[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125602-en":3,"doc-seo-125602-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125602,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems - research findings and methods","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.","arXiv :2306 . 15159v1 [ stat .ML] 27 Jun 2023  \nEvaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems  \nStephen Guth 1 , Alireza Mojahed 1 , and Themistoklis P. Sapsis* 1  \n1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  \n* corresponding author, [sapsis@mit.edu](sapsis@mit.edu)  \nABSTRACT  \nMachine 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.  \nKeywords: Uncertainty Quantification, Gaussian Process, Ensemble Neural Networks, Reduced Order Modeling  \n1 INTRODUCTION  \nFor 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.  \nFor 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] .  \nThe 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  \nof 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","cbCaioI4JhiWhsHT","https://ap.wps.com/l/cbCaioI4JhiWhsHT","pdf",2606608,1,25,"English","en",105,"# Introduction\n## Uncertainty quantification in surrogate modeling\n## Gaussian processes vs uncertainty-aware neural networks\n## Evaluation criteria and datasets\n# Methods and architectures\n## Uncertainty typology\n## Neural network and Gaussian process models","[{\"question\":\"What is the main goal of this work?\",\"answer\":\"To evaluate how different machine learning architectures quantify epistemic and aleatoric uncertainties for reduced order models in complex dynamical systems.\"},{\"question\":\"Which model families are compared for epistemic uncertainty?\",\"answer\":\"Gaussian process approaches and three deep neural network-based techniques: ensemble neural networks, Bayesian neural networks, and dropout neural networks.\"},{\"question\":\"How is UQ accuracy evaluated in the paper?\",\"answer\":\"Using two criteria on validation data: the distribution of normalized residuals and the distribution of estimated uncertainties.\"}]","Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems - 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