A Method and System for Predicting Molecular Properties Based on Multi-View Isomorphic Graph Neural Networks

Abstract

This invention belongs to the interdisciplinary field of artificial intelligence and computational chemistry, specifically relating to a method and system for predicting molecular properties based on multi-view equivariant graph neural networks, particularly suitable for high-precision molecular potential surface fitting and large-scale molecular dynamics simulations. Addressing the problems of existing equivariant networks relying on tensor products, resulting in high computational complexity, and being limited by local views in capturing long-range interactions, this invention first constructs a multi-granularity topological view encompassing microscopic atoms, mesoscopic motifs, and macroscopic pharmacophores. Second, utilizing vector inner products and scalar gating mechanisms, it performs scalar-vector decoupled equivariant interactions without tensor products, implicitly extracting local geometric features. Subsequently, it performs equivariant information fusion through cross-view attention, aggregating long-range nonlocal interactions. Finally, it combines physical priors to infer energy and forces, thereby obtaining molecular properties.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of artificial intelligence and computational chemistry, specifically relating to a method and system for predicting molecular properties based on multi-view equivariant graph neural networks, which is particularly suitable for high-precision molecular potential energy surface fitting and large-scale molecular dynamics simulation. Background Technology

[0002] In recent years, artificial intelligence has made groundbreaking progress in the application of scientific computing. In particular, in the fields of computational chemistry and materials science, the use of machine learning methods—especially graph neural networks (GNNs)—to fit molecular potential energy surfaces (PES), predict the quantum mechanical properties of molecules (such as total energy, atomic force, and dipole moment), and drive molecular dynamics (MD) simulations has become an important research paradigm to replace traditional first-principles calculations (such as density functional theory DFT).

[0003] To accurately predict physical quantities in three-dimensional Euclidean space, the model must strictly adhere to spatial symmetry, i.e., satisfy equivariance or invariance to three-dimensional rotation and translation. While existing equivariant graph neural networks have achieved extremely high accuracy on small molecule datasets, they still face several insurmountable deep-seated technical bottlenecks when applied to real-world scenarios (such as macromolecular drug design, protein folding simulation, and complex material systems): The inherent contradiction between expressive power and computational efficiency means that, in order to fully extract high-order geometric information (such as bond angles, dihedral angles, and inappropriate angles) that determines the molecular spatial conformation, existing high-precision equivariant models (such as NequIP and MACE) generally rely on irreducible representations in group representation theory and Clebsch-Gordan (CG) tensor product operations for equivariant message passing. However, the computational complexity of the CG tensor product explodes exponentially with the increase of the feature expansion order. This high computational cost results in extremely slow inference speeds when dealing with systems containing thousands of atoms, making it impossible to meet the high throughput requirements of long-term molecular dynamics simulations.

[0004] To avoid the computational curse of tensor products, some lightweight networks (such as EGNN and its variants) employ pure scalarization techniques, performing simple equivariant message passing only on first-order manipulable vectors (i.e., three-dimensional Cartesian coordinate vectors). However, recent theoretical research in geometric deep learning shows that if the model relies solely on first-order vector representations and lacks higher-order feature inputs, the network struggles to handle highly symmetric structures (such as regular polyhedral conformations, etc.). When dealing with re-rotationally symmetric molecules, "expressive capacity degradation" inevitably occurs. This means that such lightweight models cannot distinguish between symmetric or quasi-symmetric conformations with subtle local geometric differences, leading to severe local errors in potential energy surface fitting and subsequently causing system collapse in MD simulations.

[0005] Molecules are not simply stacks of atoms; their macroscopic physicochemical properties are often determined by complex nonlocal electronic effects and long-range interactions. Currently, almost all mainstream isovariant graph neural networks use a fixed "cutoff radius" (typically around 5.0 Å) to construct microscopic atomic adjacency graphs. This purely local message-passing mechanism, due to its limited "receptive field," can only capture local bonding interactions and short-range van der Waals forces, and cannot effectively model electrostatic interactions, hydrogen bond networks, and steric hindrance effects that determine the folding state of macromolecules over long distances. Blindly increasing the cutoff radius leads to a quadratic increase in the number of edges in the graph, further deteriorating computational efficiency.

