Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes
Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE problems, they typically struggle to identify multiple distinct solutions, since they are designed to find one solution at a time. To address this limitation, we introduce Deflation-PINNs, a novel framework that integrates a deflation loss with an architecture based on PINNs and Deep Operator Networks (DeepONets). By incorporating a deflation term into the loss function, our method systematically forces the Deflation-PINN to seek and converge upon distinct finitely many solution branches. W...
| Authors | Sean Disarò, Ruma Rani Maity, Aras Bacho |
|---|---|
| Primary category | math.NA |
| Published | 30 March 2026 |
| Last updated at source | 28 August 2026 |
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