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math.NA2026
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…
math.NA2026
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…