SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation

Area of Science:

• Quantum Chemistry
• Computational Physics
• Machine Learning

Background:

• Machine learning advances enable accurate solutions to the electronic Schrödinger equation (SE) using neural networks (NNs) and variational Monte Carlo.
• Current NN-based methods rely on the Born-Oppenheimer approximation (BOA) and require extensive training for each nuclear configuration.

Purpose of the Study:

• To develop a novel NN architecture, SchrödingerNet, for solving the full electronic-nuclear SE.
• To enable efficient and accurate generation of continuous potential energy surfaces.
• To incorporate non-Born-Oppenheimer (non-BOA) corrections within a single training process.

Main Methods:

• Proposed a novel NN architecture, SchrödingerNet.
• Defined a loss function to equalize local energies across the system.
• Employed a symmetry-adapted total wave function ansatz including nuclear and electronic coordinates.

Main Results:

• Achieved accurate and efficient generation of continuous potential energy surfaces.
• Successfully incorporated non-BOA corrections.
• Demonstrated accuracy and efficiency through benchmarks on atomic and small molecular systems.

Conclusions:

• SchrödingerNet offers an efficient and accurate method for solving the full electronic-nuclear SE.
• The approach overcomes limitations of BOA-based methods.
• Enables seamless integration of quantum mechanical calculations with machine learning.