AI Agent Research Hub

Oct 26, 2026 · Artificial Intelligence

Deflation-PINNs: Finding All Solutions of Nonlinear PDEs in a Single Training Run

The paper introduces Deflation-PINNs and Deflation-Deep-Ritz to discover, certify, and refine multiple solutions of nonlinear PDEs simultaneously, using a shared trunk network with branch vectors and a pairwise repulsion loss, validated via gradient flow on the Landau-de Gennes model and Allen-Cahn benchmark, achieving high accuracy after refinement.