Methods, apparatuses, devices, and storage media for determining interactions

Abstract

A method, apparatus, device, and storage medium for determining interactions are provided. The proposed method includes: acquiring a first dataset; pre-training a machine learning model using the first dataset, the machine learning model representing the potential function of a molecular system; acquiring a second dataset; and fine-tuning the pre-trained machine learning model using the second dataset to obtain the potential function. In this way, a high-precision machine learning potential function can be obtained using a relatively small number of high-precision curvature labels.

Description

Technical Field

[0001] The examples in this paper generally relate to the field of computers, and in particular to methods, apparatus, devices, computer-readable storage media, and computer program products for determining interactions. Background Technology

[0002] Accurate prediction of the thermodynamic and kinetic properties of molecular systems is a crucial bridge for interatomic interactions, and accurate characterization of the potential energy surface curvature is a prerequisite for predicting the thermodynamic and kinetic behavior of complex molecular systems. Key observables such as vibrational spectra, Gibbs free energy, and heat capacity are closely related to the potential energy surface curvature. Therefore, accurately characterizing the potential energy surface curvature of molecular systems is essential for a deeper understanding of and synthesis of molecular systems. Summary of the Invention

[0003] In a first aspect, a method for determining interactions is provided. The method includes: acquiring a first dataset corresponding to a plurality of first molecular configurations, the first dataset including corresponding first curvature labels for the plurality of first molecular configurations, the first curvature labels indicating the potential surface curvature of the corresponding first molecular configuration; pre-training a machine learning model using the first dataset, the machine learning model representing the potential function of the molecular system; acquiring a second dataset corresponding to a plurality of second molecular configurations, the plurality of second molecular configurations being divided into a first subset and a second subset, the second molecular configurations in the first subset having second curvature labels, the second molecular configurations in the second subset not having second curvature labels, the second curvature labels indicating the potential surface curvature of the corresponding second molecular configuration, the precision of the second curvature labels being greater than the precision of the first curvature labels; and fine-tuning the pre-trained machine learning model using the second dataset to obtain the potential function.

[0004] In a second aspect, an apparatus for determining interactions is provided. The apparatus includes: a first acquisition module configured to acquire a first dataset corresponding to a plurality of first molecular configurations, the first dataset including corresponding first curvature labels for the plurality of first molecular configurations, the first curvature labels indicating the potential surface curvature of the corresponding first molecular configuration; a pre-training module configured to pre-train a machine learning model using the first dataset, the machine learning model representing the potential function of a molecular system; a second acquisition module configured to acquire a second dataset corresponding to a plurality of second molecular configurations, the plurality of second molecular configurations being divided into a first subset and a second subset, the second molecular configurations in the first subset having second curvature labels, the second molecular configurations in the second subset not having second curvature labels, the second curvature labels indicating the potential surface curvature of the corresponding second molecular configuration, the precision of the second curvature labels being greater than the precision of the first curvature labels; and a fine-tuning module configured to fine-tune the pre-trained machine learning model using the second dataset to obtain the potential function.

[0005] In a third aspect, an electronic device is provided. The device includes at least one processor; and at least one memory coupled to the at least one processor and storing instructions for execution by the at least one processor. When executed by the at least one processor, the instructions cause the device to perform the method of the first aspect.

[0006] In a fourth aspect, a computer-readable storage medium is provided. The computer-readable storage medium stores computer-executable instructions that can be executed by a processor to implement the method of the first aspect.

[0007] In a fifth aspect, a computer program product is provided, which is tangibly stored in a computer storage medium and includes computer-executable instructions that, when executed by a device, cause the device to perform the method of the first aspect.

[0008] This approach overcomes the problem of excessively high computational costs associated with directly using high-precision Hessian matrix labels to train machine learning force fields, and significantly reduces the number of high-precision curvature labels required. It also substantially reduces the cost of acquiring training data while obtaining high-precision machine learning potential functions.

[0009] It should be understood that the content described in this section is not intended to limit the key or important features of the examples in this article, nor is it intended to restrict the scope of the solution. Other features will become readily apparent from the following description. Attached Figure Description

[0010] The above and other features, advantages, and aspects of the various examples herein will become more apparent when taken in conjunction with the accompanying drawings and the following detailed description. In the accompanying drawings, the same or similar reference numerals denote the same or similar elements, wherein: Figure 1 A schematic diagram of the example environment is shown; Figure 2 A schematic diagram of an example architecture for determining interactions based on several scenarios is shown; Figure 3 This diagram illustrates how the weights of the loss function change with the number of fine-tuning rounds, depending on certain scenarios. Figure 4 A flowchart illustrating the process for determining interactions based on several scenarios is shown; Figure 5 A block diagram of a device for determining interactions under certain conditions is shown; and Figure 6 Block diagrams of electronic devices according to other scenarios are shown. Detailed Implementation

[0011] The examples in the text will now be described in more detail with reference to the accompanying drawings. While some examples are shown in the drawings, it should be understood that solutions can be implemented in various forms and should not be construed as limited to the examples presented herein. Rather, these examples are provided to provide a more thorough and complete understanding of the solutions. It should be understood that the drawings and examples in this document are for illustrative purposes only and are not intended to limit the scope of protection of the solutions.

[0012] It should be noted that the headings of any section / subsection provided herein are not restrictive. Various examples are described throughout this document, and examples of any type may be included under any section / subsection. Furthermore, examples described in any section / subsection may be combined in any way with any other examples described in the same section / subsection and / or different sections / subsections.

[0013] In the description of the examples in this document, the term "including" and similar terms should be understood as open inclusion, i.e., "including but not limited to". The term "based on" should be understood as "at least partially based on". The term "an example" or "the example" should be understood as "at least one example". The term "some examples" should be understood as "at least some examples". Other explicit and implicit definitions may also be included below. The terms "first", "second", etc., may refer to different or the same objects. Other explicit and implicit definitions may also be included below.

[0014] The examples in this document may involve user data, data acquisition, and / or use. All of these aspects comply with relevant laws, regulations, and provisions. In the examples presented herein, all data collection, acquisition, processing, manipulation, forwarding, and use are conducted with the user's knowledge and confirmation. Accordingly, when implementing each example, the type, scope of use, and usage scenarios of any data or information that may be involved should be communicated to the user and their authorization obtained through appropriate means, in accordance with relevant laws and regulations. The specific methods of notification and / or authorization can vary depending on the actual situation and application scenario; the scope of the solution is not limited in this regard.

