Machine Learning-Generated Effective Interaction Models for Chemistry

In this talk, we present a physically informed neural network (NN) framework for representing the effective interactions arising from coupled-cluster downfolding models for chemical systems and processes. This approach, termed the VNet model [1,2], enables efficient evaluation of effective interactions across a wide range of molecular geometries and correlation regimes, spanning varying levels of complexity in the underlying many-body wave functions. Beyond computational efficiency, the NN representation reveals a structured relationship between bare and effective interactions, which can be expressed through a tangent functional dependence on a set of latent variables. We refer to this characterization as the tangent model of the effective interaction. We further discuss how this tangent model connects to earlier theoretical analyses that quantify the differences between bare and effective Hamiltonians within corresponding active spaces. More broadly, VNet and related NN-based techniques provide a unifying framework that brings together diverse many-body methodologies, enabling the construction of effective Hamiltonians across distinct domains of quantum mechanics, including quantum chemistry and nuclear physics.

[1] S. Liang, K. Kowalski, C. Yang, N.P. Bauman, “Effective many-body interactions in reduced-dimensionality spaces through neural network models,” Phys. Rev. Res. 6, 043287 (2024).

[2] S. Liang, K. Kowalski, C. Yang, N.P. Bauman, “Exploring the nexus of many-body theories through neural network techniques: the tangent model,” Machine Learning: Science and Technology 6, 025040 (2025).