Method and system for optimizing metal cluster structure based on dnn-tl-ga

Abstract

The application relates to the field of machine learning, and discloses a metal cluster structure optimization method and system based on DNN-TL-GA. The method comprises the following steps: according to an initial structure of a metal cluster, a first sample set is generated by using GA and a first DFT local optimization method; a pre-trained DNN is trained by using the first sample set to obtain a first DNN model; according to the offspring structure of the first S generations of DFT local optimization, the offspring structure of the S+1th generation to the Tth generation of DNN local optimization is obtained by using GA and the first DNN model; and Q low-energy structures are selected from the offspring structure of the first S generations of DFT local optimization and the offspring structure of the S+1th generation to the Tth generation of DNN local optimization to obtain a global optimal structure of the metal cluster. The application can obtain more representative low-energy samples on a potential energy surface and has better global search ability on the potential energy surface, improves the cluster structure optimization efficiency, and searches for a new Pt 16 and Pt 17 cluster global optimal structure, which indicates that the application has good global optimization capability.

Description

Technical Field

[0001] This invention relates to the field of machine learning, and specifically to an optimization method and system for metal cluster structures based on DNN-TL-GA (Deep Nueral Network-Transfer Learning-Genetic Algorithm). Background Technology

[0002] Metal clusters are widely studied due to their unique structures and physicochemical properties. The structure of metal clusters determines their properties; therefore, studying the globally optimal structure of metal clusters (i.e., the geometric configuration with the lowest energy on the potential energy surface) is fundamental to understanding other properties of metal clusters. An effective way to predict the structure of metal clusters is to use global optimization techniques, which typically consist of two parts: global search and local optimization. Generally, the differences in global optimization techniques mainly depend on the global search method, usually employing a search algorithm for global search. Density Functional Theory (DFT) is a commonly used method for local optimization of metal cluster structures. The most time-consuming step in the global optimization process is the local optimization based on the DFT method, as this involves time-consuming electronic structure calculations. Summary of the Invention

[0003] The purpose of this invention is to provide an optimization method and system for metal cluster structures based on DNN-TL-GA. Based on the global optimization method of metal cluster structures by combining DNN with transfer learning, this invention uses a genetic algorithm to sample and search the potential energy surface of the metal cluster structure. This can obtain more representative low-energy samples on the potential energy surface and have better global search capability on the potential energy surface, which further improves the optimization efficiency of metal cluster structures.

[0004] To achieve the above objectives, a first aspect of the present invention provides an optimization method for metal cluster structures based on DNN-TL-GA. The optimization method includes: generating a first sample set based on the initial structure of the metal cluster using a genetic algorithm and a first DFT local optimization method, wherein the first sample set includes the descendant structures and corresponding energies of the first S generations of DFT local optimization; training a pre-trained DNN using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-sized metal cluster using a transfer learning method; obtaining the descendant structures of the (S+1)th to (T)th generations of DNN local optimization based on the descendant structures of the first S generations of DFT local optimization using the genetic algorithm and the first DNN model; and selecting Q structures from the descendant structures of the first S generations of DFT local optimization and the descendant structures of the (S+1)th to (T)th generations of DNN local optimization, wherein the energy of the Q structures is lower than that of the other structures.

[0005] Preferably, generating the first sample set includes: generating an initial first S generation descendant structure using the genetic algorithm based on the initial structure of the metal cluster; and processing the initial first S generation descendant structure using the first DFT local optimization method.

[0006] Preferably, obtaining the descendant structure from generation S+1 to generation T of the DNN locally optimized structure includes: generating an initial descendant structure from generation S+1 to generation T using the genetic algorithm based on the descendant structure from the first S generations of the DFT locally optimized structure; and performing local optimization on the initial descendant structure from generation S+1 to generation T using the first DNN model.

[0007] Preferably, after performing the step of obtaining the descendant structure of the (S+1)th to (T)th generations of DNN local optimization, the optimization method further includes: generating a second sample set based on the descendant structure of the first S generations of DFT local optimization and the descendant structure of the (S+1)th to (T)th generations of DNN local optimization, using the genetic algorithm, the first DNN model, and the second DFT local optimization method, wherein the second sample set includes the descendant structure of the (T+1)th to (U)th generations of DFT local optimization and the corresponding energy; processing the first DNN model using the transfer learning method to obtain a second DNN model to be trained, and using the first sample set and the second sample set to train the second DNN model. Training is performed to obtain a second DNN model; based on the descendant structure of the first S generations of the locally optimized DFT, the descendant structure of the S+1 to T generations of the locally optimized DNN, and the descendant structure of the T+1 to U generations of the locally optimized DFT, the genetic algorithm and the second DNN model are used to obtain the descendant structure of the U+1 to V generations of the locally optimized DNN. The selection of Q structures includes: selecting the Q structures from the descendant structure of the first S generations of the locally optimized DFT, the descendant structure of the S+1 to T generations of the locally optimized DNN, the descendant structure of the T+1 to U generations of the locally optimized DFT, and the descendant structure of the U+1 to V generations of the locally optimized DNN.

[0008] Preferably, generating the second sample set includes: generating the initial descendant structure from generation T+1 to generation U using the genetic algorithm based on the descendant structure from the first S generations optimized by the DFT and the descendant structure from generation S+1 to generation T optimized by the DNN; pre-optimizing the initial descendant structure from generation T+1 to generation U using the first DNN model; and processing the pre-optimized descendant structure using the second DFT local optimization method.

[0009] Preferably, obtaining the descendant structure of the U+1th to Vth generations of DNN local optimization includes: generating the descendant structure of the U+1th to Vth generations using the genetic algorithm based on the descendant structure of the first S generations of DFT local optimization, the descendant structure of the S+1th to Tth generations of DNN local optimization, and the descendant structure of the T+1th to Uth generations of DFT local optimization; and performing local optimization on the descendant structure of the U+1th to Vth generations using the second DNN model.

