Learnability of hyperbolic PDEs from data

Determine whether hyperbolic partial differential equations can be learned from training data consisting of pairs of random forcing terms and corresponding solutions, extending recent provable results for elliptic PDE learning.

Background

The paper notes recent results showing data-efficient learning of elliptic PDEs from input–output data and draws an analogy to the Koopman snapshot setting. Extending these results to hyperbolic PDEs remains unsettled.

The authors suggest that their proof techniques for establishing learnability boundaries and algorithmic optimality in Koopman learning may shed light on this open problem in PDE learning.