[0015] In this manual and the sample solutions, any processing of personal information will be conducted only under legal grounds (such as obtaining the consent of the data subject or being necessary for the performance of a contract) and will only be carried out within the scope stipulated or agreed upon. A user's refusal to process personal information beyond what is necessary for basic functions will not affect the user's use of basic functions.

[0016] As used in this paper, the term "model" refers to a model that learns the relationship between inputs and outputs from training data, enabling it to generate corresponding outputs for a given input after training. Model generation can be based on machine learning techniques. Deep learning is a machine learning algorithm that processes inputs and provides corresponding outputs using multiple layers of processing units. A neural network model is an example of a deep learning-based model. In this paper, "model" may also be referred to as a "machine learning model," "learning model," "machine learning network," or "learning network," and these terms are used interchangeably.

[0017] A neural network is a machine learning network based on deep learning. A neural network can process inputs and provide corresponding outputs. It typically consists of an input layer, an output layer, and one or more hidden layers between the input and output layers. Neural networks used in deep learning applications often include many hidden layers, thus increasing the network's depth. The layers of a neural network are connected sequentially, so that the output of the previous layer is provided as the input to the next layer. The input layer receives the inputs to the neural network, while the output layer's output serves as the final output. Each layer of a neural network includes one or more nodes (also called processing nodes or neurons), each of which processes the input from the layer above.

[0018] As used in this disclosure, the term "potential surface" refers to a multidimensional surface of a molecular system as a function of atomic coordinates, which describes the energy distribution of the molecular system in different configurations.

[0019] As used in this disclosure, the term "potential energy surface curvature" refers to the second derivative information of the potential energy surface, which can be represented by the Hessian matrix. The Hessian matrix is ​​a matrix of second-order partial derivatives of energy with respect to atomic coordinates, with dimensions of . ,in This represents the number of atoms.

[0020] As used in this disclosure, the term "machine learning force field" refers to a model that learns a potential energy surface from quantum mechanical computational data using machine learning methods, which can simulate interatomic interactions with quantum mechanical precision at a lower computational cost.

[0021] As used in this disclosure, the term "molecular configuration" refers to the spatial arrangement of all atoms in a molecular system, which can be represented by the Cartesian coordinates of the atoms.

[0022] As mentioned above, accurate prediction of the thermodynamic and kinetic properties of molecular systems is a crucial bridge for interatomic interactions, and accurately characterizing the potential energy surface curvature is a prerequisite for predicting the thermodynamic and kinetic behavior of complex molecular systems. Key observables such as vibrational spectra, Gibbs free energy, and heat capacity are closely related to the potential energy surface curvature. Therefore, accurately characterizing the potential energy surface curvature of molecular systems is essential for a deeper understanding of and synthesis of molecular systems.

[0023] However, while first-principles methods for calculating the Hessian matrix to obtain this information, such as density functional theory (DFT), provide the necessary computational accuracy, their computational complexity increases dramatically with system size. The computational resources required to calculate the Hessian matrix (the second derivative of energy) for vibrational analysis grow quadratically (or worse) with the number of atoms, making high-fidelity thermodynamic analysis of complex chemical systems difficult. Although ab initio molecular dynamics (AIMD) offers an alternative approach by sampling free energies, it requires extremely long simulation timescales to converge. The computational cost and limitations are particularly pronounced for phenomena dominated by rare events or entropy-driven processes.

[0024] In recent years, the rapid development of Machine Learning Force Fields (MLFF) has brought hope to this field. It can approximate the accuracy of Density Functional Theory (DFT) while maintaining good computational efficiency, thus alleviating the predicament of high computational costs to some extent. This is achieved by analyzing energy (…). ) and force ( Learning potential energy surfaces from data, machine learning force fields have successfully accelerated the process of dynamic simulations. However, a key limitation remains: standard machine learning force fields often fail to capture the fine curvature of the potential energy surface required for reliable vibrational and thermodynamic predictions. While these models may predict forces accurately enough for short-range trajectory simulations, they often lack the second-order accuracy required for vibrational spectra, transition state analysis, and long-term dynamic stability. For example, failure modes such as imaginary frequencies may appear in stable structures.

[0025] Machine Learning Interatomic Potentials (MLIPs) incorporating Hessian matrix information promises to improve the prediction accuracy of these properties and directly enhance MLIP performance in Hessian matrix-related tasks, such as frequency calculation, thermodynamic property prediction, and even anharmonicity prediction. However, on the one hand, acquiring Hessian matrix labels is more expensive than traditional energy (E) and force (F) labels. On the other hand, a single Hessian matrix calculation is typically 10 to 100 times more expensive than a single energy scalar or force vector calculation. Furthermore, Hessian matrices are difficult to train and computationally expensive.

[0026] A scheme for determining interactions is proposed here. In this scheme, a first dataset is obtained. The first dataset corresponds to multiple first molecular configurations and includes corresponding first curvature labels for each first molecular configuration, indicating the potential surface curvature of the corresponding first molecular configuration. Using the first dataset, a machine learning model is pre-trained to represent the potential function of the molecular system. A second dataset is then obtained, corresponding to multiple second molecular configurations. These second molecular configurations are divided into a first subset and a second subset. Second molecular configurations in the first subset have second curvature labels, while those in the second subset do not. The second curvature labels indicate the potential surface curvature of the corresponding second molecular configuration, and the precision of the second curvature labels is greater than that of the first curvature labels. Using the second dataset, the pre-trained machine learning model is fine-tuned to obtain the potential function.

[0027] In this way, the machine learning model is pre-trained using a first dataset containing the first curvature label (lower precision), enabling the model to learn the fundamental relationship between the atomic environment and the curvature of the potential energy surface. Then, the pre-trained model is fine-tuned using a second dataset containing the second curvature label (higher precision). This overcomes the problem of excessively high computational costs associated with directly training the machine learning force field using high-precision Hessian matrix labels. Furthermore, since only the second molecular configurations in the first subset of the second dataset have the second curvature label, and the second molecular configurations in the second subset do not, the number of high-precision curvature labels can be significantly reduced. This allows for a substantial reduction in the cost of acquiring training data while obtaining a high-precision machine learning potential function.

[0028] The following describes various examples of this scheme in further detail with reference to the accompanying drawings.

[0029] Figure 1 A schematic diagram of example environment 100 is shown. (e.g.) Figure 1 As shown, example environment 100 may include electronic device 110, terminal device 120 and user 130.

