Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Uncertainty RepresentationsCognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
Guaranteed confidence-band enclosures for PDE surrogates
🤖 AI Summary
Existing PDE surrogate models—particularly function-space mapping models such as neural operators—lack statistically guaranteed predictive confidence.
Method: We propose the first conformalized confidence band construction method for such infinite-dimensional models. Our approach embeds the surrogate’s error into a low-dimensional SVD subspace, models the truncation error explicitly, and leverages zonotope-based set representation and set propagation to yield model-agnostic, provably valid functional confidence bands.
Contribution/Results: This work pioneers the extension of conformal inference to infinite-dimensional function spaces; ensures theoretical soundness via SVD-based error decomposition; and delivers tight, computationally tractable, black-box-compatible confidence bands with guaranteed coverage. Experiments across diverse neural operators demonstrate strict adherence to user-specified coverage levels, significantly enhancing the reliability and interpretability of scientific machine learning predictions.
Technology Category
Application Category
📝 Abstract
We propose a method for obtaining statistically guaranteed confidence bands for functional machine learning techniques: surrogate models which map between function spaces, motivated by the need build reliable PDE emulators. The method constructs nested confidence sets on a low-dimensional representation (an SVD) of the surrogate model's prediction error, and then maps these sets to the prediction space using set-propagation techniques. The result are conformal-like coverage guaranteed prediction sets for functional surrogate models. We use zonotopes as basis of the set construction, due to their well studied set-propagation and verification properties. The method is model agnostic and can thus be applied to complex Sci-ML models, including Neural Operators, but also in simpler settings. We also elicit a technique to capture the truncation error of the SVD, ensuring the guarantees of the method.
Problem
Research questions and friction points this paper is trying to address.
Partial Differential Equations
Machine Learning
Prediction Accuracy
Innovation
Methods, ideas, or system contributions that make the work stand out.
Machine Learning
Zonotopes
Prediction Intervals
🔎 Similar Papers
No similar papers found.
