Learning features from Newton's algorithm: a way to accelerate nonlinear parametrized PDE solvers

תקציר מקורי באנגליתarXiv:2607.28036v1 Announce Type: new Abstract: It is well known that Newton's method converges faster when the initial guess is closer to a root of a system of nonlinear equations. In this paper, a two-stage Newton initial guess strategy is proposed by learning features from a parameter-space sampling and a database of precomputed solutions. The method uses discrete Newton trajectories to construct two complementary reduced spaces: a solution feature space, built from converged states, and a corrective search direction feature space, built from intermediate Newton increments. For an unseen parameter, a regression model is used to predict a surrogate solution approximation. Then, in a second step, a residual-minimizing correction is computed using a dedicated GMRES-based approach. The resu