[0030] In this example environment 100, user 130 can send requests or data to electronic device 110 via terminal device 120. After processing these requests or data, electronic device 110 can return the results to terminal device 120 for user 130 to view or use. For example, user 130 can submit molecular configuration data and training parameters to electronic device 110 via terminal device 120. Electronic device 110 executes the training process of a machine learning model and returns the trained potential function or the prediction result based on the potential function to terminal device 120.

[0031] In some cases, electronic device 110 can be any suitable computing device with computing capabilities, such as a terminal device or server. The terminal device can be any type of mobile terminal, fixed terminal, or portable terminal, including mobile phones, desktop computers, laptop computers, notebook computers, netbook computers, tablet computers, media computers, multimedia tablets, handheld computers, portable gaming terminals, VR / AR devices, personal communication system (PCS) devices, personal navigation devices, personal digital assistants (PDAs), audio / video players, digital cameras / camcorders, positioning devices, television receivers, radio receivers, e-book devices, gaming devices, or any combination of the foregoing, including accessories and peripherals of these devices or any combination thereof. In some cases, the terminal device may also support any type of user-facing interface (such as "wearable" circuitry).

[0032] A server can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, content delivery networks, and big data and artificial intelligence platforms. Servers can also include computing systems / servers, such as mainframes, edge computing nodes, and computing devices in cloud environments, etc.

[0033] It should be understood that the structure and function of the various elements in environment 100 are described for illustrative purposes only and do not imply any limitation on the scope of the scheme.

[0034] The following description of the example will continue with reference to the accompanying drawings.

[0035] Figure 2 A schematic diagram of an example architecture 200 for determining interactions under certain conditions is shown. For ease of discussion, it will be combined with... Figure 1 Example environment 100 is shown to describe Figure 2 The example architecture 200 shown is exemplary, but it should be understood that it is merely illustrative. The example architecture 200 involves a pre-training phase 220, a fine-tuning phase 230, and an application phase 240 for the machine learning model 210.

[0036] Machine learning model 210 is used to represent the potential function of a molecular system. A molecular system can refer to a collection of multiple atoms (or particles) bonded together by chemical bonds or non-covalent interactions. The potential function can describe the mapping relationship between the molecular configuration of the molecular system and potential energy information (such as the curvature of the potential energy surface, energy or force, etc.). In some examples, machine learning model 210 may include an equivariant graph neural network (GNN), for example, an equivariant graph neural network can be used as the backbone network. GNN adopts a local coordinate system-based approach, which realizes three-dimensional rotational symmetry, i.e., three-dimensional special orthogonal group (SO(3)) symmetry, by constructing complete equivariant local coordinate systems and scalarizing geometric information in these coordinate systems. Using GNN as the backbone network can not only effectively handle high-order many-body interactions, but also maintain high computational efficiency. Of course, the model architecture of the above machine learning model 210 is exemplary, and any other appropriate model architecture can be selected according to actual needs. This paper does not limit the model architecture of machine learning model 210.

[0037] like Figure 2As shown, during the pre-training phase 220, the electronic device 110 can acquire a first dataset 222. The first dataset 222 corresponds to multiple first molecular configurations and includes corresponding first curvature labels for the multiple first molecular configurations. The first curvature label indicates the potential surface curvature of the corresponding first molecular configuration. In some examples, the first curvature label may include a Hessian matrix or its equivalent representation. As an example, the first dataset 222 may include multiple pre-training samples, each pre-training sample may include a sample input and a sample output, the sample input may indicate a corresponding first molecular configuration, and the sample output may include a first region label corresponding to the corresponding first molecular configuration.

[0038] In some examples, electronic device 110 can determine the first curvature label based on a first predetermined method. For example, the first predetermined method can be a method with low computational resource consumption. In this way, the computational resources required to construct the first dataset 222 can be reduced. In some examples, electronic device 110 can utilize a tight-binding algorithm to determine the first curvature label. The tight-binding algorithm is a semi-empirical quantum mechanical method with a computational cost significantly lower than density functional theory, but still provides useful information about the curvature of the potential energy surface. In some examples, electronic device 110 can utilize the GFN2-xTB (Geometry, Frequency, Noncovalent, eXtended Tight-Binding) method to determine the first curvature label. In this way, the generation efficiency of the first curvature label can be improved, the computational cost required to generate the first curvature label can be reduced, and the machine learning model 210 can learn the fundamental relationship between the atomic environment and the curvature of the potential energy surface. Of course, the above-mentioned first predetermined method is only exemplary, and any other appropriate method can be selected to obtain the first curvature label according to actual needs. This document does not impose any limitations on this.

[0039] In some examples, the first dataset 222 may also include corresponding energy and force labels for multiple first molecular configurations. Energy labels may indicate the potential energy (e.g., energy value) of the corresponding first molecular configuration. Force labels may indicate the forces acting on each atom in the corresponding first molecular configuration; for example, force labels may include force data for the first molecular configuration, which may indicate the interaction forces between individual atoms. In some examples, energy and force labels may be obtained using the same or similar methods as the first curvature labels (e.g., tight-binding algorithm or GFN2-xTB method, etc.) to ensure data consistency. Of course, energy and force labels may also be obtained using other methods, which are not limited herein.

[0040] like Figure 2As shown, in the pre-training phase 220, the electronic device 110 can pre-train the machine learning model 210 based on the first dataset 222 to obtain a pre-trained machine learning model 210. In some examples, the electronic device 110 can utilize the first dataset 222 to pre-train the machine learning model 210 with initial parameter values ​​to obtain a machine learning model 210 with pre-trained parameters.

[0041] In some examples, during the pre-training phase 220, the electronic device 110 can update the model parameters of the machine learning model 210 based on a loss function, such as updating the initial parameter values ​​of the machine learning model 210 to pre-trained parameters. In some examples, the loss function may include loss terms corresponding to energy, force, and potential energy surface curvature, respectively. As an example, the electronic device 110 can obtain pre-training samples from a first dataset 222. The pre-training samples may include sample inputs and sample outputs. The sample inputs may indicate a first molecular configuration, and the sample outputs may include, for example, a first curvature label, an energy label, and a force label. The electronic device 110 can provide the sample inputs to the machine learning model 210 to obtain the prediction results output by the machine learning model 210. The prediction results may include sub-results corresponding to the potential energy surface curvature, energy, and force. The electronic device 110 can use the loss function to update the model parameters of the machine learning model 210 based on the differences between the prediction results and the first curvature label, energy label, and force label to obtain a pre-trained machine learning model 210. Through pre-training, the machine learning model 210 can learn the basic characteristics of the potential energy surface curvature, laying the foundation for the subsequent fine-tuning phase 230. After the pre-training phase 220 is completed, the machine learning model 210 obtains the pre-trained parameter values. It should be understood that the above pre-training process is only exemplary, and other pre-training methods can be selected according to actual needs; this article does not impose any restrictions on this.