[0006] In real chemical and biological systems, molecular structures naturally possess multi-scale hierarchical structures (e.g., atom-functional group / chemical motif-pharmacophore-polymer chain). However, existing graph neural network architectures typically only perform black-box information transmission at the lowest-level "atom-atom" single graph structure, lacking explicit modeling of mesoscopic rigid substructures and macroscopic pharmacophore features. This lack of chemical topological hierarchy significantly limits the model's ability to understand the global conformational evolution of complex macromolecular systems.

[0007] Existing machine learning models for predicting force fields and molecular properties suffer from irreconcilable contradictions regarding computational complexity (due to the inability to escape tensor products), upper limits of geometric representation (symmetry degradation), and the capture of long-range physical effects (limited by local atomic graphs). Therefore, there is an urgent need in this field for a novel network architecture capable of fully extracting high-order geometric features and efficiently capturing multi-scale long-range interactions of molecules without incurring exponentially higher computational costs. Summary of the Invention

[0008] The purpose of this invention is to address the problems existing in the prior art, such as high computational complexity of isovariant graph neural networks (dependent on tensor products), difficulty in capturing long-range nonlocal interactions (limited by local atomic graphs), and easy degradation of expressive power of lightweight networks in highly symmetric structures. The purpose of this invention is to provide a molecular property prediction method and system based on multi-view isovariant graph neural networks, so as to achieve large-scale molecular dynamics simulation and property prediction with high accuracy, strict physical conservation and high computational efficiency.

[0009] The technical solution of the present invention: A method for predicting molecular properties based on a multi-view isomorphic graph neural network includes the following steps: Step 1: Obtain initial molecular data The three-dimensional structural data of the target molecule are obtained, and the atomic number and initial spatial coordinates of the target molecule are extracted as the initial molecular data.

[0010] Step 2: Construct a multi-granularity topology view Based on the initial molecular data, a microscopic atomic view of the molecule and at least one subview for characterizing the medium- and long-range structure are constructed to form a multi-granularity topological view. The microscopic atomic view uses atoms as nodes and pairs of atoms within a preset cutoff radius to form edges. The subview uses chemical rules to divide the target molecule into multiple substructures, treats each substructure as a supernode, calculates the representative spatial coordinates of atoms within the substructure as the coordinates of the supernode, and constructs edges according to the connection relationships between substructures.

[0011] The sub-views include a sequence view and a pharmacophore view, and the representative spatial coordinates are the geometric center coordinates or mass center coordinates of all atoms within the substructure.

[0012] Step 3: Perform scalar-vector decoupling interaction without tensor product within the view. The node features within each of the multi-granularity topology views are initialized as scalar features and vector features, and multi-layer equivariant message passing is performed without relying on tensor product operations. In the interactive update of each layer: local geometric invariants that are invariant to rotation and translation are extracted by calculating the inner product of the vector features of adjacent nodes; the scalar features of this layer are updated using neural network mapping by combining the local geometric invariants, the spatial relative positions between nodes, and the features of the previous layer; scalar gating weights are generated using the scalar information flow during the update process, and the vector features of this layer are updated by combining the vector features of adjacent nodes and their relative position vectors.

[0013] When performing equivariant message passing, the input spatial relative position vector is encoded using a spherical harmonic function containing a maximum order setting to generate the initial node features of the microscopic atomic view.

[0014] Step 4: Perform cross-view variable information fusion After at least one round of equivariant message passing within the multi-granularity topology view, the cross-view attention weight between the micro-atomic node and its associated meso- or macro-super node is calculated. Using the cross-view attention weight, the updated features in the meso- or macro-view are injected and fused into the micro-atomic view in the form of equivariant mapping, thereby aggregating the long-range nonlocal interaction information of molecules and completing the cross-view equivariant information fusion.

