Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.09177 |
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Inhaltsangabe:
- 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.