[0042] like Figure 2 As shown, in the fine-tuning phase 230, the electronic device 110 can acquire a second dataset 232. The second dataset 232 corresponds to multiple second molecular configurations. The multiple second molecular configurations are divided into a first subset and a second subset. The second molecular configurations in the first subset have a second curvature label, while the second molecular configurations in the second subset do not have a second curvature label. The second curvature label indicates the potential energy surface curvature of the corresponding second molecular configuration, and the precision of the second curvature label is greater than the precision of the first curvature label.

[0043] In some examples, electronic device 110 can determine the second curvature label corresponding to the second molecular configuration based on first-principles methods. As an example, electronic device 110 can determine the second curvature label based on density functional theory methods. This provides high-precision potential energy surface curvature information. Since the computational resource consumption of the second curvature label is relatively high, providing the second curvature label only for the second molecular configuration in the first subset, while the second molecular configuration in the second subset does not have a second curvature label, can reduce the computational resource consumption of the construction process of the second dataset 232.

[0044] In some examples, the second dataset 232 may also include corresponding energy and force labels for multiple second molecular configurations. A first subset may include second curvature labels, energy labels, and force labels corresponding to the second molecular configurations, and a second subset may include energy and force labels corresponding to the second molecular configurations, but the second molecular configurations in the second subset do not have second curvature labels. In some examples, the second curvature label may include a Hessian matrix or its equivalent representation. In some examples, the electronic device 110 may determine the energy and force labels in the second dataset 232 based on first principles. This allows for the acquisition of energy and force labels with relatively high accuracy.

[0045] The process of acquiring the second dataset 232 will be described below with examples. In some examples, the electronic device 110 can determine the distribution characteristics of multiple second molecular configurations. The distribution characteristics can indicate the distribution of the multiple second molecular configurations in at least one attribute space. The electronic device 110 can sample the multiple second molecular configurations based on the distribution characteristics to determine a first subset. The electronic device 110 can determine the corresponding second curvature label for each second molecular configuration based on each second molecular configuration in the first subset. By sampling the multiple second molecular configurations based on the distribution characteristics, a representative subset of molecular configurations can be selected to assign a limited number of high-precision curvature labels. This sampling strategy ensures that the first subset covers diverse chemical environments, enabling the machine learning model 210 to learn key features of the potential energy surface curvature.

[0046] In some examples, electronic device 110 can determine the structural distribution of a plurality of second molecular configurations, which can indicate the distribution of the plurality of second molecular configurations in structural space. In other words, the distribution characteristics can include the structural distribution. For each of the plurality of second molecular configurations, electronic device 110 can determine a local density based on the structural distribution, which can indicate the number of second molecular configurations similar to that second molecular configuration. Then, electronic device 110 can select second molecular configurations belonging to a first subset from the plurality of second molecular configurations based on the local density.

[0047] In some examples, the electronic device 110 can utilize multidimensional structure descriptors to represent the structural features of second molecular configurations to determine the structural distribution of multiple second molecular configurations in a multidimensional structure descriptor space. In some cases, the structure space may include, for example, a Smooth Overlap of Atomic Positions (SOAP) latent space. The electronic device 110 can transform the Cartesian coordinates of the second molecular configurations to the SOAP latent space, utilize SOAP descriptors to represent the structural features of the second molecular configurations, and determine the structural distribution of the second molecular configurations in the SOAP latent space. Using SOAP descriptors, local atomic environments can be rigorously represented, and SOAP remains invariant when the molecular system undergoes rotation, translation, and substitution. The similarity between molecular configurations can be quantitatively assessed in the SOAP latent space.

[0048] In some examples, for each second molecular configuration in the candidate set The electronic device 110 can determine the second molecular configuration using the formula shown below. Local density in the SOAP latent space : (1) in and They represent the second molecular configurations respectively. and SOAP vector, This represents a similarity function, such as a dot product function or a Gaussian function. Electronic device 110 can use formula (1) to determine the second molecular configuration. The cumulative sum of similarities between the candidate and neighboring second molecular configurations is used to determine the local density. Local density It could be in the SOAP latent space, targeting the second molecular configuration. The number or density of similar molecular configurations can be used to assess the second molecular configuration. The sparsity of the distribution in the SOAP latent space. If the local density... Higher, meaning the second molecular configuration Located in a dense region of the structural space, that is, with many similar molecular configurations, the structure has a high degree of redundancy.

[0049] In some examples, electronic device 110 can determine the sampling probability based on local density, which can be inversely proportional to the local density. In other words, a higher local density corresponds to a lower sampling probability, and vice versa. Electronic device 110 can then select a second molecular configuration belonging to a first subset from the candidate set based on the sampling probability. In this way, second molecular configurations with lower local densities can be preferentially selected. By selecting the second molecular configuration from sparse regions of the SOAP space, similar molecular configurations (e.g., those clustered near equilibrium) can be effectively reduced, and more precise second curvature labels can be assigned to a diverse set of chemical environments. This eliminates the statistical variance inherent in random sampling, allowing convergence of the machine learning model 210 to be achieved using a relatively small first subset.

[0050] In some examples, electronic device 110 can determine the energy distribution of multiple second molecular configurations, the energy distribution indicating the distribution of the multiple second molecular configurations in energy space. In other words, the distribution characteristics can include the energy distribution. Based on the energy distribution, electronic device 110 can determine multiple energy levels, including a target energy level. From the multiple second molecular configurations, electronic device 110 determines a set of molecular configurations belonging to the target energy level, and from the set of molecular configurations, selects second molecular configurations belonging to a first subset.

[0051] In some examples, electronic device 110 can determine the potential energy of multiple second molecular configurations in a candidate set, and can classify the multiple second molecular configurations into multiple energy levels based on their potential energy. For example, electronic device 110 can sort the multiple second molecular configurations from high to low potential energy, determining the top 5% of the second molecular configurations in the sort as the first energy level, the second molecular configurations between 5% and 10% in the sort as the second energy level, the 10% to 30% as the third energy level, and so on. As another example, electronic device can determine the top, such as 5%, 10%, or 30% of the second molecular configurations in the sort as high energy levels, the bottom, such as 20% or 40%, as low energy levels, and the remaining second molecular configurations as medium energy levels. The second molecular configurations in the high-energy subset correspond to the transition state region and the twisted geometry along the reaction path. The second molecular configurations in the low-energy subset typically represent reactants and products.

