Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks

Area of Science:

• Quantum chemistry
• Computational materials science

Background:

• The Schrödinger equation is fundamental to chemistry, enabling property computation for materials discovery.
• Solving the Schrödinger equation is computationally intensive, scaling exponentially with particle number.
• Current neural network methods for solving the Schrödinger equation do not leverage multi-geometry data.

Purpose of the Study:

• To accelerate the computation of molecular properties by improving neural network solutions to the Schrödinger equation.
• To develop a method that exploits synergies across different molecular geometries.

Main Methods:

• Utilized a combination of Monte Carlo techniques and unsupervised neural network optimization.
• Implemented weight-sharing across neural network models trained on different molecular geometries.
• Developed pretrained models that require minimal fine-tuning for new geometries.

Main Results:

• Weight-sharing substantially accelerated the optimization of neural networks for solving the Schrödinger equation.
• Pretrained models achieved high-accuracy solutions for new geometries with fewer optimization steps.
• The method effectively overcomes the curse of dimensionality in quantum mechanical calculations.

Conclusions:

• Sharing neural network weights across geometries is a highly effective strategy for accelerating Schrödinger equation solutions.
• This approach significantly enhances the efficiency of computational chemistry for materials discovery.
• The developed method provides a pathway to faster discovery of novel drugs and catalysts.