mlsanityData to 7 Oct 2026

Calibrated Physics-Informed Uncertainty Quantification

arXiv 2502.04406 ↗First posted 6 Feb 2025cs.LG cs.AI physics.comp-phcited by 8

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Abstract (arXiv)

Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on solving partial differential equations (PDEs) using numerical methods, which are computationally expensive and often prohibitively slow for real-time applications or large-scale simulations. Neural PDEs have emerged as efficient alternatives to these costly numerical solvers, offering significant computational speed-ups. 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 can quantify and calibrate the model's inconsistencies with the physics rather than the uncertainty arising from the data. Our approach utilises 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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 36 of its 86 references that are in the map. First posted on arXiv 6 Feb 2025.

Builds on

36 of 86 references.

References · 36

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24 more
  1. 2023Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learningcited by 57
  2. 2023Towards Stability of Autoregressive Neural Operatorscited by 54
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  4. 2022Predictive Inference with Feature Conformal Predictioncited by 33
  5. 2023Plasma Surrogate Modelling using Fourier Neural Operatorscited by 29
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  9. 2024Active Learning for Neural PDE Solverscited by 22
  10. 2021The Importance of Being a Band: Finite-Sample Exact Distribution-Free Prediction Sets for Functional Datacited by 16
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 7.

8 papers.

  1. 2025Plasma State Monitoring and Disruption Characterization using Multimodal VAEscited by 2
  2. 2026Learning Physical Operators using Neural Operatorscited by 1
  3. 2026Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regimecited by 1
  4. 2026Distribution-Free Robust Predict-Then-Optimize in Function Spacescited by 0
  5. 2026Data-Efficient Neural Operator Training via Physics-Based Active Learningcited by 0
  6. 2026Hybrid Neural World Modelscited by 0
  7. 2026Conformal Uncertainty Quantification Guarantees for Neural Operatorscited by 0
  8. 2026Predictive Uncertainty for Neural CAE Surrogatescited by 0