[0015] Step 5: Predict and output molecular properties After obtaining the final microscopic atomic node features through cross-view isovariant information fusion, a prediction network is used to map these features into the local energy prediction values ​​of each atom. Based on the task level of the molecular attribute to be predicted, when the prediction task is a global attribute, the local energy prediction values ​​of each atom are summed with the prior reference energy of a single isolated atom to obtain the total energy prediction value of the target molecule. When the prediction task is a local attribute, based on the total energy prediction value, an automatic differentiation mechanism is used to calculate its negative gradient relative to the initial spatial coordinates of the atom, obtaining the force prediction value of each atom. Finally, the energy prediction value or force prediction value is used as the molecular attribute prediction value.

[0016] A molecular attribute prediction system based on a multi-view isomorphic graph neural network, used to implement the above method, includes: Data acquisition module: used to acquire initial molecular data and extract the atomic number and initial spatial coordinates of the target molecule; View construction module: used to construct multi-granularity topological views, based on the initial molecular data, constructing a microscopic atomic view of the molecule, and at least one subview for characterizing medium- and long-range structures; wherein, the microscopic atomic view uses atoms as nodes, and the subview uses substructures as supernodes; Equivariant Interaction Module: Used to perform scalar-vector decoupling interactions without tensor product within each view, updating the scalar and vector features of nodes through local geometric invariants and scalar gating mechanisms; Feature fusion module: used to perform cross-view isovariant information fusion, injecting and fusing updated features from subviews into the microscopic atomic views; The attribute prediction module is used to predict and output molecular attributes. It maps the features of the microscopic atomic nodes to the local energy prediction values ​​of each atom, and sums the local energy prediction values ​​of each atom with the prior reference energy of a single isolated atom to obtain the total energy prediction value of the target molecule. When the prediction task involves forces, it uses an automatic differentiation mechanism to calculate the gradient of the total energy prediction value with respect to the initial spatial coordinates of the atom, obtains the force prediction value, and outputs it.

[0017] Beneficial results of the present invention: (1) Break through the "precision-efficiency" bottleneck and achieve linear computational complexity. This invention proposes a scalar-vector decoupling interaction mechanism without tensor product. By extracting geometric invariants through a simple vector inner product and updating 3D vector features using a scalar gating mechanism, it implicitly and completely extracts high-order geometric information (such as angles and dihedrals) while completely eliminating the time-consuming Clebsch-Gordan tensor product transformation. This reduces the algorithm's time complexity from exponential to linear, enabling efficient simulation of large molecular systems containing thousands of atoms.

[0018] (2) Multi-scale topology modeling accurately captures long-range nonlocal interactions This invention overcomes the limitations of traditional models that are confined to a single local atomic map, and innovatively introduces multi-granularity views at the microscopic (atomic), mesoscopic (chemical motif), and macroscopic (pharmacentor) levels. Through a carefully designed cross-view attention fusion mechanism, local microscopic atoms can instantly perceive and aggregate the global macroscopic topological environment, greatly improving the model's prediction accuracy for nonlocal physical effects such as long-range electrostatic interactions, hydrogen bond networks, and steric hindrance.

[0019] (3) Balancing strict physical energy conservation with the ultimate upper limit of structural expression This invention directly utilizes an automatic differentiation mechanism at the output end to derive the potential energy surface to obtain the atomic force, strictly ensuring the law of conservation of energy in physics. On the other hand, it introduces a high-order spherical harmonic function in the feature initialization stage, effectively breaking the problem of symmetry expression degradation that easily occurs when pure scalar lightweight networks deal with highly symmetric molecules, and significantly enhancing the network's ability to distinguish small changes in three-dimensional local conformation. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall process of the molecular property prediction method based on a multi-view equivariant graph neural network provided in an embodiment of the present invention; Figure 2 This is an architecture diagram of multi-granularity topology view construction and cross-view information fusion provided in the embodiments of the present invention; Figure 3 This is a structural diagram of the scalar-vector decoupling interactive update module without tensor product provided in an embodiment of the present invention. Detailed Implementation

[0021] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0022] The method provided in this embodiment aims to construct a computational framework called a "multi-view equivariant network," and the overall process is as follows: Figure 1 As shown, the specific steps include: Step S1: Obtain initial molecular data.

