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Quantum Machine Learning Quantum Chemistry

From {\tt Ferminet} to PINN. Connections between neural network-based algorithms for high-dimensional Schrödinger Hamiltonian

arXiv
Authors: Mashhood Khan, Emmanuel Lorin

Year

2024

Paper ID

38205

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

In this note, we establish some connections between standard (data-driven) neural network-based solvers for PDE and eigenvalue problems developed on one side in the applied mathematics and engineering communities (e.g. Deep-Ritz and Physics Informed Neural Networks (PINN)), and on the other side in quantum chemistry (e.g. Variational Monte Carlo algorithms, {\tt Ferminet} or {\tt Paulinet} following the pioneer work of {\it Carleo et. al}. In particular, we re-formulate a PINN algorithm as a {\it fitting} problem with data corresponding to the solution to a standard Diffusion Monte Carlo algorithm initialized thanks to neural network-based Variational Monte Carlo. Connections at the level of the optimization algorithms are also established.

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  • In this note, we establish some connections between standard (data-driven) neural network-based solvers for PDE and eigenvalue problems developed on one side in the applied...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2410.09177 [2] arXiv https://arxiv.org/abs/2410.09177 [3] Publisher https://arxiv.org/abs/2410.09177

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