提出固定内存的自适应概率微分方程求解器，解决长时序模拟中内存不可控问题。
Adaptive Probabilistic ODE Solvers Without Adaptive Memory Requirements
- 基于鲁棒状态估计，设计内存恒定的自适应求解框架。
- 实现长时序模拟零内存超限，速度提升数个数量级。
- 兼容JAX科学计算，适合高精度仿真与自动微分场景。
尽管近年来进展显著，具有自适应步长的概率求解器仍无法处理内存需求高的微分方程——除非仅关注单一时刻（过于受限；我们需整个时间序列）。令人意外的是，问题根源正是自适应性本身：其不可预测的内存消耗极易超出机器承载能力，导致模拟意外失败且无预警。但放弃自适应性将前功尽弃，显然不可行。本文提出一种新型自适应概率求解器，具备固定内存开销，基于近期鲁棒状态估计进展。采用该方法后，(i) 长时间序列模拟彻底消除内存问题，(ii) 通过启用即时编译实现模拟加速数个数量级，(iii) 使自适应概率求解器与JAX科学计算环境兼容。
原文摘要 · Abstract (English)
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.
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