[0010] Preferably, after performing the step of obtaining the descendant structure of the U+1th to Vth generations of the DNN local optimization, the optimization method further includes: generating a third sample set by using the genetic algorithm, the second DNN model, and the third DFT local optimization method based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the S+1th to Tth generations of the DNN local optimization, the descendant structure of the T+1th to Uth generations of the DFT local optimization, and the descendant structure of the U+1th to Vth generations of the DNN local optimization, wherein the third sample set includes the descendant structure of the V+1th to Wth generations of the DFT local optimization and the corresponding energy; processing the second DNN model using the transfer learning method to obtain the third DNN model to be trained, and training the third DNN model to be trained using the first sample set, the second sample set, and the third sample set to obtain the third DNN model; according to the... The descendant structures of the first S generations of DFT local optimization, the descendant structures of the (S+1)th to Tth generations of DNN local optimization, the descendant structures of the (T+1)th to Uth generations of DFT local optimization, the descendant structures of the (U+1)th to Vth generations of DNN local optimization, and the descendant structures of the (V+1)th to Wth generations of DFT local optimization are used. The genetic algorithm and the third DNN model are then employed to obtain the descendant structures of the (W+1)th to Xth generations of DNN local optimization. The selection of Q structures includes: selecting the Q structures from the descendant structures of the first S generations of DFT local optimization, the descendant structures of the (S+1)th to Tth generations of DNN local optimization, the descendant structures of the (T+1)th to Uth generations of DFT local optimization, the descendant structures of the (U+1)th to Vth generations of DNN local optimization, the descendant structures of the (V+1)th to Wth generations of DFT local optimization, and the descendant structures of the (W+1)th to Xth generations of DNN local optimization.

[0011] Preferably, after performing the step of selecting the Q structures, the optimization method further includes: processing the Q structures using a fourth DFT local optimization method to obtain the globally optimal structure of the metal cluster, wherein the accuracy of the fourth DFT local optimization method is higher than the accuracy of the following: the first DFT local optimization method, the second DFT local optimization method, or the third DFT local optimization method.

[0012] Through the above technical solution, this invention creatively generates a first sample set based on the initial structure of the metal cluster using a genetic algorithm and a first DFT local optimization method. Then, the first sample set is used to train a pre-trained DNN to obtain a first DNN model. Next, based on the descendant structure of the first S generations of the DFT local optimization, the genetic algorithm and the first DNN model are used to obtain the descendant structure of the (S+1)th to Tth generations of the DNN local optimization. Finally, Q low-energy structures are selected from the descendant structure of the first S generations of the DFT local optimization and the descendant structure of the (S+1)th to Tth generations of the DNN local optimization. Therefore, this invention, based on the method of globally optimizing metal cluster structures using DNN combined with transfer learning, uses a genetic algorithm to sample and globally search the potential energy surface of the metal cluster structure, which can obtain more representative low-energy samples on the potential energy surface and has better global search capabilities on the potential energy surface, further improving the optimization efficiency of the metal cluster structure.

[0013] A second aspect of the present invention provides an optimization system for metal cluster structures. The optimization system includes: a generation device for generating a first sample set based on an initial structure of the metal cluster using a genetic algorithm and a first DFT local optimization method, wherein the first sample set includes the descendant structures and corresponding energies of the first S generations of DFT local optimization; a model acquisition device for training a pre-trained DNN using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-sized metal cluster using a transfer learning method; a structure acquisition device for acquiring the descendant structures of the first S generations of DFT local optimization using the genetic algorithm and the first DNN model, from the (S+1)th generation to the Tth generation of DNN local optimization; and a structure selection device for selecting Q structures from the descendant structures of the first S generations of DFT local optimization and the descendant structures of the (S+1)th generation to the Tth generation of DNN local optimization, wherein the energy of the Q structures is lower than that of the other structures.

[0014] For specific details and benefits of the optimization system for metal cluster structures provided in the embodiments of the present invention, please refer to the above description of the optimization method applicable to metal cluster structures based on DNN-TL-GA, which will not be repeated here.

[0015] A third aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned optimization method for metal cluster structures based on DNN-TL-GA.

[0016] A fourth aspect of the present invention provides a computer program product comprising a computer program that, when executed by a processor, implements the aforementioned optimization method for metal cluster structures based on DNN-TL-GA.

[0017] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0018] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0019] Figure 1 This is a flowchart of an optimization method for metal cluster structures based on DNN-TL-GA provided in an embodiment of the present invention;

[0020] Figure 2 This is a flowchart of an optimization method for metal cluster structures based on DNN-TL-GA provided in an embodiment of the present invention;

[0021] Figure 3 This is a flowchart of an optimization method for metal cluster structures based on DNN-TL-GA provided in an embodiment of the present invention;

[0022] Figure 4 This is a schematic diagram illustrating the principle of the optimization process of metal cluster structure based on DNN-TL-GA provided in an embodiment of the present invention;

[0023] Figure 5 This is an embodiment of the present invention that provides an optimization method for metal cluster structures based on DNN-TL-GA, resulting in Pt optimized from these structures. 9-17 Global optimal structure diagram of metal clusters; and

[0024] Figure 6 This is an embodiment of the present invention that provides an optimization method for metal cluster structures based on DNN-TL-GA for Rh2V7. - Global optimal structure diagram of metal clusters. Detailed Implementation

[0025] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0026] Figure 1 This is a flowchart of an optimization method for metal cluster structures based on DNN-TL-GA provided in an embodiment of the present invention. Figure 1As shown, the optimization method may include: step S101, generating a first sample set based on the initial structure of the metal cluster using a genetic algorithm and a first DFT local optimization method, wherein the first sample set includes the descendant structures and corresponding energies of the first S generations of DFT local optimization; step S102, training a pre-trained DNN using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-sized metal cluster using a transfer learning method; step S103, obtaining the descendant structures of the (S+1)th to (T)th generations of DNN local optimization based on the descendant structures of the first S generations of DFT local optimization using the genetic algorithm and the first DNN model; and step S104, selecting Q structures from the descendant structures of the first S generations of DFT local optimization and the descendant structures of the (S+1)th to (T)th generations of DNN local optimization, wherein the energy of the Q structures is lower than the energy of the other structures.

[0027] The following sections will explain and illustrate each of the above steps (steps S101-S104).

[0028] Before executing step S101, the elemental composition, size, charge, and multiplicity of the metal clusters to be optimized can be set in advance; then, N initial structures of metal clusters are generated, where the value of N can be in the range of 10 to 100.

[0029] The elemental composition of the metal cluster can be any metal element; the types of elements can be one, two, or three; the charge carried by the metal cluster is not limited, and it can be a neutral metal cluster, anionic metal cluster, or cationic metal cluster.

[0030] Specifically, the initial structure of metal clusters can be randomly generated using the Bond Length Distribution Algorithm (BLDA), but other methods commonly used in algorithms such as Basin Jump and Simulated Annealing can also be employed for random generation of the initial structure.

[0031] Step S101: Based on the initial structure of the metal clusters, a first sample set is generated using a genetic algorithm and a first DFT local optimization method.

[0032] The first sample set includes the descendant structure and corresponding energy of the first S generations of DFT local optimization.

[0033] For step S101, generating the first sample set includes: generating an initial descendant structure of the first S generations using the genetic algorithm based on the initial structure of the metal cluster; and processing the initial descendant structure of the first S generations using the first DFT local optimization method.

