Adaptive Probabilistic ODE Solvers Without Adaptive Memory Requirements

Abstract: Despite substantial progress in recent years, probabilistic solvers with adaptive step sizes can still not solve memory-demanding differential equations -- unless we care only about a single point in time (which is far too restrictive; we want the whole time series). Counterintuitively, the culprit is the adaptivity itself: Its unpredictable memory demands easily exceed our machine's capabilities, making our simulations fail unexpectedly and without warning. Still, dropping adaptivity would abandon years of progress, which can't be the answer. In this work, we solve this conundrum. We develop an adaptive probabilistic solver with fixed memory demands building on recent developments in robust state estimation. Switching to our method (i) eliminates memory issues for long time series, (ii) accelerates simulations by orders of magnitude through unlocking just-in-time compilation, and (iii) makes adaptive probabilistic solvers compatible with scientific computing in JAX.