{"title":"Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification","authors":"","doi":"10.1016/j.cma.2024.117314","DOIUrl":null,"url":null,"abstract":"<div><p>We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method possesses a unique capability: it seamlessly integrates SciML into UQ and vice versa, which allows it to quantify the uncertainties in SciML tasks effectively and leverage SciML for improved uncertainty assessment during UQ-related tasks. The proposed surrogate model can effectively incorporate a variety of physical constraints, such as governing partial differential equations (PDEs) with associated initial and boundary conditions constraints, inequality-type constraints (e.g., monotonicity, convexity, non-negativity, among others), and additional a priori information in the training process to supplement limited data. This ensures physically realistic predictions and significantly reduces the need for expensive computational model evaluations to train the surrogate model. Furthermore, the proposed method has a built-in uncertainty quantification (UQ) feature to efficiently estimate output uncertainties. To demonstrate the effectiveness of the proposed method, we apply it to a diverse set of problems, including linear/non-linear PDEs with deterministic and stochastic parameters, data-driven surrogate modeling of a complex physical system, and UQ of a stochastic system with parameters modeled as random fields.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S004578252400570X","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method possesses a unique capability: it seamlessly integrates SciML into UQ and vice versa, which allows it to quantify the uncertainties in SciML tasks effectively and leverage SciML for improved uncertainty assessment during UQ-related tasks. The proposed surrogate model can effectively incorporate a variety of physical constraints, such as governing partial differential equations (PDEs) with associated initial and boundary conditions constraints, inequality-type constraints (e.g., monotonicity, convexity, non-negativity, among others), and additional a priori information in the training process to supplement limited data. This ensures physically realistic predictions and significantly reduces the need for expensive computational model evaluations to train the surrogate model. Furthermore, the proposed method has a built-in uncertainty quantification (UQ) feature to efficiently estimate output uncertainties. To demonstrate the effectiveness of the proposed method, we apply it to a diverse set of problems, including linear/non-linear PDEs with deterministic and stochastic parameters, data-driven surrogate modeling of a complex physical system, and UQ of a stochastic system with parameters modeled as random fields.
期刊介绍:
Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.