Journal ArticleDOI
Physics-informed neural networks for high-speed flows
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TLDR
In this article, a physics-informed neural network (PINN) was used to approximate the Euler equations that model high-speed aerodynamic flows in one-dimensional and two-dimensional domains.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2020-03-01. It has received 485 citations till now. The article focuses on the topics: Euler equations & Inverse problem.read more
Citations
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B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
TL;DR: Compared with PINNs, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting and dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty.
Journal ArticleDOI
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
TL;DR: In cPINN, locally adaptive activation functions are used, hence training the model faster compared to its fixed counterparts, and it efficiently lends itself to parallelized computation, where each sub-domain can be assigned to a different computational node.
Journal ArticleDOI
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
TL;DR: The proposed XPINN method is the generalization of PINN and cPINN approaches, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation.
Journal ArticleDOI
Physics-Informed Neural Networks for Heat Transfer Problems
TL;DR: In this paper, physics-informed neural networks (PINNs) have been applied to various prototype heat transfer problems, targeting in particular realistic conditions not readily tackled with traditional computational methods.
Journal ArticleDOI
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
TL;DR: A general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space of high-order polynomials is formulated.
References
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Book
Riemann Solvers and Numerical Methods for Fluid Dynamics
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.
Proceedings Article
Practical Bayesian Optimization of Machine Learning Algorithms
TL;DR: This work describes new algorithms that take into account the variable cost of learning algorithm experiments and that can leverage the presence of multiple cores for parallel experimentation and shows that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization for many algorithms.
Journal ArticleDOI
Efficient Implementation of Weighted ENO Schemes
Guang-Shan Jiang,Chi-Wang Shu +1 more
TL;DR: A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the caser= 3, instead of the fourth-order with the original smoothness measurement by Liuet al.
Journal ArticleDOI
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
TL;DR: In this article, the authors introduce physics-informed neural networks, which are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations.
Proceedings Article
Algorithms for Hyper-Parameter Optimization
TL;DR: This work contributes novel techniques for making response surface models P(y|x) in which many elements of hyper-parameter assignment (x) are known to be irrelevant given particular values of other elements.