[0034] Before generating each new structure in each generation using the genetic algorithm, the structures of all previous generations are sorted by energy. Then, structures with low energy are selected for crossover and mutation operations to generate new structures. The structure is checked by bond length, and unreasonable structures are removed. For generations 1-10, generation 2 is based on generation 1, generation 3 on generation 2, and so on, generating structures for generations 1-10 sequentially (the aim is to generate diverse structures). Of course, S in this embodiment is not limited to the first 10 generations; the number 10 is merely an example. Specific genetic algorithms can be found in existing algorithms, which are not improvements in this application and will not be elaborated upon here. For example, based on the N initial metal cluster structures generated above, the genetic algorithm can be used to generate the initial first 10 generations (e.g., generations 1-10) of descendant structures, which include a total of T1 descendant structures. Each structure undergoes M-step DFT local optimization using a small basis set to generate T1×M structure / energy samples (e.g., Figure 4 The sample set shown is 1), where the value of M can range from 5 to 30.

[0035] Therefore, by using genetic algorithms to sample and search the potential energy surface of metal clusters, more representative low-energy samples can be obtained on the potential energy surface, and the global search capability of the potential energy surface can be improved. This helps to obtain the globally optimal structure of metal clusters more efficiently.

[0036] Step S102: Use the first sample set to train the pre-trained DNN to obtain the first DNN model.

[0037] The pre-trained DNN is obtained by processing a trained DNN model of a small-sized metal cluster using a transfer learning method.

[0038] Specifically, transfer learning is used to perform transfer learning on a pre-trained DNN model of a small-sized (fewer atoms) metal cluster to obtain a pre-trained DNN for the metal cluster to be optimized. Since transfer learning can transfer knowledge learned from the source task to a related but different target task, less data is needed to train the target task's neural network. For example, the pre-trained neural network for Pt9 is obtained through transfer learning from a pre-trained neural network for Pt8. Then, using sample set 1, the pre-trained DNN is trained into a DNN model 1 with better performance, such as... Figure 4 As shown. It should be noted that the metal clusters in this application are larger than the smaller metal clusters with trained DNN models, but are not limited to the two metal clusters having the same elements.

[0039] Step S103: Based on the descendant structure of the first S generations of the DFT local optimization, the genetic algorithm and the first DNN model are used to obtain the descendant structure of the S+1th to Tth generations of the DNN local optimization.

[0040] For step S103, obtaining the descendant structure from generation S+1 to generation T of the DNN locally optimized structure includes: generating the initial descendant structure from generation S+1 to generation T using the genetic algorithm based on the descendant structure of the first S generations of the DFT locally optimized structure; and performing local optimization on the initial descendant structure from generation S+1 to generation T using the first DNN model.

[0041] For example, based on the original (initial) first 10 generations of offspring structure, the genetic algorithm is used to generate the offspring structure for generations 11-100. Specifically, before the genetic algorithm generates a new structure for each generation, the structures of all previous generations are sorted by energy, and then the structures with low energy are selected for crossover and mutation operations to generate new structures. For generations 11-100, generation 11 is based on the previous 10 generations, generation 12 is based on the previous 11 generations, and so on, generating the structures for generations 11-100 in sequence (the aim is to generate diverse structures).

[0042] Then, a DNN model 1 (or a DNN model 1 combined with a preset structure optimization algorithm) is used instead of the DFT method to locally optimize the new structure generated by the genetic algorithm (i.e., fit the potential energy surface of the metal cluster structure). The preset structure optimization algorithm can be a limited-memory Bryden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, Newton's method, or other BFGS methods. DNNs are very effective at fitting complex potential energy surfaces, and a well-fitted potential energy surface can be effectively used for local optimization of metal cluster structures. Therefore, using a neural network method and a small number of training samples to fit the potential energy surface of the metal cluster structure reduces the computation time in the optimization of the metal cluster structure, thereby greatly reducing computational costs.

[0043] Step S104: Select Q structures from the descendant structures of the first S generations of the DFT local optimization and the descendant structures of the (S+1)th to Tth generations of the DNN local optimization.

[0044] The Q structures have lower energy than the other structures. The value of Q can range from 5 to 35.

[0045] Specifically, all locally optimized structures generated in the P generations of the genetic algorithm (P can range from 50 to 200, for example, 100) are sorted by energy, and Q low-energy structures are selected (for example, if the lowest energy structure is ranked first, the next highest energy structure is ranked second, and the others are ranked in descending order of energy, then the top Q structures are selected). Then, DFT optimization is performed using a basis set with higher accuracy, and finally the globally optimal structure of the metal cluster is obtained.

[0046] DNNs possess stronger capabilities for fitting complex potential energy surfaces, but require a large number of training samples. Using only a DNN combined with TL (DNN-TL) global optimization method for metal cluster structures suffers from low potential energy surface sampling efficiency and weak global search capabilities, also requiring significant training samples and computation time. This embodiment proposes a DNN combined with TL and GA (DNN-TL-GA) global optimization method for metal cluster structures. Specifically, it uses a genetic algorithm to sample and globally search the potential energy surface of the metal cluster structure, obtaining more representative low-energy samples and possessing better global search capabilities. This helps to more efficiently obtain the globally optimal structure of the metal cluster. Compared to the DNN combined with TL global optimization method for metal cluster structures, this embodiment reduces the training samples by approximately half, saving about 70-80% of the computation time, further improving the optimization efficiency of metal cluster structures.

[0047] The above embodiment uses a first sample set to train the DNN once, obtaining a first DNN model. This model is then used to replace the DFT method for local optimization of the new structure generated by the genetic algorithm, thereby accelerating the local optimization speed of the metal cluster structure. In the next embodiment, to increase the number of low-energy samples, a genetic algorithm is used to generate multiple progeny structures. The DNN is trained twice using two sample sets (a first sample set and a second sample set) to obtain a second DNN model. This model is then used to replace the DFT method for local optimization of the new structure generated by the genetic algorithm, further accelerating the local optimization speed of the metal cluster structure.

[0048] like Figure 2As shown, after performing the step of obtaining the descendant structure of the (S+1)th to (T)th generations of DNN local optimization (i.e., step S103), the optimization method further includes: step S105, based on the descendant structure of the first S generations of DFT local optimization and the descendant structure of the (S+1)th to (T)th generations of DNN local optimization, using the genetic algorithm, the first DNN model, and the second DFT local optimization, to generate a second sample set, wherein the second sample set includes the descendant structure of the (T+1)th to (U)th generations of DFT local optimization and the corresponding energy; step S106, using the transfer learning algorithm... The learning method processes the first DNN model to obtain a second DNN model to be trained, and trains the second DNN model to be trained using the first sample set and the second sample set to obtain the second DNN model; Step S107, based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the S+1th to Tth generations of the DNN local optimization, and the descendant structure of the T+1th to Uth generations of the DFT local optimization, the genetic algorithm and the second DNN model are used to obtain the descendant structure of the U+1th to Vth generations of the DNN local optimization.