[0052] The target energy level here can be any suitable energy level. In some examples, the target energy level can be an energy level with relatively high potential energy (also referred to as, for example, a "high energy level"), such as any one of the first energy level, second energy level, third energy level, or high energy level. The second molecular configuration in the high energy level typically corresponds to a region with complex curvature of the potential energy surface, such as a transition state region. Sampling the second molecular configuration based on the energy level allows for the assignment of more accurate second curvature labels to the second molecular configurations of the high energy level, enabling the machine learning model 210 to better learn the key curvature features of the potential energy surface. For example, the electronic device 110 can determine the top, for example, 5% of the sorted configurations as the target energy level, and the electronic device 110 can construct a first subset from, for example, 0.1% of the second molecular configurations in the target energy level.

[0053] In some examples, the machine learning model 210 can be used to perform predictions of the properties of a molecular system, with at least one attribute space relating to that property. For example, if the machine learning model 210 performs a prediction task related to a transition state, the attribute space may include an energy space to assign a second curvature label to a high-energy-level second molecular configuration associated with the transition state. As another example, if the machine learning model 210 performs a prediction task related to the vibrational properties or superconducting temperature of the molecular system, the attribute space may include a structure space. In this way, by constructing a first subset based on different task requirements, the number of highly accurate second curvature labels can be significantly reduced while maintaining the prediction accuracy of the machine learning model 210, thus lowering the cost of acquiring training data. Of course, the attribute spaces described above are merely exemplary. In practical applications, any appropriate attribute space can be selected based on the task requirements of the machine learning model 210. This document does not impose any restrictions on this.

[0054] like Figure 2 As shown, in the fine-tuning stage 230, the electronic device 110 can use the second dataset 232 to fine-tune the pre-trained machine learning model 210 to obtain the potential function. That is, the pre-trained machine learning model can be used as the potential function (also called the machine learning potential function).

[0055] In some examples, the pre-trained machine learning model 210 may have pre-trained parameter values, and the electronic device 110 may fine-tune the parameter values ​​of the machine learning model 210 using a second dataset 232 to obtain a fine-tuned (or "trained") machine learning model 210. The trained machine learning model 210 may have pre-trained parameter values. Adjusting the parameter values ​​of the machine learning model 210 in the fine-tuning phase 230 can improve the prediction accuracy of the potential energy surface curvature and preserve the structural representation learned in the pre-training phase 220, which is beneficial for improving the convergence and stability of the machine learning model 210. In some examples, the learning rate in the fine-tuning phase 230 may be lower than the learning rate in the pre-training phase 220 to carefully adjust the pre-trained weights.

[0056] In some examples, electronic device 110 can fine-tune machine learning model 210 based on a loss function. That is, electronic device 110 can use the loss function to update the parameter values ​​of machine learning model 210 to achieve the purpose of fine-tuning machine learning model 210. In some cases, the loss function may include a first loss term corresponding to the curvature of the potential energy surface. Electronic device 110 can use machine learning model 210 to obtain a prediction result based on a second molecular configuration in a first subset, the prediction result indicating the predicted curvature of the potential energy surface of the second molecular configuration. Electronic device 110 can determine the difference between the prediction result and the second curvature label. Then, electronic device 110 can determine the first loss term based on the projection vector and the difference, the projection vector satisfying predetermined conditions.

[0057] In some examples, the predetermined condition may include the projection vector following a discrete probability distribution. For example, the projection vector may be a random vector following a Rademacher distribution. This random vector may have a mean of zero, and can be represented as follows: Alternatively and / or additionally, this random vector can also satisfy the condition that its covariance is an identity matrix, for example, it can be represented as... In other words, the predetermined conditions can include the mean of the projected vectors being zero and the covariance of the projected vectors being the identity matrix. This allows for an unbiased estimation of the Hessian matrix error.

[0058] For example, electronic device 110 can determine the first loss term based on the following formula: (2) in This represents the first loss item. This indicates that the distribution follows a Radmach distribution (e.g., taking values ​​with equal probability). A random vector (i.e., a projection vector) of ). Indicates the prediction result. This represents the second curvature label. Therefore, a fully random vector can be used. By using a dense vector where each component is non-zero, the loss function can simultaneously probe all elements of the Hessian matrix. This allows for a more comprehensive capture of the curvature characteristics of the potential energy surface (PES) in each training step, significantly improving the convergence speed and accuracy of vibrational property prediction.

[0059] If we directly compare the predicted Hessian matrix (i.e., the prediction result) with the reference Hessian matrix (i.e., the curvature label), we need to construct a complete... The matrix, the time complexity required is quadratic, that is... The machine learning model 210 is fine-tuned using the first loss function described above, without the need to build a complete... A matrix can be directly used to calculate the product between the difference and the random vector (also known as the "Hessian product"). Electronic device 110 only needs to perform calculations on matrices of size... The random vector is processed, and the time complexity is linear, that is... This approach not only significantly reduces the computational resources required for fine-tuning but also significantly reduces memory usage, making it possible to perform high-fidelity training of machine learning models using large-scale molecular systems.

[0060] In some examples, the loss function may include a first loss term and at least one second loss term. The first loss term corresponds to the curvature of the potential energy surface, and the second loss term corresponds to at least one of energy or force. Electronic device 110 may obtain the first loss term and at least one second loss term based on a pre-trained machine learning model 210. Then, electronic device 110 may determine a loss function based on the first loss term, a first weight, at least one second loss term, and at least one second weight. As an example, electronic device 110 may fine-tune the machine learning model 210 based on a loss function as shown below: (3) in This represents the second loss term corresponding to energy. Indicates the second loss item The corresponding second weight (also known as the "energy weight") This represents the second loss term corresponding to the force. Indicates the second loss item The corresponding weights (also known as, for example, "force weights"), Indicates the first loss item. This represents the first weight (also known as the "Hessian matrix weight"). In this way, the machine learning model can be fine-tuned by combining the second curvature label, energy label, and force label.

