Physics-informed neural ODE (PINODE): embedding physics into models using collocation points DOI Creative Commons
Aleksei Sholokhov, Yuying Liu, Hassan Mansour

et al.

Scientific Reports, Journal Year: 2023, Volume and Issue: 13(1)

Published: June 22, 2023

Abstract Building reduced-order models (ROMs) is essential for efficient forecasting and control of complex dynamical systems. Recently, autoencoder-based methods building such have gained significant traction, but their demand data limits use when the scarce expensive. We propose aiding a model’s training with knowledge physics using collocation-based physics-informed loss term. Our innovation builds on ideas from classical collocation numerical analysis to embed known equation into latent-space dynamics ROM. show that addition our allows exceptional supply strategies improves performance ROMs in data-scarce settings, where high-quality data-driven impossible. Namely, problem modeling high-dimensional nonlinear PDE, experiments $$\times$$ × 5 gains, measured by prediction error, low-data regime, 10 gains tasks high-noise learning, 100 efficiency utilizing dimension, 200 far-out out-of-distribution relative purely models. These improvements pave way broader adoption network-based compressive sensing applications.

Language: Английский

Enhancing computational fluid dynamics with machine learning DOI
Ricardo Vinuesa, Steven L. Brunton

Nature Computational Science, Journal Year: 2022, Volume and Issue: 2(6), P. 358 - 366

Published: June 27, 2022

Language: Английский

Citations

299
Error estimates for DeepONets: a deep learning framework in infinite dimensions DOI Creative Commons
Samuel Lanthaler, Siddhartha Mishra, George Em Karniadakis

et al.

Transactions of Mathematics and Its Applications, Journal Year: 2022, Volume and Issue: 6(1)

Published: Jan. 1, 2022

Abstract DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite-dimensional Banach spaces. We analyze and prove estimates on the resulting approximation generalization errors. In particular, we extend universal property of to include measurable mappings in non-compact By decomposition error into encoding, reconstruction errors, both lower upper bounds total error, relating it spectral decay properties covariance operators, associated with underlying measures. derive almost optimal very general affine reconstructors random sensor locations well using covering number arguments. illustrate our four prototypical examples namely those arising forced ordinary differential equation, an elliptic partial equation (PDE) variable coefficients parabolic hyperbolic PDEs. While arbitrary Lipschitz by accuracy $\epsilon $ is argued suffer from ‘curse dimensionality’ (requiring neural networks exponential size $1/\epsilon $), contrast, all above concrete interest, rigorously that can break this curse dimensionality (achieving grow algebraically $).Thus, demonstrate efficient potentially large class machine framework.

Language: Английский

Citations

129
Physics-informed neural networks for phase-field method in two-phase flow DOI
Rundi Qiu, Renfang Huang, Yao Xiao

et al.

Physics of Fluids, Journal Year: 2022, Volume and Issue: 34(5)

Published: April 25, 2022

The complex flow modeling based on machine learning is becoming a promising way to describe multiphase fluid systems. This work demonstrates how physics-informed neural network promotes the combination of traditional governing equations and advanced interface evolution without intricate algorithms. We develop networks for phase-field method (PF-PINNs) in two-dimensional immiscible incompressible two-phase flow. Cahn–Hillard equation Navier–Stokes are encoded directly into residuals fully connected network. Compared with interface-capturing method, model has firm physical basis because it Ginzburg–Landau theory conserves mass energy. It also performs well at large density ratio. However, high-order differential nonlinear term Cahn–Hilliard poses great challenge obtaining numerical solutions. Thus, this work, we adopt tackle by solving derivate terms capture adaptively. To enhance accuracy efficiency PF-PINNs, use time-marching strategy forced constraint viscosity. PF-PINNs tested two cases presenting ability PINNs evaluating ratio (up 1000). shape both coincides reference results, dynamic behavior second case precisely captured. quantify variations center increasing velocity over time validation purposes. results show that exploit automatic differentiation sacrificing high method.

Language: Английский

Citations

75
Promising directions of machine learning for partial differential equations DOI
Steven L. Brunton,

J. Nathan Kutz

Nature Computational Science, Journal Year: 2024, Volume and Issue: 4(7), P. 483 - 494

Published: June 28, 2024

Language: Английский

Citations

20
Applying machine learning to study fluid mechanics DOI Creative Commons
Steven L. Brunton

Acta Mechanica Sinica, Journal Year: 2021, Volume and Issue: 37(12), P. 1718 - 1726

Published: Dec. 1, 2021

Abstract This paper provides a short overview of how to use machine learning build data-driven models in fluid mechanics. The process is broken down into five stages: (1) formulating problem model, (2) collecting and curating training data inform the (3) choosing an architecture with which represent (4) designing loss function assess performance (5) selecting implementing optimization algorithm train model. At each stage, we discuss prior physical knowledge may be embedding process, specific examples from field Graphic abstract

Language: Английский

Citations

103
Operator inference for non-intrusive model reduction with quadratic manifolds DOI Creative Commons
Rudy Geelen, Stephen J. Wright, Karen Willcox

et al.