[0049] Accordingly, the selection of Q structures (i.e., step S104) specifically includes: step S108, selecting the Q structures from the descendant structures of the first DFT local optimization for the first S generations, the descendant structures of the first DNN local optimization for the S+1 to T generations, the descendant structures of the second DFT local optimization for the T+1 to U generations, and the descendant structures of the second local optimization for the U+1 to V generations.

[0050] The following sections will explain and illustrate each of the above steps (steps S105-S108).

[0051] Step S105: Based on the descendant structure of the first S generations of the DFT local optimization and the descendant structure of the S+1 to T generations of the DNN local optimization, the genetic algorithm, the first DNN model, and the second DFT local optimization method are used to generate a second sample set.

[0052] The second sample set includes the descendant structures and corresponding energies of the T+1 to U generations of DFT local optimization.

[0053] For step S105, generating the second sample set includes: generating the offspring structure from generation T+1 to generation U using the genetic algorithm based on the offspring structure of the first S generations optimized by the DFT and the offspring structure from generation S+1 to generation T optimized by the DNN; pre-optimizing the offspring structure from generation T+1 to generation U using the first DNN model; and processing the pre-optimized offspring structure using the second DFT local optimization method.

[0054] For details on the specific processes of steps S101-S103, please refer to the relevant description above, except that the values ​​of S and T can be adjusted.

[0055] Based on the offspring structures of the first T generations (e.g., the first 100 generations) generated above, the genetic algorithm described above can be used to generate the initial offspring structures of generations 101-110, which include a total of T2 offspring structures. Each structure is first pre-optimized using DNN model 1, and then the pre-optimized structures undergo M-step DFT local optimization to obtain T2×M structure / energy samples (where M can range from 5 to 30). These samples are then merged with sample set 1 to form sample set 2 (e.g., ...). Figure 4 (as shown), including One sample.

[0056] Step S106: The first DNN model is processed using the transfer learning method to obtain a second DNN model to be trained, and the second DNN model to be trained is trained using the first sample set and the second sample set to obtain the second DNN model.

[0057] Specifically, initialization parameters are obtained by transferring the parameters of DNN model 1. These initialization parameters are then used to initialize the parameters of DNN model 2. Since transfer learning can transfer knowledge learned from the source task to a related but different target task, less data is needed to train the neural network for the target task. Then, sample set 2 is used to train the initialized DNN model 2 into a higher-performing DNN model 2, such as... Figure 4 As shown.

[0058] Step S107: Based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the S+1 to T generations of the DNN local optimization, and the descendant structure of the T+1 to U generations of the DFT local optimization, the genetic algorithm and the second DNN model are used to obtain the descendant structure of the U+1 to V generations of the DNN local optimization.

[0059] For step S107, obtaining the locally optimized descendant structure from generation U+1 to generation V includes: generating the descendant structure from generation U+1 to generation V using the genetic algorithm based on the locally optimized descendant structure from generation S of the first S generations of the DFT, the locally optimized descendant structure from generation S+1 to generation T of the DNN, and the locally optimized descendant structure from generation T+1 to generation U of the DFT; and performing local optimization on the descendant structure from generation U+1 to generation V using the second DNN model.

[0060] For example, based on the offspring structure of the first 110 generations, the genetic algorithm is used to generate the offspring structure of generations 111-180. Then, a DNN model 2 (or a DNN model 2 combined with a preset structure optimization algorithm) is used to locally optimize the new structure generated by the genetic algorithm instead of the DFT method. The preset structure optimization algorithm can be the L-BFGS algorithm, Newton's method, or BFGS, etc.

[0061] Step S108: Select the Q structures from the descendant structures of the first S generations of the DFT local optimization, the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, the descendant structures of the (T+1)th to Uth generations of the DFT local optimization, and the descendant structures of the (U+1)th to Vth generations of the DNN local optimization.

[0062] The Q structures have lower energy than the other structures. The value of Q can range from 5 to 35.

[0063] Specifically, all locally optimized structures generated in the P generations of the genetic algorithm (P can range from 50 to 200, for example, 180) are sorted by energy, and Q low-energy structures are selected (for example, if the lowest energy structure is ranked first, the next highest energy structure is ranked second, and the others are ranked in descending order of energy, then the top Q structures are selected). Then, DFT optimization is performed using a basis set with higher accuracy, and finally the globally optimal structure of the metal cluster is obtained.

[0064] The above embodiment uses two sample sets (a first sample set and a second sample set) to train the DNN twice, obtaining a second DNN model. This model is then used to replace the DFT method for local optimization of the new structure generated by the genetic algorithm, thereby accelerating the local optimization speed of the metal cluster structure. In the next embodiment, to further increase the number of low-energy samples, a genetic algorithm is used to generate multiple progeny structures. The DNN is then trained three times using three sample sets (a first sample set, a second sample set, and a third sample set), obtaining a third DNN model. This model is then used to replace the DFT method for local optimization of the new structure generated by the genetic algorithm, further accelerating the local optimization speed of the metal cluster structure.

[0065] like Figure 3 As shown, after performing the step of obtaining the descendant structure of the (U+1)th to (V)th generations of DNN local optimization (i.e., step 107), the optimization method further includes: step S109, generating a third sample set by using the genetic algorithm, the second DNN model, and the third DFT local optimization method based on the descendant structure of the first S generations of DFT local optimization, the descendant structure of the (S+1)th to (T)th generations of DNN local optimization, the descendant structure of the (T+1)th to (U)th generations of DFT local optimization, and the descendant structure of the (U+1)th to (V)th generations of DNN local optimization; wherein the third sample set includes the descendant structure of the (V+1)th to (W)th generations of DFT local optimization and the corresponding energy; step S110, using the transfer learning method... The second DNN model is processed to obtain a third DNN model to be trained, and the third DNN model to be trained is trained using the first sample set, the second sample set, and the third sample set to obtain a third DNN model; Step S111: Based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the S+1 to T generations of the DNN local optimization, the descendant structure of the T+1 to U generations of the DFT local optimization, the descendant structure of the U+1 to V generations of the DNN local optimization, and the descendant structure of the V+1 to W generations of the DFT local optimization, the genetic algorithm and the third DNN model are used to obtain the descendant structure of the W+1 to X generations of the DNN local optimization.

[0066] The selection of Q structures (i.e., step S104 or S108) specifically includes: step S112 selecting the Q structures from the descendant structures of the first S generations of the DFT local optimization, the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, the descendant structures of the (T+1)th to Uth generations of the DFT local optimization, the descendant structures of the (U+1)th to Vth generations of the DNN local optimization, the descendant structures of the (V+1)th to Wth generations of the DFT local optimization, and the descendant structures of the (W+1)th to Xth generations of the DNN local optimization.

