Neural and Tensor Networks for PDEs: PINNs, Neural Operators, and Low-Rank Approximation
| When |
May 12, 2026
from 01:00 to 02:00 |
|---|---|
| Where | M7 101 |
| Attendees |
Carlo Marcati |
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Carlo Marcati
Title: Neural and Tensor Networks for PDEs: PINNs, Neural Operators, and Low-Rank Approximation
In this talk, I will present some recent work in scientific machine learning and nonlinear approximation. I will introduce neural operators, i.e., neural network (NN)-based methods designed to learn the mapping from coefficients to solutions of partial differential equations (PDEs). I will present both approximation-theoretic results for elliptic PDEs and computational results for a new architecture tailored to PDEs posed on complex domains.
I will then discuss two (unrelated) applications of low-rank decompositions: first, how low-rank preconditioners can be used to improve the training of Physics-Informed Neural Networks (PINNs); and second, how tensor train decompositions and Riemannian optimization can be employed to accelerate the computation of ground states of the Gross–Pitaevskii equation.
Website: https://math.univ-lyon1.fr/~marcati/
In Room M7 101, 1st floor, Monod campus, ENSL (to be confirmed).