18 citations · 21 across the 8 of their papers we have counts for
3 papers · 1 filter
Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes
Sean Disarò, Ruma Rani Maity, Aras Bacho
Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful…
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
Beatrice Lorenz, Aras Bacho, Gitta Kutyniok
This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training err…
KROM: Kernelized Reduced Order Modeling
Aras Bacho, Jonghyeon Lee, Houman Owhadi
We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-proc…