[0067] The following sections will explain and illustrate each of the above steps (steps S109-S112).

[0068] Step S109: Based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the S+1 to T generations of the DNN local optimization, the descendant structure of the T+1 to U generations of the DFT local optimization, and the descendant structure of the U+1 to V generations of the DNN local optimization, the genetic algorithm, the second DNN model, and the third DFT local optimization method are used to generate a third sample set.

[0069] The third sample set includes the descendant structures and corresponding energies from generation V+1 to generation W of DFT local optimization.

[0070] For step S109, generating the third sample set includes: generating an initial descendant structure from generation V+1 to generation W using the genetic algorithm based on the descendant structure of the first V generations; pre-optimizing the initial descendant structure from generation V+1 to generation W using the second DNN model; and processing the pre-optimized descendant structure using the third DFT local optimization method.

[0071] For the detailed process of steps S101-S103 and S105-S107, please refer to the relevant description above, except that the values ​​of S, T, U, and V can be adjusted. For example, S=5, T=10, U=15, V=20.

[0072] Based on the offspring structures of the first V generations (e.g., the first 20 generations) generated above, the genetic algorithm described above can be used to generate the initial offspring structures of generations 21-25, which include a total of T3 offspring structures. Each structure is first pre-optimized using DNN model 2, and then the pre-optimized structures undergo M-step DFT local optimization to obtain T3×M structure / energy samples (where M can range from 5 to 30). These samples are then merged with sample set 2 to form sample set 3 (e.g., ...). Figure 4 (as shown), including There are 10 samples. Among them, T1, T2 and T3 have the following relationship: T1>T2≥T3.

[0073] Each "sample set" in this application consists of many data pairs of metal cluster structures (i.e., Cartesian coordinates) and energies (i.e., each sample data in the sample set consists of Cartesian coordinates and energy). The DFT local optimization process continuously adjusts the structure of the metal clusters in the direction of decreasing energy until the energy converges to a local minimum.

[0074] Step S110: The second DNN model is processed using the transfer learning method to obtain a third DNN model to be trained, and the third DNN model to be trained is trained using the first sample set, the second sample set, and the third sample set to obtain the third DNN model.

[0075] Specifically, initialization parameters are obtained by transferring the parameters of DNN model 2. These initialization parameters are then used to initialize the parameters of DNN model 3. Since transfer learning can transfer knowledge learned by the neural network from the source task to a related but different target task, less data is needed to train the neural network for the target task. Then, sample set 3 is used to train the initialized DNN model 3 into a higher-performing DNN model 3, such as... Figure 4 As shown.

[0076] Step S111: Based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the S+1th to Tth generations of the DNN local optimization, the descendant structure of the T+1th to Uth generations of the DFT local optimization, the descendant structure of the U+1th to Vth generations of the DNN local optimization, and the descendant structure of the V+1th to Wth generations of the DFT local optimization, the genetic algorithm and the third DNN model are used to obtain the descendant structure of the W+1th to Xth generations of the DNN local optimization.

[0077] For step S111, obtaining the descendant structure from generation W+1 to generation X of the DNN local optimization includes: generating the descendant structure from generation W+1 to generation X using the genetic algorithm based on the descendant structure of the previous W generations; and using the third DNN model to perform local optimization on the descendant structure from generation W+1 to generation X.

[0078] For example, based on the offspring structure of the first 25 generations, the genetic algorithm is used to generate the offspring structure for generations 26-50. Then, a DNN model 3 (or a DNN model 3 combined with a preset structure optimization algorithm) is used to locally optimize the new structure generated by the genetic algorithm, instead of the DFT method. The preset structure optimization algorithm can be an L-BFGS algorithm, Newton's method, or BFGS, etc.

[0079] Step S112: Select the Q structures from the descendant structures of the first S generations of the DFT local optimization, the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, the descendant structures of the (T+1)th to Uth generations of the DFT local optimization, the descendant structures of the (U+1)th to Vth generations of the DNN local optimization, the descendant structures of the (V+1)th to Wth generations of the DFT local optimization, and the descendant structures of the (W+1)th to Xth generations of the DNN local optimization.

[0080] The Q structures have lower energy than the other structures. The value of Q can range from 5 to 35.

[0081] Specifically, all locally optimized structures generated in the genetic algorithm of generation P (where P can range from 50 to 200, for example, 50) are sorted by energy, and Q low-energy structures are selected (for example, if the lowest energy structure is ranked first, the next highest energy structure is ranked second, and the others are ranked in descending order of energy, then the top Q structures are selected). Then, DFT optimization is performed using a basis set with higher accuracy, and finally the globally optimal structure of the metal cluster is obtained.

[0082] In one embodiment, after performing the step of selecting the Q structures (i.e., step S104, step S108, or step S112), the optimization method further includes: processing the Q structures using a fourth DFT local optimization method to obtain the globally optimal structure of the metal cluster.

[0083] The accuracy of the fourth DFT local optimization method is higher than that of the following: the first DFT local optimization method, the second DFT local optimization method, or the third DFT local optimization method.

[0084] Specifically, after sorting all locally optimized structures generated by the genetic algorithm through P iterations by energy and selecting Q low-energy structures, a more precise basis set can be used for DFT optimization to finally obtain the globally optimal structure of the metal cluster. Since high-precision DFT processing is only applied to a few structures, a globally better metal cluster structure can be obtained without affecting the local optimization rate of the metal cluster structure.

[0085] Specifically, the following describes a method for global optimization of metal cluster structures using a combination of DNN, TL, and GA. This method includes the following steps.

[0086] Step 1: Set the elemental composition, size, charge, and multiplicity of the metal clusters to be optimized;

[0087] Step 2: Generate N random initial structures for metal clusters;

[0088] Step 3: Use a genetic algorithm to generate T1 offspring structures. Each structure is subjected to M-step DFT local optimization using a small basis set to generate T1×M structure / energy samples (sample set 1).

[0089] Step 4: Use transfer learning to obtain a pre-trained deep neural network for the metal clusters to be optimized;

[0090] Step 5: Use sample set 1 to train the pre-trained deep neural network into a deep neural network model 1 with better performance;

[0091] Step 6: Deep neural network model 1 combines a local optimization algorithm to replace the DFT method for local optimization of the new structure generated by the genetic algorithm;

[0092] Step 7: To increase the number of low-energy samples, a genetic algorithm is used to generate T2 offspring structures. Each structure is pre-optimized using Deep Neural Network Model 1, and then M-step DFT optimization is performed on the pre-optimized structures to obtain T2×M structure / energy samples. These samples are then merged with sample set 1 to form sample set 2, containing... One sample;

[0093] Step 8: Initialize the parameters of deep neural network model 2. These parameters are obtained by transferring the parameters of deep neural network model 1. Then, use sample set 2 to train the initialized deep neural network model 2 into a high-performance deep neural network model 2.

