Learns stable, interpretable Koopman generators for nonlinear PDEs from trajectory data alone without any physics supervision.
April 1, 2026
Original Paper
Lie Generator Networks for Nonlinear Partial Differential Equations
arXiv · 2603.29264
The Takeaway
By decomposing the generator into skew-symmetric and positive-definite components, it guarantees long-horizon stability—a major problem in neural operators. It allows direct spectral access to the dynamics, enabling practitioners to extract dispersion relations and dissipation scales directly from model weights.
From the abstract
Linear dynamical systems are fully characterized by their eigenspectra, accessible directly from the generator of the dynamics. For nonlinear systems governed by partial differential equations, no equivalent theory exists. We introduce Lie Generator Network-Koopman (LGN-KM), a neural operator that lifts nonlinear dynamics into a linear latent space and learns the continuous-time Koopman generator ($L_k$) through a decomposition $L_k = S - D_k$, where $S$ is skew-symmetric representing conservati