Permutation invariant polynomial neural network approach to fitting potential energy surfaces

Area of Science:

• Computational chemistry
• Molecular modeling
• Machine learning in quantum chemistry

Background:

• Accurately representing molecular potential energy surfaces is crucial for chemical reaction dynamics.
• Incorporating permutation symmetry into models is essential for molecular systems with identical atoms.
• Neural networks offer powerful tools for fitting complex potential energy surfaces.

Purpose of the Study:

• To develop a general and rigorous scheme for adapting permutation symmetry in molecular systems.
• To apply this scheme for fitting global potential energy surfaces using neural networks.
• To validate the accuracy of the proposed method through quantum scattering calculations.

Main Methods:

• A symmetry adaptation scheme using low-order permutation invariant polynomials (PIPs) as inputs for neural networks (NNs).
• The PIP-NN approach was applied to the H + H2 and Cl + H2 systems.
• Neural network models were trained to represent the potential energy surfaces.

Main Results:

• The PIP-NN approach accurately reproduced the analytical potential energy surfaces for H + H2 and Cl + H2.
• The developed neural network potentials demonstrated high fidelity compared to existing surfaces.
• Quantum scattering calculations confirmed the accuracy of the generated NN potential energy surfaces.

Conclusions:

• The PIP-NN method provides a simple, general, and rigorous way to incorporate permutation symmetry.
• This approach enables accurate global potential energy surface fitting for molecular systems.
• The validated accuracy of PIP-NN potentials is suitable for high-fidelity chemical dynamics simulations.