Orbital mixer machine learning method for predicting an electronic structure of an atomic system
A machine learning (ML) method for predicting an electronic structure of an atomic system. The method includes receiving an atomic identifier and an atomic position for atoms in the atomic system; receiving a basis set including rules for forming atomic orbitals of the atomic system; forming the atomic orbitals of the atomic system; and predicting an electronic structure of the atomic system based on the atom identifier, the atom position for the atoms in the atomic system, and the atomic orbitals of the atomic system. The ML method is capable of extremely accurate and fast molecular property prediction. The ML can directly purpose basis dependent information to predict molecular electronic structure. The ML method, which may be referred to as an orbital mixer model, uses multi-layer perception (MLP) mixer layers within a simple, intuitive, and scalable architecture to achieve competitive Hamiltonian and molecular orbital energy and coefficient prediction accuracies.
1 . A machine learning method for predicting an electronic structure of an atomic system, the method comprising:
receiving an atomic identifier and an atomic position for atoms in the atomic system;
receiving a basis set including rules for forming atomic orbitals of the atomic system;
forming the atomic orbitals of the atomic system; and
predicting an electronic structure of the atomic system based on the atom identifier, the atom position for the atoms in the atomic system, and the atomic orbitals of the atomic system, the basis set and the atomic orbitals of the atomic system are introduced into the machine learning method during training such that the machine learning method predicts the electronic structure with a reduced number of self-consistent iterations with reduced computational expense.
2 . The machine learning method of claim 1 , further comprising forming an overlap matrix based on the atomic orbitals of the atomic system and the atomic positions for the atoms in the atomic system, where the overlap matrix includes entries (i n ,j n ) between 0 and 1, the entries (i n ,j n ) including entry (i,j) representing an overlap of atomic orbitals i and j i n space where 1 represents the i and j atomic orbitals are identical and 0 represents the i and j atomic orbitals do not overlap.
3 . The machine learning method of claim 2 , further comprising applying a linear transformation to rows of the overlap matrix to obtain an overlap matrix representation.
4 . The machine learning method of claim 3 , further comprising passing the overlap matrix representation through L 1 multi-layer perception (MLP) mixer layers.
5 . The machine learning method of claim 4 , further comprising determining a multi-feature embedding for one or more of the atomic orbitals by embedding categorical features of each of the atomic orbitals to form a set of embedded categorical features and summing the set of embedded categorical features to obtain multi-feature atomic orbital embeddings.
6 . The machine learning method of claim 5 , further comprising summing the multi-feature atomic orbital embeddings and the overlap matrix representation to obtain a molecular representation.
7 . The machine learning method of claim 6 , further comprising applying a linear transformation to rows of the molecular representation to obtain a diagonal correction term.
8 . The machine learning method of claim 7 , further comprising passing the molecular representation through L 2 MLP mixer layers to obtain a mixer layer output, the L 2 MLP mixer layers are in addition to the L 1 MLP mixer layers, and applying a linear transformation to the mixer layer output to obtain a refined molecular representation.
9 . The machine learning method of claim 8 , further comprising adding the diagonal correction term and the diagonal of the refined molecular representation to obtain a diagonal-corrected refined molecular representation.
10 . The machine learning method of claim 9 , further comprising adding a transpose of the diagonal-corrected refined molecular representation to the diagonal-corrected refined molecular representation to obtain a predicted Hamiltonian matrix indicative of the electronic structure of the atomic system.
11 . The machine learning method of claim 1 , wherein the machine learning method is a deep neural network learning method.
12 . A machine learning training method for training parameters of a machine learning model for predicting an electronic structure of an atomic system, the method comprising:
receiving a true electronic structure of the atomic system;
receiving a basis set including rules for forming first and second atomic orbitals of the atomic system;
predicting a predicted electronic structure of the atomic system by performing a forward pass through the machine learning model using the basis set;
determining a loss by comparing the true electronic structure and the predicted electronic structure of the atomic system; and
training the machine learning model by updating the parameters of the machine learning model based on the loss and a machine learning optimizer, the basis set and the atomic orbitals of the atomic system are introduced into the machine learning model during training such that the machine learning model predicts the electronic structure with a reduced number of self-consistent iterations with reduced computational expense.
13 . The machine learning training method of claim 12 , further comprising controlling a device utilizing the first and second atomic systems depending on the updated parameters of the machine learning model.
14 . The machine learning training method of claim 12 , wherein the machine learning model is a deep neural network.
15 . The machine learning training method of claim 14 , wherein the deep neural network is modified by a deep neural network modification.
16 . The machine learning training method of claim 15 , wherein the deep neural network modification is selected from the group consisting of: dropout, batch normalization, layer normalization, and weight decay.
17 . The machine learning training method of claim 12 , wherein the machine learning model has a multi-layer perception (MLP) mixer layer.
18 . A machine learning method for predicting molecular orbital characteristics of a molecule, the method comprising:
receiving atomic positions and atomic identifiers of atoms in the molecule;
receiving a basis set including rules for forming atomic orbitals of the molecule;
predicting a predicted electronic structure and calculating an overlap matrix of the molecule by performing a forward pass using the atomic positions, the atomic identifiers, and the basis set; and
predicting the molecular orbital characteristics based on the predicted electronic structure and the overlap matrix, the basis set and the atomic orbitals of the atomic system are introduced into the machine learning method during training such that the machine learning method predicts the electronic structure with a reduced number of self-consistent iterations with reduced computational expense.
19 . The machine learning method of claim 18 , wherein the molecular orbital characteristics include molecular orbital coefficients and/or molecular orbital energies.
20 . The machine learning method of claim 18 , wherein the second predicting step uses the predicted electronic structure and the overlap matrix to solve the eigenvalue problem of {circumflex over (F)}C=SCE to obtain the molecular orbital characteristics.