Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization

ArXi:2605.07157v1 Announce Type: new We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range predictions. We develop an optimization-based integrator that minimizes the squared Euler--Lagrange residual via a mesh-free near-symplectic construction on local space-time patches.