reached; the convergence criterion is one of the following three criteria:

[0067] (1) Set the number of generations to be optimized and stop the optimization after the specified number of iterations is reached;

[0068] (2) setting the expected energy value of the optimal structure, and stopping the optimization when the energy of the surface catalytic structure reaches the expected energy value;

[0069] (3) When the energy of the optimal structure no longer changes after multiple iterations, stop the optimization.

[0070] Embodiment 1:

[0071] The lowest energy structure is obtained after a layer of oxygen atoms is covered on the surface of platinum (111). The method of the present invention is used to optimize 100 generations, and the energy function is solved 4500 times in total. The front view and side view of the lowest energy structure are shown as follows: Figure 2 , Figure 3 shown.

Claims

1. A hybrid evolutionary method for global optimization of surface catalytic structures accelerated by machine learning, characterized in that: The atomic coordinates of n surface catalytic structures are known to be q i , i = 1, 2, ... n, the energy function of each surface catalytic structure on the potential energy surface is E i =f(q i ), i = 1, 2, ... n, the energy function solution method includes the first principle density functional method and the neural network potential function method, which specifically includes the following steps: Step 1, parameter setting: set the element ratio, the number of new structures generated by crossover operation and difference operation in each generation, the number of sampled structures, and the total number of surface catalytic structures in the structure pool; Step 2, initialization: according to the preset element ratio, a number of surface catalytic structures are randomly generated as the initial structure pool, and the number of generated structures is also preset; according to the selected solution method, the energy function of each structure is solved to obtain the energy, and the energy values ​​corresponding to all the structures obtained are used to form the training set of the Gaussian process regression model; Step 3: training a Gaussian process regression model to establish the corresponding relationship between the atomic coordinates of the surface catalytic structure and the energy of the surface catalytic structure; Step 4: Repeat the crossover operation to generate the first set of new surface catalytic structures q ga ; include: Randomly select two surface catalytic structures from the structure pool, take half of the two structures respectively, cross and merge them to generate a new structure, and ensure that the number of atoms and stoichiometric ratio before and after generation are consistent, and all atomic distances in the surface catalytic structure are more than 0.8 times the covalent bond length between the two atoms. The probability of each surface catalytic structure being selected for the crossover operation is related to the energy of the surface catalytic structure. The surface catalytic structure with lower energy has a higher probability of being selected; each surface catalytic structure q in the structure pool i The probability of being selected is P(q i ) Follow the roulette wheel selection method: E i is the energy function of each surface catalytic structure on the potential energy surface, and n is the total number of surface catalytic structures in the structure pool; Repeating this step until a set number of first sets of new surface catalytic structures are generated; Step 5: Repeat the difference operation to generate a second set of new surface catalytic structures q de ;include: The new surface catalytic structure q is generated using the following three difference operations: de : q de =q r3 +F*(q r1 -q r2 ) q de =q best +F*(q r1 -q r2 ) q de =q r3 +F*(q best -q r3 )+F*(q r1 -q r2 ) where q r1 ,q r2 and q r3 is a surface catalytic structure randomly selected from the structure pool, q best is the surface catalytic structure with the lowest energy in the structure pool, and F is the scaling factor; Repeat step 5 until a set number of second sets of new surface catalytic structures are generated; Step 6: mutation operation: merging the first group of new surface catalytic structures and the second group of new surface catalytic structures, randomly selecting some atoms in the merged surface catalytic structures, and moving the coordinates of these atoms to generate new surface catalytic structures; Step 7: Use the trained Gaussian process regression model in step 3 to predict the new surface catalytic structure generated in step 6 to obtain a posterior distribution, the average value of the posterior distribution is used as the energy prediction value μ(q) of the newly generated surface catalytic structure, and the variance of the posterior distribution is used as the estimated value σ(q) of the accuracy of the energy prediction value μ(q); Step 8: By defining a sampling function f(q), a set number of surface catalytic structures with the lowest sampling function values ​​among all newly generated surface catalytic structures are selected to solve the energy function, and the structures are added to the Gaussian process regression model training set and the structure pool; Step 9: re-arrange all the surface catalytic structures in the structure pool according to their energy levels, and select a set number of surface catalytic structures with the lowest energy to ensure that the total number of the structure pool remains unchanged; Step 10: Repeat steps 3 to 9, with each repetition constituting one generation, until the convergence criterion is reached.

2. The hybrid evolutionary method for global optimization of surface catalytic structures accelerated by machine learning according to claim 1, characterized in that: The sampling function f(q) described in step 8 uses a Gaussian confidence lower bound, and the specific expression is as follows: f(q)=μ(q)-k*σ(q) Among them, k is a control parameter used to adjust the emphasis on uncertainty in the sampling function.

3. The hybrid evolutionary method for global optimization of surface catalytic structures accelerated by machine learning according to claim 1, characterized in that: The convergence criterion in step 10 is one of the following three criteria: (1) Set the number of generations to be optimized and stop the optimization after the specified number of iterations is reached; (2) setting the expected energy value of the optimal structure, and stopping the optimization when the energy of the surface catalytic structure reaches the expected energy value; (3) When the energy of the optimal structure does not change after multiple iterations, stop the optimization.

Images