From Data to Laws: Symbolic Regression and Differentiable Analytic Networks for (Astro)physics

Over the next few years, Rubin/LSST, Euclid, Roman, SKA, and other instruments will produce petascale, information‑rich datasets that trace stars, galaxies, and large-scale structure with unprecedented fidelity. Hidden in these data may be regularities that point to new and unexpected physical relationships. Can we build modelling frameworks that can discover such relationships accurately, efficiently, and in forms we can interpret?

I will present two complementary directions we are developing to address this question. The first, PhySO, is a physics-aware symbolic regression engine which proposes compact mathematical equations using deep reinforcement learning with a dimensional-analysis grammar and imposable constraints. The second, NestyNet, assembles networks with analytic derivatives and trains them using second-order methods, yielding fast, high accuracy fits to datasets, solvers for ODEs/PDEs, action-angle transformations, Gaussian-mixture inference, and dynamical modelling, with exact gradients and Hessians throughout.

I will demonstrate how symbolic search coupled with accurate derivatives and with PDE constraints can rediscover analytic solutions from textbook physics. This approach is a practical route toward explainable, robust models for the forthcoming data deluge-aimed less at "automating Kepler" than at accelerating analysis while keeping physical insight.