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

Carrie J. Lei-Cramer; Michael S. Jones; Laura J. Wendelberger

stat.MLSep 30, 2026

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

Authors: Carrie J. Lei-Cramer, Michael S. Jones, Laura J. Wendelberger

Organizations: Department of Statistics, Texas A&M University, College Station, TX, USA. · Lawrence Livermore National Laboratory, Livermore, CA, USA.

Abstract

Uncertainty quantification is critical in scientific machine learning, where black-box, image-based models are increasingly deployed in high-stakes settings. In many such applications, model outputs inform costly decisions, yet most methods provide only point estimates without quantifying predictive uncertainty. This challenge is compounded by the limited accessibility and interpretability of model internals, making it difficult to assess reliability across different regions of the input space. As a result, there is a growing need for methods that can provide input-dependent uncertainty estimates to guide both model development and downstream experimentation. To address this need, we propose Adaptive Conformal Prediction using Nearest Neighbors (ACPNN), an input-adaptive conformal framework for image regression. ACPNN leverages information from neighboring samples to produce locally adaptive uncertainty estimates while maintaining low computational cost. The neighborhood structure is defined using a scaled distance metric learned via a Gaussian Process with an automatic relevance determination (ARD) kernel. We demonstrate the effectiveness of ACPNN on a diffusion model for emulating inertial confinement fusion (ICF) simulations, showing that it achieves reliable and adaptive uncertainty quantification.

Figures & tables

Figure 1 : Schematic overview of ICF simulation, experiment, and emulation workflows. (A) HYDRA simulations, driven by input parameters such as capsule scale and asymmetry, are performed in parallel with NIF implosion experiments. Both workflows produce diagnostic X-ray images; however, HYDRA simulations require substantial computational resources, while NIF experiments are limited by the weeks-long timescale between shots. (B) In the generative forward setting, models are conditioned on input parameters to produce corresponding diagnostic X-ray images. (C) In the generative inverse setting, models are conditioned on diagnostic X-ray images to produce input parameter values.

Figure 2 : Examples of X-ray images from the BigFoot dataset. From left to right, the images were selected based on their relatively large scores along principal components 1–6, respectively (approximately the 500th largest score among 90,000 images for each component). These images highlight characteristic image features associated with each principal component.

Figure 3 : Visualization of the first six principal components (PCs) obtained from PCA of the 90,000 training X-ray images in the BigFoot dataset.Each component is displayed as an eigenimage by reshaping the corresponding PCA loading vector to the original image dimensions. The PCs represent the dominant modes of variation in the training data, with PC1 explaining the greatest amount of variance and subsequent PCs explaining progressively less.

Panel of Figure 4 — Figure 4 : Visualization comparing conformal prediction sets with the true response values across different conformal prediction methods. The first row displays results for the predicted values of mode 2 asymmetry while the second row shows predictions for mode 1 asymmetry. All three methods achieve the desired coverage of the true responses. The compactness of the conformal sets reflects model performance, with adaptive conformal prediction and scaled conformal prediction producing similarly tight prediction intervals.

	Mode 2 asymmetry				Mode 1 asymmetry
Method	Q1	Median	Q3	Cov. Rate	Q1	Median	Q3	Cov. Rate
CP	0.152	0.152	0.152	0.898	0.121	0.121	0.121	0.898
SCP	0.119	0.144	0.174	0.905	0.079	0.112	0.141	0.890
ACPNN3	0.149	0.179	0.211	0.900	0.105	0.143	0.177	0.902
ACPNN5	0.137	0.165	0.195	0.898	0.094	0.128	0.158	0.899
ACPNN10	0.135	0.162	0.192	0.903	0.086	0.117	0.145	0.884

Table 1 : Comparison of uncertainty interval distributions (Q1, median, Q3) and empirical coverage rates across methods for two drive asymmetry response variables: mode 2 asymmetry and mode 1 asymmetry.

Panel of Figure 5 — Figure 5 : Violin plots of uncertainty magnitudes across input bins. In Panel (a) PC 6 is used as the binned input and mode 2 asymmetry as the response variable; in panel (b) PC 1 is used as the input and mode 1 asymmetry as the response variable. The x-axis represents the input regions (bins), and the y-axis denotes the magnitude of predictive uncertainty. Numbers shown above each panel indicate the number of test samples within each corresponding input region.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 6 — Figure 6 : Visualization comparing conformal prediction sets with the true response values across ACPNN method with different number of ensembles. The first row displays results for the predicted values of mode 2 asymmetry, while the second row shows predictions for mode 1 asymmetry. All three methods achieve the desired coverage of the true responses. The compactness of the conformal sets reflects method performance, with increase of number of ensembles used in the calculation, higher compactness of the conformal sets.

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SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors

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Online Conformal Prediction Conformal Inference

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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.

Abstract

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