【论文速递】Conformal Prediction for Time-Dependent PDEs

英文标题：Conformal Prediction for Time-Dependent PDEs

arXiv编号：2611.08409
作者：Joshua Stiller, Annika Schneider, Eyke Hüllermeier
来源：arXiv
原文链接：https://arxiv.org/abs/2611.08409

中文摘要：
Uncertainty quantification is crucial in scientific machine learning, where models inform safety-critical tasks such as flood forecasting, financial risk management, and thermal control in machines. Conformal prediction provides distribution-free coverage guarantees, but in time-dependent settings common to physics and engineering, these guarantees can break down, leading to systematic undercoverage. We study this problem in the context of surrogate models for time-dependent physical systems described by partial differential equations. We prove that in a function space setting, distributions at arbitrarily close times can be mutually singular, making exact coverage guarantees impossible. We further show that in discretized settings, the total variation distance between distributions often saturates exponentially fast with the grid resolution, mandating restrictions on the spatial discretization to ensure coverage. Finally, for certain settings, we show how to use principled weighted conformal prediction to obtain finite-sample coverage guarantees over growing time horizons.

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