Modelling nonlinear systems at scale: the Physics-Informed鈥擜I perspective

Nonlinearities are pervasive in Physics, but notoriously difficult to model. Nonlinear interactions between a system’s degrees of freedom transform the solution space, leading to novel branches which have no counterpart in the linear regime. As the number of degrees of freedom is scaled up, the emergence of qualitatively different dynamical modes becomes increasingly important. All of these issues demand a fully nonlinear and scalable approach. In this talk, I will explain how tools from the emerging field of Physics-Informed Artificial Intelligence can enhance traditional computational modelling of nonlinear systems, enabling a more thorough reconstruction of their solution manifolds. In particular, I will focus on three tasks: (i) how the inclusion of prior knowledge enables classic AI algorithms to “learn with less”, a key requirement towards sustainable AI in the age of large models; (ii) how compressed model approximations can be constructed, which are cheaper to compute but still capture all the relevant nonlinear effects; (ii) how these models can be used to generate novel dynamics of clear physical interpretability, and the related problem of out-of-distribution generalisation. Finally, I will describe how my group is directing these techniques towards the discovery of anomalous, extreme dynamics, a task for which the correct inclusion of nonlinear effects is paramount.