[0094] Step 9: Deep neural network model 2, combined with a structure optimization algorithm, performs local optimization on the new structure generated by the genetic algorithm;

[0095] Step 10: To further increase the number of low-energy samples, the genetic algorithm generates T3 offspring structures. Each structure is pre-optimized using a deep neural network model 2. Then, the pre-optimized structures undergo M-step DFT optimization to obtain T3×M structure / energy samples. These samples are merged with sample set 2 to form sample set 3, containing... One sample;

[0096] Step 11: Initialize the parameters of deep neural network model 3. These parameters are obtained by transferring the parameters of deep neural network model 2. Then, use sample set 3 to train the initialized deep neural network model 3 into a deep neural network model 3 with better performance.

[0097] Step 12: The genetic algorithm continuously generates new metal cluster structures in subsequent iterations, while the deep neural network model 3 combined with the structure optimization algorithm completely replaces the DFT method to perform local optimization of the new metal cluster structures.

[0098] Step 13: Sort all locally optimized structures generated by the genetic algorithm after P iterations by energy, select Q low-energy structures, and then perform DFT optimization with a more accurate basis set to finally obtain the globally optimal structure of the metal cluster.

[0099] Example 1

[0100] The atom type is set to Pt, the number of atoms is 9, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0101] In the first 5 generations of the genetic algorithm, a total of 10 offspring structures were generated. Each structure underwent 5-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 50 structure / energy samples (sample set 1).

[0102] The pre-trained neural network of Pt9 is obtained by transfer learning from the neural network trained in Pt8.

[0103] In generations 11-15 of the genetic algorithm, a total of 5 offspring structures were generated. Each structure underwent 5-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 25 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 75 samples).

[0104] In generations 21-25 of the genetic algorithm, a total of 5 offspring structures are generated. Each structure undergoes 5-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 25 structure / energy samples. These samples are then merged with sample set 2 to generate sample set 3 (containing approximately 100 samples).

[0105] In executing this invention, the genetic algorithm has a maximum generation count of 150, generating approximately 100 structures. Ten low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain the globally optimal structure of the Pt9 metal cluster and the zero-point correction energy -1074.0958 Hartree. Spin multipliencies of 3, 5, and 7 are performed using the same steps described above.

[0106] Example 2

[0107] The atom type is set to Pt, the number of atoms is 10, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0108] In the first 5 generations of the genetic algorithm, a total of 10 offspring structures were generated. Each structure underwent 10 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 100 structure / energy samples (sample set 1).

[0109] Pt 10 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0110] In generations 11-15 of the genetic algorithm, a total of 5 offspring structures were generated. Each structure underwent 10-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 50 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 150 samples).

[0111] In generations 21-25 of the genetic algorithm, a total of 5 offspring structures were generated. Each structure underwent 10-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 50 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 200 samples).

[0112] Executing this invention, the genetic algorithm has a maximum generation of 150, generating approximately 300 structures. Ten low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 10 The globally optimal structure of the metal cluster and the zero-point correction energy -1193.4881 Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0113] Example 3

[0114] The atom type is set to Pt, the number of atoms is 11, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0115] In the first 5 generations of the genetic algorithm, a total of 40 offspring structures were generated. Each structure underwent 10-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 400 structure / energy samples (sample set 1).

[0116] Pt 11 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0117] In generations 11-15 of the genetic algorithm, a total of 3 offspring structures were generated. Each structure underwent 10-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 30 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 430 samples).

[0118] In generations 21-25 of the genetic algorithm, two offspring structures are generated. Each structure undergoes 10-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 20 structure / energy samples. These samples are then merged with sample set 2 to generate sample set 3 (containing approximately 450 samples).

[0119] Executing this invention, the genetic algorithm has a maximum generation of 150, generating approximately 100 structures. Ten low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 11The globally optimal structure of the metal cluster and the zero-point correction energy -1312.8484 Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0120] Example 4

[0121] The atom type is set to Pt, the number of atoms is 12, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0122] In the first 5 generations of the genetic algorithm, a total of 47 offspring structures were generated. Each structure underwent 10-step DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 470 structure / energy samples (sample set 1).

[0123] Pt 12 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0124] In generations 11-15 of the genetic algorithm, a total of 10 offspring structures were generated. Each structure underwent 10 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 100 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 570 samples).

[0125] In generations 21-25 of the genetic algorithm, a total of 8 offspring structures were generated. Each structure underwent 10-step DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 80 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 650 samples).

[0126] Executing this invention, the genetic algorithm has a maximum generation of 150, generating approximately 1400 structures. Ten low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 12 The globally optimal structure of the metal cluster and the zero-point correction energy -1432.2231Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0127] Example 5

[0128] The atom type is set to Pt, the number of atoms is 13, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0129] In the first 5 generations of the genetic algorithm, a total of 15 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 300 structure / energy samples (sample set 1).

[0130] Pt 13 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0131] In generations 11-15 of the genetic algorithm, a total of 12 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 240 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 540 samples).

[0132] In generations 21-25 of the genetic algorithm, a total of 10 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 200 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 540 samples).

[0133] Executing this invention, the genetic algorithm has a maximum generation of 150, generating approximately 940 structures. Ten low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 13 The globally optimal structure of the metal cluster and the zero-point correction energy -1551.6044 Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0134] Example 6

[0135] The atom type is set to Pt, the number of atoms is 14, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0136] In the first 5 generations of the genetic algorithm, a total of 24 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 480 structure / energy samples (sample set 1).

[0137] Pt 14 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0138] In generations 11-15 of the genetic algorithm, a total of 8 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 160 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 640 samples).

[0139] In generations 21-25 of the genetic algorithm, a total of 5 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 100 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 740 samples).

[0140] The genetic algorithm of this invention has a maximum generation of 150, generating approximately 1060 structures. Ten low-energy structures are selected, and then, while keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 14 The globally optimal structure of the metal cluster and the zero-point correction energy -1670.9858 Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0141] Example 7

[0142] The atom type is set to Pt, the number of atoms is 15, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0143] In the first 5 generations of the genetic algorithm, a total of 24 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 480 structure / energy samples (sample set 1).

[0144] Pt 15 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0145] In generations 11-15 of the genetic algorithm, a total of 12 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 240 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 720 samples).

[0146] In generations 21-25 of the genetic algorithm, a total of 9 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 180 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 900 samples).

