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.

翻译：计算模型支撑着工程与科学领域的高风险决策，实践者日益寻求概率预测以量化此类模型的不确定性。现有方法通过采样输入参数分布，或通过为确定性输出附加不确定性表示（包括无分布方法和分布方法）来生成预测。然而，基于采样的方法在实时应用中往往计算成本过高，且许多现有不确定性表示要么忽略输入依赖性，要么依赖未能捕捉非对称性和重尾行为的高斯假设。因此，我们将精确可靠不确定性估计（ACCRUE）框架扩展为学习依赖于输入的非高斯不确定性分布，具体采用双片高斯和不对称拉普拉斯形式，通过使用平衡预测精度与可靠性的损失函数训练神经网络实现。通过合成实验和真实世界实验，我们证明所提方法能够捕捉输入相关的不确定性结构，并在保持对偏态与非高斯误差建模灵活性的同时，相较于现有方法提升了概率预测性能。