CD Technical Meeting (ML1): Calibrated Physics-Informed Uncertainty Quantification for Neural PDE Solvers

Thursday 29 May 2025, 14:00 → 14:30 Europe/London

Vignesh Gopakumar (UKAEA)

Machine Learning, Uncertainty Quantification and Data Science 

 

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Paper: Calibrated Physics-Informed Uncertainty Quantification

1 Talk: Calibrated Physics-Informed Uncertainty Quantification for Neural PDE Solvers

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.

Speaker: Vignesh Gopakumar (UKAEA)

2 Q&A

Speaker: Vignesh Gopakumar (UKAEA)