Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems - research findings and methods

Aug 5, 2026

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Machine learning methods for data-driven reduced order modeling are increasingly used in engineering, often to complement expensive computational fluid dynamics. Reliability depends on uncertainty quantification (UQ), which estimates surrogate model error and thus affects both training data needs and usable safety factors. This study compares Gaussian processes with UQ-augmented neural networks—ensemble, Bayesian, dropout, and Gaussian networks—using validation residuals and estimated uncertainty distributions on two complex dynamical systems datasets, yielding conclusions on architecture and hyperparameter tuning.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages25

Reading Time1 h 3 min

AccessFree to download

Introduction

Uncertainty quantification in surrogate modeling

Gaussian processes vs uncertainty-aware neural networks

Evaluation criteria and datasets

Methods and architectures

Uncertainty typology

Neural network and Gaussian process models

arXiv :2306 . 15159v1 [ stat .ML] 27 Jun 2023 Evaluation of machine learning architectures on the quantiﬁcation of epistemic and aleatoric uncertainties in complex dynamical systems Stephen Guth 1 , Alireza Mojahed 1 , and Themistoklis P. Sapsis* 1 1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA * corresponding author, [sapsis@mit.edu](sapsis@mit.edu) ABSTRACT Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational ﬂuid dynamics for design problems. An important check on the reliability of surrogate models is Uncertainty Quantiﬁcation (UQ), a self assessed estimate of the model error. Accurate UQ allows for cost savings by reducing both the required size of training data sets and the required safety factors, while poor UQ prevents users from conﬁdently relying on model predictions. We examine several machine learning techniques, including both Gaussian processes and a family UQ-augmented neural networks: Ensemble neural networks (ENN), Bayesian neural networks (BNN), Dropout neural networks (D-NN), and Gaussian neural networks (G-NN) . We evaluate UQ accuracy (distinct from model accuracy) using two metrics: the distribution of normalized residuals on validation data, and the distribution of estimated uncertainties. We apply these metrics to two model data sets, representative of complex dynamical systems: an ocean engineering problem in which a ship traverses irregular wave episodes, and a dispersive wave turbulence system with extreme events, the Majda-McLaughlin-Tabak model. We present conclusions concerning model architecture and hyperparameter tuning. Keywords: Uncertainty Quantiﬁcation, Gaussian Process, Ensemble Neural Networks, Reduced Order Modeling 1 INTRODUCTION For a wide variety of engineering problems, numerical predictions are only a ﬁrst step–also necessary isan estimate of the result error. The economic costs of unconstrained errors are evidenced by the costs of conservative tolerances and safety factors. For design problems, uncertainty quantiﬁcation (UQ) is the general problem of estimating the magnitude of the error between model results and the (unobserved) ground truth [4, 1], and it has wide application across many modeling domains [29, 53, 2, 15] . Traditional design methodologies based on theory or simulation allow for error propagation, sensitivity analysis, and convergence studies, however these approaches are difﬁcult to extend to the black box techniques currently available from machine learning. For UQ, the applied machine learning literature has primarily drawn from Gaussian Process (GP) techniques [43], which have built-in UQ in the form of a posterior distribution [21, 24, 22] . GP techniques, sometimes called kriging, are especially useful for active learning (optimal experimental design) problems [36, 6, 7, 56] and multi-ﬁdelity problems [40, 3, 14] . However, GP techniques are limited in two signiﬁcant ways: the O (n3s) scaling of computation time with the number of training samples, and the more subtle breakdown with the dimensionality of the problem input [41] . The other main approach in the machine learning literature is to augment neural networks with some kind of uncertainty quantiﬁcation [1, 42] . The ﬁrst thread is to use ensemble techniques to implement the Bayes Model Average from Variational Inference [41, 17] . The second thread is to combine GP and neural network technology to combine the scalability of neural networks with the posterior distribution of GP. Various works in the direction include the marginal likelihood loss function [50, 45] the sparse inducing point framework [26, 55, 11, 38], Deep Gaussian Process [16, 10], and Deep Kernel Learning [51, 39] . These techniques seek to avoid the O(n3s) scaling costs of exact GP inference by replacing exact ca

FAQs

What is the main goal of this work?

To evaluate how different machine learning architectures quantify epistemic and aleatoric uncertainties for reduced order models in complex dynamical systems.

Which model families are compared for epistemic uncertainty?

Gaussian process approaches and three deep neural network-based techniques: ensemble neural networks, Bayesian neural networks, and dropout neural networks.

How is UQ accuracy evaluated in the paper?

Using two criteria on validation data: the distribution of normalized residuals and the distribution of estimated uncertainties.

Aug 5, 2026

Upload by Patrick