[0061] In some examples, the first weight can be increased with each fine-tuning round. Thus, during the fine-tuning phase 230, the mean absolute error of the Hessian matrix can be suppressed, resulting in a potential function that combines energy prediction accuracy with vibration robustness. Figure 3 A schematic diagram 300 illustrates how the weights in the loss function change with each fine-tuning round, according to an example of this disclosure. For example... Figure 3 As shown, in the early stage of fine-tuning phase 230, the force weight is 306 (i.e. The largest, with an energy weight of 304 (i.e.) The weight of the Hessian matrix is ​​the smallest, less than the force weight 306. As the fine-tuning rounds increase, the Hessian matrix weight 302 gradually increases, while the force weight 306 and energy weight 304 can remain unchanged. Towards the end of fine-tuning phase 230, the Hessian matrix weight 302 is much larger than the force weight 306 and energy weight 304. In some cases, this weight change strategy can be called an increasing weight strategy.

[0062] In some examples, in the current round out of multiple rounds, electronic device 110 can determine the first weight based on the current round and a mapping relationship. This mapping relationship is used to determine the first weight corresponding to the current round. As an example, the mapping relationship can be represented by the formula shown below. In other words, electronic device 110 can determine the first weight corresponding to the current round based on the formula shown below: (4) in This indicates the starting round of the fine-tuning phase 230. This indicates the end of the fine-tuning phase 230. This indicates the current round of fine-tuning phase 230. , Indicates the starting round The corresponding initial weights, This represents the weighting coefficient.

[0063] In some cases, at the beginning of the fine-tuning phase 230, the first weight can be configured as follows: This ensures that the machine learning model 210 retains the global situational energy surface accuracy established during the pre-training phase. In the fine-tuning phase 230... Within, as the number of fine-tuning rounds increases, Linear growth. The machine learning model can gradually integrate high-fidelity curvature information while avoiding instability in the learning process caused by sparse Hessian gradients. It should be understood that the above method for determining the first weight is only exemplary, and any other appropriate method can be selected according to actual needs, as long as the first weight can gradually increase with the fine-tuning rounds. This paper does not impose any restrictions on the method for determining the first weight.

[0064] like Figure 2 As shown, in application phase 240, the trained machine learning model 210 has trained parameter values ​​and can be used as a potential function. Electronic device 110 can acquire model input 242. Model input 242 may include the molecular configuration of the molecular system to be predicted. Electronic device 110 can provide model input 242 to machine learning model 210. Machine learning model 210 generates model output 244 based on model input 242. Model output 244 may indicate at least one of the potential surface curvature, energy, or force of the molecular system.

[0065] In some examples, model output 244 can be used for downstream application tasks. For instance, model output 244 can be used for tasks such as vibrational spectrum prediction, Gibbs free energy calculation, heat capacity calculation, transition state search, reaction kinetic analysis, or superconducting transition temperature prediction. Because machine learning model 210 can accurately capture the curvature information of the potential energy surface, it can support these downstream application tasks that require second-order derivative information.

[0066] Figure 4 A flowchart of a process 400 for determining an interaction under certain conditions is shown. Process 400 can be implemented at electronic device 110. (See below for reference.) Figure 1 To describe process 400.

[0067] In box 410, electronic device 110 acquires a first dataset, which corresponds to multiple first molecular configurations. The first dataset includes corresponding first curvature labels for the multiple first molecular configurations, and the first curvature labels indicate the potential energy surface curvature of the corresponding first molecular configuration.

[0068] In box 420, electronic device 110 uses the first dataset to pre-train a machine learning model, which is used to represent the potential function of the molecular system.

[0069] In box 430, electronic device 110 acquires a second dataset, which corresponds to multiple second molecular configurations. The multiple second molecular configurations are divided into a first subset and a second subset. The second molecular configurations in the first subset have a second curvature label, while the second molecular configurations in the second subset do not have a second curvature label. The second curvature label indicates the potential energy surface curvature of the corresponding second molecular configuration, and the precision of the second curvature label is greater than that of the first curvature label.

[0070] In box 440, electronic device 110 uses a second dataset to fine-tune a pre-trained machine learning model to obtain a potential function.

[0071] In some examples, obtaining the second dataset includes: determining the distribution characteristics of a plurality of second molecular configurations, the distribution characteristics indicating the distribution of the plurality of second molecular configurations in at least one attribute space; sampling the plurality of second molecular configurations based on the distribution characteristics to determine a first subset; and determining a corresponding second curvature label for each second molecular configuration based on each second molecular configuration in the first subset.

[0072] In some examples, the distribution characteristics include a structural distribution, which indicates the distribution of multiple second molecular configurations in a structural space, and sampling of the multiple second molecular configurations includes: for each of the multiple second molecular configurations, determining a local density based on the structural distribution, the local density indicating the number of second molecular configurations similar to that second molecular configuration; and selecting, based on the local density, second molecular configurations belonging to a first subset from the multiple second molecular configurations.

[0073] In some examples, the distribution characteristics include an energy distribution that indicates the distribution of multiple second molecular configurations in an energy space, and sampling of the multiple second molecular configurations includes: determining multiple energy levels based on the energy distribution, the multiple energy levels including a target energy level; determining a set of molecular configurations belonging to the target energy level from the multiple second molecular configurations; and selecting second molecular configurations belonging to a first subset from the set of molecular configurations.

[0074] In some examples, machine learning models are used to perform predictions of the properties of molecular systems, with at least one property space relating to the properties.

[0075] In some examples, fine-tuning is based on a loss function that includes a first loss term corresponding to the curvature of the potential energy surface, and process 400 further includes: obtaining a prediction result based on a pre-trained machine learning model, the prediction result indicating the predicted curvature of the potential energy surface for a second molecular configuration in a first subset; determining the difference between the prediction result and the second curvature label; and determining the first loss term based on the projection vector and the difference, the projection vector satisfying predetermined conditions.

[0076] In some examples, fine-tuning is based on a loss function that includes a first loss term and at least one second loss term. The first loss term corresponds to the curvature of the potential energy surface, and the second loss term corresponds to at least one of energy or force. The first weight of the first loss term in the loss function increases with the number of fine-tuning rounds.

[0077] In some examples, in the current round of multiple rounds, the loss function is determined as follows: based on a pre-trained machine learning model, a first loss term and at least one second loss term are obtained; based on the current round and a mapping relationship, a first weight is determined, the mapping relationship being used to linearly increase the first weight relative to the current round; and based on the first loss term, the first weight, at least one second loss term, and at least one second weight, the loss function is determined.

[0078] In some examples, the first curvature label is obtained using a tight-binding algorithm, and the second curvature label is obtained using density functional theory.

[0079] A corresponding apparatus for implementing the above methods or processes is also provided. Figure 5 A schematic structural block diagram of an example device 500 for determining interactions under certain conditions is shown. Device 500 can be implemented as or included in electronic device 110. The various modules / components in device 500 can be implemented by hardware, software, firmware, or any combination thereof.

