Title: Weighted Conformal Prediction for Time-Dependent PDEs
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Uncertainty Quantification, Neural Operators, Conformal Prediction, PDE Surrogates, Scientific Machine Learning

Abstract: Uncertainty quantification is crucial in scientific machine learning, where models inform safety-critical tasks such as flood forecasting, aerodynamic optimization, and financial risk management. 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 (PDEs). We prove that in a function space setting, distributions at arbitrarily close times can be mutually singular, making exact coverage guarantees impossible. As a solution, we facilitate weighted conformal prediction for a broad class of PDE problems arising from discretized models and validate these results in experiments. While prior work often sidesteps time dependence—by assuming exchangeability, focusing on short horizons, or ignoring long-term deployment—we address it directly by providing exact coverage guarantees through reweighting calibration scores.

TL;DR: We derive weighted conformal prediction for linear time-dependent PDEs, restoring exact coverage for surrogate models.