arXiv paper studies conformal prediction for time-dependent PDEs
Original title: Conformal Prediction for Time-Dependent PDEs
Conformal prediction guarantees break down in time-dependent PDE settings, requiring discretization restrictions for coverage.
Researchers examine uncertainty quantification for surrogate models of time-dependent physical systems described by partial differential equations. Exact coverage guarantees become impossible as distributions at close times can be mutually singular in function space. Weighted conformal prediction is proposed to obtain finite-sample coverage over growing time horizons in discretized settings.
- Distributions at close times are mutually singular
- Total variation distance saturates exponentially with grid resolution
- Weighted conformal prediction ensures finite-sample guarantees
From the original article
1 min read at arxiv.orgUncertainty 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.
By Joshua Stiller · arxiv.org
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