Computer Methods in Applied Mechanics and Engineering, Journal Year: 2022, Volume and Issue: 403, P. 115717 - 115717

Published: Nov. 19, 2022

Language: Английский

Citations

64
Reduced basis methods for time-dependent problems DOI Creative Commons
Jan S. Hesthaven, Cecilia Pagliantini, Gianluigi Rozza

et al.

Acta Numerica, Journal Year: 2022, Volume and Issue: 31, P. 265 - 345

Published: May 1, 2022

Numerical simulation of parametrized differential equations is crucial importance in the study real-world phenomena applied science and engineering. Computational methods for real-time many-query such problems often require prohibitively high computational costs to achieve sufficiently accurate numerical solutions. During last few decades, model order reduction has proved successful providing low-complexity high-fidelity surrogate models that allow rapid simulations under parameter variation, thus enabling increasingly complex problems. However, many challenges remain secure robustness efficiency needed nonlinear time-dependent The purpose this article survey state art reduced basis draw together recent advances three main directions. First, we discuss structure-preserving designed retain key physical properties continuous problem. Second, localized adaptive based on approximations solution space. Finally, consider data-driven techniques non-intrusive which an approximation map between space coefficients learned. Within each class methods, describe different approaches provide a comparative discussion lends insights advantages, disadvantages potential open questions.

Language: Английский

Citations

60
Physics guided neural networks for modelling of non-linear dynamics DOI
Haakon Robinson, Suraj Pawar, Adil Rasheed

et al.

Neural Networks, Journal Year: 2022, Volume and Issue: 154, P. 333 - 345

Published: July 26, 2022

Language: Английский

Citations

44
Comparing different nonlinear dimensionality reduction techniques for data-driven unsteady fluid flow modeling DOI
Hunor Csala, Scott T. M. Dawson, Amirhossein Arzani

et al.

Physics of Fluids, Journal Year: 2022, Volume and Issue: 34(11)

Published: Nov. 1, 2022

Computational fluid dynamics (CFD) is known for producing high-dimensional spatiotemporal data. Recent advances in machine learning (ML) have introduced a myriad of techniques extracting physical information from CFD. Identifying an optimal set coordinates representing the data low-dimensional embedding crucial first step toward data-driven reduced-order modeling and other ML tasks. This usually done via principal component analysis (PCA), which gives linear approximation. However, flows are often complex nonlinear structures, cannot be discovered or efficiently represented by PCA. Several unsupervised algorithms been developed branches science dimensionality reduction (NDR), but not extensively used flows. Here, four manifold two deep (autoencoder)-based NDR methods investigated compared to These tested on canonical flow problems (laminar turbulent) biomedical brain aneurysms. The reconstruction capabilities these compared, challenges discussed. temporal vs spatial arrangement its influence mode extraction investigated. Finally, modes qualitatively compared. results suggest that using would beneficial building more efficient models All resulted smaller errors reduction. Temporal was harder task; nevertheless, it physically interpretable modes. Our work one comprehensive comparisons various unsteady

Language: Английский

Citations

40
Digital Twins in Wind Energy: Emerging Technologies and Industry-Informed Future Directions DOI Creative Commons
Florian Stadtmann, Adil Rasheed, Trond Kvamsdal

et al.

IEEE Access, Journal Year: 2023, Volume and Issue: 11, P. 110762 - 110795

Published: Jan. 1, 2023

This article presents a comprehensive overview of the digital twin technology and its capability levels, with specific focus on applications in wind energy industry. It consolidates definitions levels scale from 0-5; 0-standalone, 1-descriptive, 2-diagnostic, 3-predictive, 4-prescriptive, 5-autonomous. then, an industrial perspective, identifies current state art research needs sector. is concluded that main challenges hindering realization highly capable twins fall into one four categories; standards-related, data-related, model-related, acceptance related. The proposes approaches to identified perspective institutes offers set recommendations for various stakeholders facilitate technology. contribution this lies synthesis knowledge identification future industry ultimately providing roadmap development field

Language: Английский

Citations

29