Speaker
Description
We present a novel machine learning approach to develop energy-preserving reduced-order models (ROMs) by exploiting the multi-symplectic structure of partial differential equations (PDEs). Traditional energy-preserving ROMs often rely on the symplectic Galerkin projection, which requires fully discrete operators - often unavailable in black-box PDE solvers. Our method circumvents this limitation by inferring the PDE dynamics directly from the data, eliminating the need for fully discrete operators and maintaining a non-intrusive framework. The proposed approach is gray-box in the sense that it requires only minimal knowledge of the multi-symplectic model at the PDE level. We show that our method ensures spatially discrete local energy conservation and preserves multi-symplectic conservation laws. Validation of the method is performed on the linear wave equation, the Korteweg-de Vries equation, and the Zakharov-Kuznetsov equation, with successful generalization beyond the training time interval.