[0080] like Figure 5 As shown, the device 500 includes: a first acquisition module 510 configured to acquire a first dataset, the first dataset corresponding to a plurality of first molecular configurations, the first dataset including corresponding first curvature labels for the plurality of first molecular configurations, the first curvature labels indicating the potential energy surface curvature of the corresponding first molecular configuration; a pre-training module 520 configured to pre-train a machine learning model using the first dataset, the machine learning model being used to represent the potential function of the molecular system; a second acquisition module 530 configured to acquire a second dataset, the second dataset corresponding to a plurality of second molecular configurations, the plurality of second molecular configurations being divided into a first subset and a second subset, the second molecular configurations in the first subset having second curvature labels, the second molecular configurations in the second subset not having second curvature labels, the second curvature labels indicating the potential energy surface curvature of the corresponding second molecular configuration, the precision of the second curvature labels being greater than the precision of the first curvature labels; and a fine-tuning module 540 configured to fine-tune the pre-trained machine learning model using the second dataset to obtain the potential function.

[0081] In some examples, the second acquisition module 530 is further configured to: determine the distribution characteristics of a plurality of second molecular configurations, the distribution characteristics indicating the distribution of the plurality of second molecular configurations in at least one attribute space; sample the plurality of second molecular configurations based on the distribution characteristics to determine a first subset; and determine a corresponding second curvature label for each second molecular configuration based on each second molecular configuration in the first subset.

[0082] In some examples, the distribution characteristics include a structural distribution, which indicates the distribution of multiple second molecular configurations in a structural space, and the second acquisition module 530 is further configured to: for each of the multiple second molecular configurations, determine a local density based on the structural distribution, the local density indicating the number of second molecular configurations similar to that second molecular configuration; and select, based on the local density, a second molecular configuration belonging to a first subset from the multiple second molecular configurations.

[0083] In some examples, the distribution characteristics include an energy distribution that indicates the distribution of multiple second molecular configurations in an energy space, and the second acquisition module 530 is further configured to: determine multiple energy levels based on the energy distribution, the multiple energy levels including a target energy level; determine a set of molecular configurations belonging to the target energy level from the multiple second molecular configurations; and select second molecular configurations belonging to a first subset from the set of molecular configurations.

[0084] In some examples, machine learning models are used to perform predictions of the properties of molecular systems, with at least one property space relating to the properties.

[0085] In some examples, fine-tuning is based on a loss function that includes a first loss term corresponding to the curvature of the potential energy surface, and the fine-tuning module 540 is further configured to: obtain a prediction result based on a pre-trained machine learning model, the prediction result indicating the predicted curvature of the potential energy surface for a second molecular configuration in a first subset; determine the difference between the prediction result and the second curvature label; and determine the first loss term based on the projection vector and the difference, the projection vector satisfying predetermined conditions.

[0086] In some examples, fine-tuning is based on a loss function that includes a first loss term and at least one second loss term. The first loss term corresponds to the curvature of the potential energy surface, and the second loss term corresponds to at least one of energy or force. The first weight of the first loss term in the loss function increases with the number of fine-tuning rounds.

[0087] In some examples, in the current round of multiple rounds, the loss function is determined as follows: based on a pre-trained machine learning model, a first loss term and at least one second loss term are obtained; based on the current round and a mapping relationship, a first weight is determined, the mapping relationship being used to linearly increase the first weight relative to the current round; and based on the first loss term, the first weight, at least one second loss term, and at least one second weight, the loss function is determined.

[0088] In some examples, the first curvature label is obtained using a tight-binding algorithm, and the second curvature label is obtained using density functional theory.

[0089] The modules included in device 500 can be implemented in various ways, including software, hardware, firmware, or any combination thereof. In some cases, one or more modules can be implemented using software and / or firmware, such as machine-executable instructions stored on a storage medium. In addition to or as an alternative to machine-executable instructions, some or all of the units in device 500 can be implemented at least partially by one or more hardware logic components. By way of example, and not limitation, exemplary types of hardware logic components that can be used include field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard parts (ASSPs), systems on a chip (SOCs), complex programmable logic devices (CPLDs), and so on.

[0090] Figure 6 A block diagram of an electronic device 600 according to other scenarios is shown. It should be understood that... Figure 6 The electronic device 600 shown is merely exemplary and should not be construed as limiting the functionality and scope of the examples described herein. Figure 6 The electronic device 600 shown can be implemented as the same or different electronic device as the electronic device 110 discussed above.

[0091] like Figure 6 As shown, electronic device 600 is in the form of a general-purpose electronic device. Components of electronic device 600 may include, but are not limited to, one or more processing units or processors 610, memory 620, storage device 630, one or more communication units 640, one or more input devices 650, and one or more output devices 660. Processor 610 may be a physical or virtual processor and is capable of performing various processes according to programs stored in memory 620. In a multiprocessor system, multiple processors execute computer-executable instructions in parallel to improve the parallel processing capability of electronic device 600.

[0092] Electronic device 600 typically includes multiple computer storage media. Such media can be any accessible media that is accessible to electronic device 600, including but not limited to volatile and non-volatile media, removable and non-removable media. Memory 620 can be volatile memory (e.g., registers, cache, random access memory (RAM)), non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof). Storage device 630 can be removable or non-removable media and can include machine-readable media, such as flash drives, disks, or any other media that can be used to store information and / or data and can be accessed within electronic device 600.

[0093] Electronic device 600 may further include additional removable / non-removable, volatile / non-volatile storage media. Although not explicitly stated... Figure 6 As shown, disk drives for reading from or writing to removable, non-volatile disks (e.g., "floppy disks") and optical disk drives for reading from or writing to removable, non-volatile optical disks can be provided. In these cases, each drive can be connected to a bus (not shown) via one or more data media interfaces. Memory 620 may include computer program product 625 having one or more program modules configured to perform various methods or actions of various examples.

[0094] The communication unit 640 enables communication with other electronic devices via a communication medium. Additionally, the functionality of the components of the electronic device 600 can be implemented using a single computing cluster or multiple computing machines capable of communicating via communication connections. Therefore, the electronic device 600 can operate in a networked environment using logical connections to one or more other servers, networked personal computers, or another network node.