[0023] Obtain the three-dimensional conformational data of the target molecule from a database (such as QM9, MD22, etc.) or external simulation software. Specifically, parse the given molecular data file to extract the atomic number of each atom in the target molecule containing N atoms. (Characterizing element type, serving as the initial scalar feature source) and initial three-dimensional spatial coordinates .

[0024] Step S2: Construct a multi-granularity topology view Traditional graph neural networks operate only on local atomic graphs, making it difficult to capture nonlocal effects. This invention constructs a hierarchical topological view (such as...). Figure 2 (As shown in the left figure) (1) Atom View: Atoms are the nodes. For each atom, the neighboring atoms within the cutoff radius (e.g., set to 5.0 Å) are searched to form an edge, which is used to capture short-range chemical bonding and van der Waals repulsion.

[0025] (2) Motif / JTView: The molecule is divided into multiple rigid or semi-rigid chemical substructure motifs (such as benzene rings, carboxyl groups, etc.) using chemical bond-breaking rules (e.g., the BRICS algorithm). Each substructure is considered a "supernode". The geometric center coordinates or mass center coordinates of all atoms within the substructure are calculated as the representative spatial coordinates of the supernode. The edges of the mesoscopic view are constructed based on the chemical bond connections between the substructures.

[0026] (3) Pharmacophore View: Based on the pharmacophore features of molecules (such as hydrogen bond donors / acceptors, hydrophobic groups, aromatic rings, etc.), atoms or motifs with similar pharmacophore features are clustered into supernodes to construct a macroscopic topological view.

[0027] Step S3: Perform scalar-vector decoupling interaction without tensor product within the view. This is the core feature extraction module of this invention (e.g., Figure 3 As shown). Feature updates are performed independently within each view. First, to overcome the representational degradation of lightweight networks on highly symmetric structures, features containing the maximum order (such as...) are utilized. The spherical harmonic function is defined to encode the spatial relative position vector of the microscopic atomic view input, generating initial node features. Subsequently, the features of nodes within each view are decoupled into scalar features. and three-dimensional vector features Without relying on expensive tensor product operations, perform Layer-by-layer iterative updates. layer to the first The formula for equivariant message passing in a layer is as follows: Extracting local geometric invariants: ,in, For nodes With nodes In the Local geometric invariants of the layer For nodes In the The three-dimensional vector features of the layer For nodes In the The three-dimensional vector features of the layer This represents the vector dot product. Value representation node With nodes The rotation-invariant geometric features such as angles and dihedrals are implicitly extracted from the hidden space.

[0028] Scalar feature update: ,in, For nodes In the scalar characteristics of layers For nodes In the scalar characteristics of layers Represents a node The set of neighboring nodes, To represent nodes With nodes The spatial relative position vectors between them Represents the magnitude of a vector. For distance, This represents a scalar update function parameterized by a multilayer perceptron.

[0029] Vector feature update: ,in, The first scalar gating weights, generated by mapping the updated scalar information stream through a neural network, are used to adjust the vector features of neighboring nodes. It is a second scalar gating weight generated by mapping the updated scalar information stream through a neural network, used to adjust the spatial relative position vector. By utilizing the rotation of the scalar gating vector, the directional equivariance in three-dimensional space is strictly guaranteed.

[0030] Step S4: Perform cross-view isovariant information fusion (e.g.) Figure 2 (As shown in the right figure). After multiple (e.g., 2) independent message passes between different views, cross-scale bidirectional or unidirectional information fusion is performed. The feature fusion process from subgraph view to micro-atomic view: First, the micro-atomic nodes are calculated. and its subgraph view node Cross-view attention weights Then, the updated features in the subgraph view are broadcast down to the micro-atomic view, and the specific fusion formula is as follows: Scalar feature fusion: Vector feature fusion: in, Nodes in the fused microscopic atomic view scalar characteristics, Nodes in the fused microscopic atomic view Vector features, and These are nodes in the microscopic atomic view. scalar and vector features; and Super nodes in the subgraph view scalar and vector features; Indicates atomic nodes A set of basal sequence nodes with a mapping relationship. and These represent the parameterized scalar feature alignment mapping function and the vector feature alignment mapping function, respectively. This step allows the underlying atoms to instantly acquire the global structural context.

