Calibrated Physics-Informed Uncertainty Quantification

• URL: http://arxiv.org/abs/2502.04406v1
• Date: Thu, 06 Feb 2025 09:23:06 GMT
• Title: Calibrated Physics-Informed Uncertainty Quantification
• Authors: Vignesh Gopakumar, Ander Gray, Lorenzo Zanisi, Timothy Nunn, Stanislas Pamela, Daniel Giles, Matt J. Kusner, Marc Peter Deisenroth,
• Abstract summary: We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. We are able to quantify and calibrate the model's inconsistencies with the PDE rather than the uncertainty arising from the data.
• Score: 16.985414812517252
• License:
• Abstract: Neural PDEs offer efficient alternatives to computationally expensive numerical PDE solvers for simulating complex physical systems. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we are able to quantify and calibrate the model's inconsistencies with the PDE rather than the uncertainty arising from the data. Our approach uses convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

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