ConfEviSurrogate: A Conformalized Evidential Surrogate Model for Uncertainty Quantification

TL;DR

ConfEviSurrogate combines deep evidential regression with conformal prediction to provide calibrated, interval-valued uncertainty estimates for data-driven surrogates of ensemble simulations. It models outputs via a higher-order Student-$t$ predictive framework enabled by a Normal-Inverse-Gamma prior, separating aleatoric and epistemic uncertainty and offering principled predictive intervals. Conformal calibration secures finite-sample coverage guarantees, while an interactive visualization interface supports uncertainty-aware exploration of cosmology, ocean, and fluid dynamics simulations. The approach yields state-of-the-art accuracy, reliable uncertainty quantification, and efficient inference, contributing a practical tool for uncertainty-aware scientific visualization and decision-making.

Abstract

Surrogate models, crucial for approximating complex simulation data across sciences, inherently carry uncertainties that range from simulation noise to model prediction errors. Without rigorous uncertainty quantification, predictions become unreliable and hence hinder analysis. While methods like Monte Carlo dropout and ensemble models exist, they are often costly, fail to isolate uncertainty types, and lack guaranteed coverage in prediction intervals. To address this, we introduce ConfEviSurrogate, a novel Conformalized Evidential Surrogate Model that can efficiently learn high-order evidential distributions, directly predict simulation outcomes, separate uncertainty sources, and provide prediction intervals. A conformal prediction-based calibration step further enhances interval reliability to ensure coverage and improve efficiency. Our ConfEviSurrogate demonstrates accurate predictions and robust uncertainty estimates in diverse simulations, including cosmology, ocean dynamics, and fluid dynamics.

Figures (6)

• Figure 1: Overview of our approach. (1) Simulations are conducted with different simulation parameters, yielding a range of output data. (2) These data and their associated parameters are then used to train our Conformal Evidential Surrogate Model, which provides uncertainty quantification. (3) An interactive visualization interface allows users to explore parameters, predicted results, and associated uncertainties.
• Figure 2: Architecture of ConfEviSurrogate, which generates the hyperparameters $(\gamma,\nu,\alpha,\beta)$ of the higher-order evidential distribution given input simulation parameters. The size of our model is defined by $\text{ch}$ and $k$. Here, $\text{ch}$ controls the number of channels in the intermediate layers, while $k$ determines how many times we upsample the low-resolution tensor $(h,w,d)$ to match the final output resolution $(H,W,D)$.
• Figure 3: Visual interface for ConfEviSurrogate exploration. (a) Parameter View for selecting simulation parameters of interest. (b) Visualization View-1 for visualizing the predicted output and associated two uncertainties. (c) Visualization View-2 for visualizing the prediction intervals.
• Figure 4: Volume rendering of Cloverleaf3D and Mpas-O data for predictive outputs (top row) and corresponding error maps (bottom row). In Mpas-O, SurroFlow operates at a lower resolution, we include a zoomed-in view of the ground truth (bottom row) to ensure a fair visual comparison.
• Figure 5: Volume rendering of NYX and MPAS-Ocean data for error maps between ground truth and predicted output (left) and predicted epistemic uncertainty (right).

Theorems & Definitions (1)

• Theorem 1