Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions

TL;DR

This paper extends the ACCRUE framework to learn input-dependent, non-Gaussian uncertainty distributions using neural networks, improving probabilistic forecasts for deterministic models in high-stakes applications.

Contribution

It introduces a neural network-based method to model asymmetric, non-Gaussian uncertainties, addressing limitations of existing Gaussian and sampling-based approaches.

Findings

Captures input-dependent, non-Gaussian uncertainty structures.

Improves probabilistic forecast accuracy over existing methods.

Maintains flexibility to model skewed and heavy-tailed errors.

Abstract

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by sampling input parameter distributions or by augmenting deterministic outputs with uncertainty representations, including distribution-free and distributional methods. However, sampling-based methods are often computationally prohibitive for real-time applications, and many existing uncertainty representations either ignore input dependence or rely on restrictive Gaussian assumptions that fail to capture asymmetry and heavy-tailed behavior. Therefore, we extend the ACCurate and Reliable Uncertainty Estimate (ACCRUE) framework to learn input-dependent, non-Gaussian uncertainty distributions, specifically two-piece Gaussian and asymmetric Laplace forms, using a neural network trained with a loss function that balances predictive accuracy and reliability. Through synthetic and real-world experiments, we show that the proposed approach captures an input-dependent uncertainty structure and improves probabilistic forecasts relative to existing methods, while maintaining flexibility to model skewed and non-Gaussian errors.