[0031] Step S5: Predict and output molecular properties The prediction network consists of multiple stacked MLP layers. Activation functions are used for scalar features, and linear transformations are applied to vector features. This prediction network maps the fused atomic scalar features to predicted local energies of those atoms. .

[0032] Typically, to accelerate model convergence and ensure adherence to the physical context, a reference energy of a single isolated atom is introduced as a priori. Summing these values ​​yields the predicted total energy of the molecules. : in, The total number of atoms in the target molecule. For atoms Local energy prediction values, For a single isolated atom, This is the predicted total energy of the molecule.

[0033] Finally, to ensure that the force field prediction strictly follows the law of energy conservation, the automatic differentiation mechanism of the deep learning framework is used to calculate the negative gradient of the total energy prediction value with respect to the initial spatial coordinates of the atom as the force prediction value. : in, For atoms The initial spatial coordinates, For atoms The predicted stress values.

[0034] During the training phase, the network parameters are updated using a weighted sum of energy loss and force loss.

Claims

1. A method for predicting molecular attributes based on a multi-view isomorphic graph neural network, characterized in that, Includes the following steps: Step 1: Obtain initial molecular data The three-dimensional structural data of the target molecule are obtained, and the atomic number and initial spatial coordinates of the target molecule are extracted as the initial molecular data. Step 2: Construct a multi-granularity topology view Based on the initial molecular data, a microscopic atomic view of the molecule and at least one sub-view for characterizing the medium- and long-range structure are constructed to form a multi-granularity topological view. The microscopic atomic view uses atoms as nodes and pairs of atoms within a preset cutoff radius to form edges. The sub-view uses chemical rules to divide the target molecule into multiple substructures, treats each substructure as a super node, calculates the representative spatial coordinates of atoms within the substructure as the coordinates of the super node, and constructs edges according to the connection relationships between substructures. Step 3: Perform scalar-vector decoupling interaction without tensor product within the view. The node features within each of the multi-granularity topological views are initialized as scalar features and vector features, and multi-layer equivariant message passing is performed without relying on tensor product operations. In the interactive update of each layer: local geometric invariants that are invariant to rotation and translation are extracted by calculating the inner product of the vector features of adjacent nodes; the scalar features of this layer are updated using neural network mapping by combining the local geometric invariants, the spatial relative positions between nodes, and the features of the previous layer; scalar gating weights are generated using the scalar information flow during the update process, and the vector features of this layer are updated by combining the vector features and relative position vectors of adjacent nodes. Step 4: Perform cross-view variable information fusion After at least one round of equivariant message passing within the multi-granularity topology view, the cross-view attention weight between the micro-atomic node and its corresponding meso- or macro-view supernode is calculated. Using the cross-view attention weight, the updated features in the meso- or macro-view are injected and fused into the micro-atomic view in the form of equivariant mapping to aggregate the long-range nonlocal interaction information of molecules and complete the cross-view equivariant information fusion. Step 5: Predict and output molecular properties After obtaining the final microscopic atomic node features through cross-view isovariant information fusion, a prediction network is used to map these features into the local energy prediction values ​​of each atom. Based on the task level of the molecular attribute to be predicted, when the prediction task is a global attribute, the local energy prediction values ​​of each atom are summed with the prior reference energy of a single isolated atom to obtain the total energy prediction value of the target molecule. When the prediction task is a local attribute, based on the total energy prediction value, an automatic differentiation mechanism is used to calculate its negative gradient relative to the initial spatial coordinates of the atom, obtaining the force prediction value of each atom. Finally, the energy prediction value or force prediction value is used as the molecular attribute prediction value.

2. The molecular attribute prediction method based on a multi-view isomorphic graph neural network according to claim 1, characterized in that, The sub-graph view includes a sequence view and a pharmacophore view, and the representative spatial coordinates are the geometric center coordinates or mass center coordinates of all atoms within the substructure.