[0147] Executing this invention, the genetic algorithm has a maximum generation of 150, generating approximately 900 structures. Ten low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 15The globally optimal structure of the metal cluster and the zero-point correction energy -1790.3518 Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0148] Example 8

[0149] The atom type is set to Pt, the number of atoms is 16, the charge is 0, the spin multiplicity is 1, and the initial population size N of the metal cluster is 20.

[0150] In the first 5 generations of the genetic algorithm, a total of 38 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 760 structure / energy samples (sample set 1).

[0151] Pt 16 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0152] In generations 11-15 of the genetic algorithm, a total of 25 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 500 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 1260 samples).

[0153] In generations 21-25 of the genetic algorithm, a total of 17 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 340 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 1600 samples).

[0154] Executing this invention, the genetic algorithm has a maximum generation of 150, generating approximately 1230 structures. Fifteen low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 16 The globally optimal structure of the metal cluster and the zero-point correction energy -1909.7376 Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0155] Example 9

[0156] The atom type is set to Pt, the number of atoms is 17, the charge is 0, the spin multiplicity is 1, and the initial population size of the metal cluster is 40.

[0157] In the first 5 generations of the genetic algorithm, a total of 74 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 1480 structure / energy samples (sample set 1).

[0158] Pt 17 The pre-trained neural network is obtained by transfer learning from the neural network trained by Pt8.

[0159] In generations 11-15 of the genetic algorithm, a total of 12 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization, generating 240 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 1720 samples).

[0160] In generations 21-25 of the genetic algorithm, a total of 14 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSSh functional and def2-SVP basis set) local optimization to generate 280 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 2000 samples).

[0161] Executing this invention, the genetic algorithm has a maximum generation of 150, generating approximately 700 structures. Fifteen low-energy structures are selected, and then, keeping the TPSSh functional unchanged, DFT optimization is performed using the more precise def2-TZVP basis set to obtain Pt. 17 Global optimal structure and zero-point correction energy of metal clusters - 2029.1219Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0162] Example 10

[0163] The atom types are set as Rh and V, with 2 Rh atoms, 7 V atoms, a charge of -1, a spin multiplicity of 1, and an initial population size N of 20 for the metal cluster.

[0164] In the first 5 generations of the genetic algorithm, a total of 52 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSS functionals, where Rh uses the SDD basis set and V uses the SVP basis set) local optimization, generating 1040 structure / energy samples (sample set 1).

[0165] Rh2V7 - The pre-trained neural network is from Rh3V6 - The trained neural network achieves transfer learning.

[0166] In generations 11-15 of the genetic algorithm, a total of 15 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSS functionals, where Rh uses the SDD basis set and V uses the SVP basis set) local optimization, generating 300 structure / energy samples. These samples were then merged with sample set 1 to generate sample set 2 (containing approximately 1340 samples).

[0167] In generations 21-25 of the genetic algorithm, a total of 10 offspring structures were generated. Each structure underwent 20 steps of DFT (using TPSS functionals, where Rh uses the SDD basis set and V uses the SVP basis set) local optimization, generating 200 structure / energy samples. These samples were then merged with sample set 2 to generate sample set 3 (containing approximately 1540 samples).

[0168] The genetic algorithm of this invention has a maximum generation of 150, generating approximately 1070 structures. Fifteen low-energy structures are selected, and then, keeping the TPSS functional unchanged, DFT optimization is performed using a higher-precision TZVP basis set to obtain Rh2V7. - The globally optimal structure of the metal cluster and the zero-point correction energy -6829.5077Hartree. Spin multiplicity 3, 5 and 7 are operated on in the same manner as described above.

[0169] This invention yielded a more stable Pt than reported in the prior art. 16 and Pt 17 Metal cluster structure (e.g.) Figure 5 As shown, where M represents multiplicity) and Rh2V7 - Metal cluster structure (e.g.) Figure 6 As shown in the figure, this indicates that the present invention has a good global optimization capability.

[0170] Where S, T, U, V, W, X, and Q are all integers.

[0171] In summary, this invention creatively generates a first sample set based on the initial structure of the metal cluster using a genetic algorithm and a first DFT local optimization method. Then, the first sample set is used to train a pre-trained DNN to obtain a first DNN model. Next, based on the descendant structures of the first S generations of the DFT local optimization, the genetic algorithm and the first DNN model are used to obtain the descendant structures of the (S+1)th to Tth generations of local optimization. Finally, Q low-energy structures are selected from the descendant structures of the first S generations of the DFT local optimization and the descendant structures of the (S+1)th to Tth generations of local optimization. Therefore, this invention, based on the DNN combined with TL global optimization method for metal cluster structures, uses a genetic algorithm to sample and globally search the potential energy surface of the metal cluster structure, which can obtain more representative low-energy samples on the potential energy surface and has better global search capabilities, further improving the optimization efficiency of the metal cluster structure.

[0172] An embodiment of the present invention provides an optimization system for metal cluster structures. The optimization system includes: a generation device for generating a first sample set based on the initial structure of the metal cluster using a genetic algorithm and a first DFT local optimization method, wherein the first sample set includes the descendant structures and corresponding energies of the first S generations of DFT local optimization; a model acquisition device for training a pre-trained DNN using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-sized metal cluster using a transfer learning method; a structure acquisition device for acquiring the descendant structures of the first S generations of DFT local optimization using the genetic algorithm, the first DNN model, and a preset structure optimization algorithm; and a structure selection device for selecting Q structures from the descendant structures of the first S generations of DFT local optimization and the descendant structures of the first S+1 generations of DNN local optimization, wherein the energy of the Q structures is lower than that of the other structures.

[0173] For specific details and benefits of the optimization system for metal cluster structures provided in the embodiments of the present invention, please refer to the above description of the optimization method applicable to metal cluster structures based on DNN-TL-GA, which will not be repeated here.

[0174] One embodiment of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the optimization method for metal cluster structures based on DNN-TL-GA.

[0175] One embodiment of the present invention provides a computer program product, the computer program product including a computer program, which, when executed by a processor, implements the optimization method for metal cluster structures based on DNN-TL-GA.

[0176] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

[0177] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

[0178] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a microcontroller, chip, or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0179] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.

