Adaptive Conformal Prediction for Image Regression Models with Application to an Inertial Confinement Fusion Emulator

Conformal Prediction (CP) provides robust uncertainty guarantees for predictive models, but is typically applied post hoc, which misaligns model training with the conformal goal of producing efficient (i.e., narrow) intervals. We propose SPACR (Single-Pass Adaptive Conformal Regressor), a novel method for directly training uncertainty-aware regressors within a differentiable loss. SPACR jointly optimizes accuracy, efficiency, and validity without batch-splitting or a predefined confidence level during training. As a result, a single SPACR model yields valid prediction intervals at multiple confidence levels during inference, avoiding the costly retraining required by methods like Directly Optimized Inductive Conformal Regression (DOICR). Experiments on diverse tabular and image datasets show that SPACR consistently gives tighter intervals and better coverage-efficiency trade-offs compared to standard CP and DOICR, while significantly reducing computational costs relative to retraining-dependent baselines.

Neural operators such as the Fourier Neural Operator (FNO) have emerged as powerful surrogates for solving partial differential equations (PDEs), achieving speedups of several orders of magnitude over traditional numerical solvers. However, deploying these models in safety-critical engineering applications -- such as thermal management of electronic components and battery systems -- requires not only accurate point predictions but also rigorous uncertainty guarantees. Existing uncertainty quantification (UQ) methods for neural operators, including Monte Carlo Dropout and Deep Ensembles, provide only relative uncertainty estimates without formal coverage guarantees. In this work, we propose the first application of split conformal prediction to neural operator-based physics simulation, providing distribution-free prediction intervals with finite-sample coverage guarantees. We further introduce a normalized conformal prediction scheme that leverages MC Dropout uncertainty to produce adaptive-width intervals, yielding tighter intervals in regions of low uncertainty and wider intervals where the model is less certain. Full-scale experiments (33.7M parameters, 800 training samples, 5 ensemble members, NVIDIA V100) on steady-state heat conduction benchmarks demonstrate that our method achieves 89.1% empirical coverage at the target level of alpha=0.1, while producing spatially adaptive prediction intervals that reflect the underlying physical uncertainty structure. We also provide an uncertainty decomposition framework that separates epistemic uncertainty (68% of total) from aleatoric uncertainty (32% of total), offering actionable guidance for data collection and model improvement. Our method is implemented in an open-source platform with REST API endpoints and interactive 3D visualization.

Conformal Prediction provides distribution-free prediction intervals with guaranteed coverage, but its reliance on a single global calibration threshold obscures the sources of uncertainty at the instance level. In particular, it conflates irreducible noise with uncertainty induced by heterogeneous training data (aleatoric), model limitations, or calibration mismatch (epistemic), offering little insight into why an interval is wide or whether it could be reduced. We introduce an uncertainty-aware explainability framework that analyses the reducibility of calibration-induced epistemic conformal uncertainty via progressive calibration localisation for regression tasks. The approach is diagnostic rather than causal: it does not estimate true aleatoric or epistemic uncertainty, but explains how conformal intervals contract and stabilise as calibration support is localised around a test instance. Across benchmarks and real-world data, absolute reducible uncertainty aligns with epistemic proxies, while its relative contribution varies by task, revealing regimes hidden by interval width. This instance-level view complements conformal uncertainty, enhancing interpretability without altering the predictor or coverage.