3. The molecular attribute prediction method based on a multi-view isomorphic graph neural network according to claim 1, characterized in that, When performing equivariant message passing, the input spatial relative position vector is encoded using a spherical harmonic function containing a maximum order setting to generate the initial node features of the microscopic atomic view.

4. The molecular attribute prediction method based on a multi-view isomorphic graph neural network according to claim 1, characterized in that, In step 3, the features of nodes within each view are decoupled into scalar features. and three-dimensional vector features ,conduct Layer iterative update; the first layer to the first The formula for equivariant message passing in a layer is as follows: Extracting local geometric invariants: ,in, For nodes With nodes In the Local geometric invariants of the layer For nodes In the 3D vector features of the layer For nodes In the The three-dimensional vector features of the layer Represents the dot product of vectors; Scalar feature update: ,in, For nodes In the scalar characteristics of layers For nodes In the scalar characteristics of layers Represents a node The set of neighboring nodes, To represent nodes With nodes The spatial relative position vectors between them Represents the magnitude of a vector. For distance, This represents a scalar update function parameterized by a multilayer perceptron; Vector feature update: ,in, The first scalar gating weights, generated by mapping the updated scalar information stream through a neural network, are used to adjust the vector features of neighboring nodes. It is a second scalar gating weight generated by mapping the updated scalar information stream through a neural network, used to adjust the spatial relative position vector.

5. The molecular attribute prediction method based on a multi-view isomorphic graph neural network according to claim 1, characterized in that, In step 4, the feature fusion process from the sub-graph view to the micro-atomic view involves: first, calculating the micro-atomic nodes. Its subgraph view supernode Cross-view attention weights ; Then, the updated features in the subgraph view are broadcast down to the micro-atomic view, and the specific fusion formula is as follows: Scalar feature fusion: Vector feature fusion: in, Nodes in the fused microscopic atomic view scalar characteristics, Nodes in the fused microscopic atomic view Vector features, and These are nodes in the microscopic atomic view. scalar and vector features; and Super nodes in the subgraph view scalar and vector features; Indicates atomic nodes A set of base sequence nodes with a mapping relationship. and These represent the parameterized scalar feature alignment mapping function and the vector feature alignment mapping function, respectively.

6. The molecular attribute prediction method based on a multi-view isomorphic graph neural network according to claim 1, characterized in that, In step 5, a prediction network is used to map the fused atomic scalar features to the predicted local energy values ​​of the atoms. The prediction network consists of multiple stacked MLP layers. Activation functions are used for scalar features, and linear transformations are used for vector features. The calculation of predicted and output molecular properties satisfies the following formula: Total energy forecast: in, The total number of atoms in the target molecule. For atoms Local energy prediction values, For a single isolated atom, This is the predicted total energy of the molecule. Predicted stress values: in, For atoms The initial spatial coordinates, For atoms The predicted stress values.

7. A molecular attribute prediction system based on a multi-view equivariant graph neural network, used to implement the method described in any one of claims 1-6, characterized in that, include: Data acquisition module: used to acquire initial molecular data and extract the atomic number and initial spatial coordinates of the target molecule; View construction module: used to construct multi-granularity topological views, based on the initial molecular data, constructing a microscopic atomic view of the molecule, and at least one subview for characterizing medium- and long-range structures; wherein, the microscopic atomic view uses atoms as nodes, and the subview uses substructures as supernodes; Equivariant Interaction Module: Used to perform scalar-vector decoupling interactions without tensor product within each view, updating the scalar and vector features of nodes through local geometric invariants and scalar gating mechanisms; Feature fusion module: used to perform cross-view isovariant information fusion, injecting and fusing updated features from subviews into the microscopic atomic view; The attribute prediction module is used to predict and output molecular attributes. It maps the features of the microscopic atomic nodes to the local energy prediction values ​​of each atom, and sums the local energy prediction values ​​of each atom with the prior reference energy of a single isolated atom to obtain the total energy prediction value of the target molecule. When the prediction task involves forces, it uses an automatic differentiation mechanism to calculate the gradient of the total energy prediction value with respect to the initial spatial coordinates of the atom, obtains the force prediction value, and outputs it.

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