Claims

1. An optimization method for metal cluster structures based on DNN-TL-GA, characterized in that, The optimization method includes: Based on the initial structure of the metal cluster, a first sample set is generated using a genetic algorithm and a first DFT local optimization method. The first sample set includes the descendant structure and corresponding energy of the first S generations of DFT local optimization. The first sample set is used to train the pre-trained DNN to obtain the first DNN model, wherein the pre-trained DNN is obtained by processing the trained DNN model of small-sized metal clusters using the transfer learning method. Based on the descendant structure of the first S generations of the DFT local optimization, the genetic algorithm and the first DNN model are used to obtain the descendant structure of the (S+1)th to Tth generations of the DNN local optimization; and From the descendant structures of the first S generations of the DFT local optimization and the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, Q structures are selected, wherein the energy of the Q structures is lower than that of the other structures. The generation of the first sample set includes: Based on the initial structure of the metal cluster, the genetic algorithm is used to generate the initial first S generations of offspring structure; and The initial descendant structure of the first S generations is processed using the first DFT local optimization method. The process of obtaining the descendant structure from generation S+1 to generation T of the DNN local optimization includes: Based on the descendant structure of the first S generations after local optimization using the DFT, the initial descendant structure from the (S+1)th generation to the Tth generation is generated using the genetic algorithm described above; and The first DNN model is used to locally optimize the descendant structure from the initial generation S+1 to the generation T.

2. The optimization method according to claim 1, characterized in that, After performing the step of obtaining the descendant structure from generation S+1 to generation T of the DNN local optimization, the optimization method further includes: Based on the descendant structure of the first S generations of the DFT local optimization and the descendant structure of the S+1 to T generations of the DNN local optimization, a second sample set is generated using the genetic algorithm, the first DNN model, and the second DFT local optimization method. The second sample set includes the descendant structure of the T+1 to U generations of the DFT local optimization and the corresponding energy. The first DNN model is processed using the transfer learning method to obtain a second DNN model to be trained, and the second DNN model to be trained is trained using the first sample set and the second sample set to obtain the second DNN model. Based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the (S+1)th to Tth generations of the DNN local optimization, and the descendant structure of the (T+1)th to Uth generations of the DFT local optimization, the genetic algorithm and the second DNN model are used to obtain the descendant structure of the (U+1)th to Vth generations of the DNN local optimization. The selection of Q structures includes: selecting the Q structures from the descendant structures of the first S generations of the DFT local optimization, the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, the descendant structures of the (T+1)th to Uth generations of the DFT local optimization, and the descendant structures of the (U+1)th to Vth generations of the DNN local optimization.

3. The optimization method according to claim 2, characterized in that, The generation of the second sample set includes: Based on the descendant structure of the first S generations of the DFT local optimization and the descendant structure of the S+1 to T generations of the DNN local optimization, the genetic algorithm is used to generate the initial descendant structure of the T+1 to U generations. The first DNN model is used to pre-optimize the initial descendant structure from generation T+1 to generation U; and The pre-optimized descendant structure is processed using the second DFT local optimization method.

4. The optimization method according to claim 2, characterized in that, The descendant structure from generation U+1 to generation V for obtaining local optimization of the DNN includes: Based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the (S+1)th to Tth generations of the DNN local optimization, and the descendant structure of the (T+1)th to Uth generations of the DFT local optimization, the descendant structure of the (U+1)th to Vth generations is generated using the genetic algorithm; and The second DNN model is used to locally optimize the descendant structure from generation U+1 to generation V.

5. The optimization method according to claim 2, characterized in that, After performing the step of obtaining the descendant structures of generations U+1 to V of the DNN local optimization, the optimization method further includes: Based on the descendant structure of the first S generations of the DFT local optimization, the descendant structure of the (S+1)th to Tth generations of the DNN local optimization, the descendant structure of the (T+1)th to Uth generations of the DFT local optimization, and the descendant structure of the (U+1)th to Vth generations of the DNN local optimization, a third sample set is generated using the genetic algorithm, the second DNN model, and the third DFT local optimization method. The third sample set includes the descendant structure of the (V+1)th to Wth generations of the DFT local optimization and the corresponding energy. The transfer learning method is used to process the second DNN model to obtain a third DNN model to be trained, and the first sample set, the second sample set and the third sample set are used to train the third DNN model to obtain the third DNN model. Based on the descendant structures of the first S generations of the DFT local optimization, the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, the descendant structures of the (T+1)th to Uth generations of the DFT local optimization, the descendant structures of the (U+1)th to Vth generations of the DNN local optimization, and the descendant structures of the (V+1)th to Wth generations of the DFT local optimization, the genetic algorithm and the third DNN model are used to obtain the descendant structures of the (W+1)th to Xth generations of the DNN local optimization. The selection of Q structures includes: selecting the Q structures from the descendant structures of the first S generations of the DFT local optimization, the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, the descendant structures of the (T+1)th to Uth generations of the DFT local optimization, the descendant structures of the (U+1)th to Vth generations of the DNN local optimization, the descendant structures of the (V+1)th to Wth generations of the DFT local optimization, and the descendant structures of the (W+1)th to Xth generations of the DNN local optimization.

6. The optimization method according to claim 5, characterized in that, After performing the step of selecting the Q structures, the optimization method further includes: processing the Q structures using a fourth DFT local optimization method to obtain the globally optimal structure of the metal cluster. The accuracy of the fourth DFT local optimization method is higher than that of the following: the first DFT local optimization method, the second DFT local optimization method, or the third DFT local optimization method.

7. An optimization system for metal cluster structures based on DNN-TL-GA, characterized in that, The optimization system includes: A generation device is used to generate a first sample set based on the initial structure of the metal cluster using a genetic algorithm and a first DFT local optimization method, wherein the first sample set includes the descendant structure and corresponding energy of the first S generations of DFT local optimization. A model acquisition device is used to train a pre-trained DNN using the first sample set to obtain a first DNN model, wherein the pre-trained DNN is obtained by processing a trained DNN model of a small-sized metal cluster using a transfer learning method. A structure acquisition device is used to acquire, based on the descendant structure of the first S generations of the locally optimized DFT, the genetic algorithm and the first DNN model, the descendant structure of the locally optimized DNN from the (S+1)th generation to the Tth generation; and A structure selection device is used to select Q structures from the descendant structures of the first S generations of the DFT local optimization and the descendant structures of the (S+1)th to Tth generations of the DNN local optimization, wherein the energy of the Q structures is lower than that of the other structures. The generation of the first sample set includes: Based on the initial structure of the metal cluster, the genetic algorithm is used to generate the initial first S generations of offspring structure; and The initial descendant structure of the first S generations is processed using the first DFT local optimization method. The process of obtaining the descendant structure from generation S+1 to generation T of the DNN local optimization includes: Based on the descendant structure of the first S generations after local optimization using the DFT, the initial descendant structure from the (S+1)th generation to the Tth generation is generated using the genetic algorithm described above; and The first DNN model is used to locally optimize the descendant structure from the initial generation S+1 to the generation T.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the optimization method for metal cluster structures based on DNN-TL-GA as described in any one of claims 1-6.

9. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the optimization method for metal cluster structures based on DNN-TL-GA as described in any one of claims 1-6.

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