[0095] Input device 650 can be one or more input devices, such as a mouse, keyboard, trackball, etc. Output device 660 can be one or more output devices, such as a monitor, speaker, printer, etc. Electronic device 600 can also communicate with one or more external devices (not shown) via communication unit 640 as needed. These external devices include storage devices, display devices, etc., and can communicate with one or more devices that enable user interaction with electronic device 600, or with any device that enables electronic device 600 to communicate with one or more other electronic devices (e.g., network card, modem, etc.). Such communication can be performed via an input / output (I / O) interface (not shown).

[0096] A computer-readable storage medium is provided that stores computer-executable instructions thereon, wherein the computer-executable instructions are executed by a processor to implement the methods described above. A computer program product is also provided, which is tangibly stored on a non-transitory computer-readable medium and includes computer-executable instructions, which are executed by a processor to implement the methods described above.

[0097] The flowcharts and / or block diagrams of the methods, apparatus, devices, and computer program products referred to herein describe various aspects. It should be understood that each block of the flowcharts and / or block diagrams, as well as combinations of blocks in the flowcharts and / or block diagrams, can be implemented by computer-readable program instructions.

[0098] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0099] Computer-readable program instructions can be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions that execute on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0100] The flowcharts and block diagrams in the accompanying figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products under various scenarios. In this respect, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the figures. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0101] Various examples have been described above. The foregoing descriptions are exemplary and not exhaustive, nor are they limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is chosen to best explain the principles, practical applications, or improvements to technology in the market, or to enable others skilled in the art to understand the various implementations disclosed herein.

Claims

1. A method for determining interactions, comprising: Obtain a first dataset, which corresponds to a plurality of first molecular configurations. The first dataset includes corresponding first curvature labels for the plurality of first molecular configurations, and the first curvature labels indicate the potential energy surface curvature of the corresponding first molecular configuration. Using the first dataset, a machine learning model is pre-trained, which is used to represent the potential function of the molecular system; Obtain a second dataset, which corresponds to multiple second molecular configurations. The multiple second molecular configurations are divided into a first subset and a second subset. The second molecular configurations in the first subset have a second curvature label, while the second molecular configurations in the second subset do not have a second curvature label. The second curvature label indicates the potential energy surface curvature of the corresponding second molecular configuration, and the precision of the second curvature label is greater than that of the first curvature label. as well as Using the second dataset, the pre-trained machine learning model is fine-tuned to obtain the potential function.

2. The method according to claim 1, wherein obtaining the second dataset comprises: Determine the distribution characteristics of the plurality of second molecular configurations, the distribution characteristics indicating the distribution of the plurality of second molecular configurations in at least one property space; Based on the distribution characteristics, the plurality of second molecular configurations are sampled to determine the first subset; as well as Based on each of the second molecular configurations in the first subset, the corresponding second curvature label for each of the second molecular configurations is determined.

3. The method of claim 2, wherein the distribution characteristic includes a structural distribution, the structural distribution indicating the distribution of the plurality of second molecular configurations in a structural space, and sampling the plurality of second molecular configurations includes: For each of the plurality of second molecular configurations, a local density is determined based on the structural distribution, the local density indicating the number of second molecular configurations similar to that configuration; and Based on the local density, a second molecular configuration belonging to the first subset is selected from the plurality of second molecular configurations.

4. The method of claim 2, wherein the distribution characteristic includes an energy distribution, the energy distribution indicating the distribution of the plurality of second molecular configurations in an energy space, and sampling the plurality of second molecular configurations includes: Based on the energy distribution, multiple energy levels are determined, including a target energy level; From the plurality of second molecular configurations, determine the set of molecular configurations belonging to the target energy level; as well as From the set of molecular configurations, select a second molecular configuration that belongs to the first subset.

5. The method of claim 2, wherein the machine learning model is used to perform prediction of the properties of the molecular system, and the at least one attribute space is related to the properties.

6. The method of claim 1, wherein the fine-tuning is based on a loss function, the loss function including a first loss term corresponding to the curvature of the potential energy surface, and the method further includes: Based on the pre-trained machine learning model, a prediction result is obtained, which indicates the predicted potential energy surface curvature for the second molecular configuration in the first subset. Determine the difference between the prediction result and the second curvature label; as well as Based on the projection vector and the difference, the first loss term is determined, wherein the projection vector satisfies a predetermined condition.

7. The method of claim 1, wherein the fine-tuning is based on a loss function, the loss function comprising a first loss term and at least one second loss term, the first loss term corresponding to the potential energy surface curvature, the second loss term corresponding to at least one of energy or force, and a first weight of the first loss term in the loss function increasing with the number of fine-tuning rounds.

8. The method of claim 7, wherein in the current round of the plurality of rounds, the loss function is determined as follows: Based on the pre-trained machine learning model, the first loss term and the at least one second loss term are obtained; Based on the current round and the mapping relationship, the first weight is determined, wherein the mapping relationship is used to linearly increase the first weight relative to the current round; and The loss function is determined based on the first loss term, the first weight, the at least one second loss term, and the at least one second weight.

9. The method of claim 1, wherein the first curvature label is obtained using a tight-binding algorithm, and the second curvature label is obtained using density functional theory.

10. An apparatus for determining an interaction, comprising: The first acquisition module is configured to acquire a first dataset, which corresponds to a plurality of first molecular configurations. The first dataset includes corresponding first curvature labels for the plurality of first molecular configurations, and the first curvature labels indicate the potential energy surface curvature of the corresponding first molecular configuration. The pre-training module is configured to pre-train a machine learning model using the first dataset, the machine learning model being used to represent the potential function of the molecular system; The second acquisition module is configured to acquire a second dataset, which corresponds to a plurality of second molecular configurations. The plurality of second molecular configurations are divided into a first subset and a second subset. The second molecular configurations in the first subset have a second curvature label, while the second molecular configurations in the second subset do not have a second curvature label. The second curvature label indicates the potential energy surface curvature of the corresponding second molecular configuration, and the precision of the second curvature label is greater than that of the first curvature label. as well as The fine-tuning module is configured to fine-tune the pre-trained machine learning model using the second dataset to obtain the potential function.

11. An electronic device, comprising: At least one processor; as well as At least one memory coupled to the at least one processor and storing instructions for execution by the at least one processor, the instructions causing the electronic device to perform the method according to any one of claims 1 to 9 when executed by the at least one processor.

12. A computer-readable storage medium having stored thereon computer-executable instructions that can be executed by a processor to implement the method according to any one of claims 1 to 9.

13. A computer program product tangibly stored in a computer storage medium and comprising computer-executable instructions that, when executed by a device, cause the device to perform the method according to any one of claims 1 to 9.

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