Výsledky vyhľadávania - "Journal of computational physics"

When and why PINNs fail to train: A neural tangent kernel perspective Autor Wang, Sifan, Yu, Xinling, Perdikaris, Paris

“…•We analyze the training dynamics of PINNs using neural tangent kernel theory.•We derive the NTK of PINNs and study its limiting behavior.•Our analysis reveals…”
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NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations Autor Jin, Xiaowei, Cai, Shengze, Li, Hui, Karniadakis, George Em

“…•NSFnets involve the VP and VV formulations of the Navier-Stokes equations.•NSFnets can directly simulate and sustain turbulence at Reτ∼1,000.•A study on the…”
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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data Autor Yang, Liu, Meng, Xuhui, Karniadakis, George Em

“…We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations…”
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Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons Autor Psaros, Apostolos F., Meng, Xuhui, Zou, Zongren, Guo, Ling, Karniadakis, George Em

“…Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound…”
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Self-adaptive physics-informed neural networks Autor McClenny, Levi D., Braga-Neto, Ulisses M.

“…Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear…”
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Autor Raissi, M., Perdikaris, P., Karniadakis, G.E.

“…We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics…”
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PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain Autor Gao, Han, Sun, Luning, Wang, Jian-Xun

“…•Enable CNN-based physics-informed deep learning for PDEs on irregular domain.•The proposed network can be trained without any labeled data.•Boundary…”
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks Autor Jagtap, Ameya D., Kawaguchi, Kenji, Karniadakis, George Em

“…•We employed adaptive activation functions in deep and physics-informed neural networks.•The proposed method is very simple and it is shown to accelerate…”
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Physics-informed neural networks for inverse problems in supersonic flows Autor Jagtap, Ameya D., Mao, Zhiping, Adams, Nikolaus, Karniadakis, George Em

“…Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider…”
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DGM: A deep learning algorithm for solving partial differential equations Autor Sirignano, Justin, Spiliopoulos, Konstantinos

“…High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep…”
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Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders Autor Lee, Kookjin, Carlberg, Kevin T.

“…•Two model-reduction methods that project dynamical systems on nonlinear manifolds.•Analysis including conditions under which the two methods are equivalent.•A…”
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data Autor Zhu, Yinhao, Zabaras, Nicholas, Koutsourelakis, Phaedon-Stelios, Perdikaris, Paris

“…Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data…”
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Parallel physics-informed neural networks via domain decomposition Autor Shukla, Khemraj, Jagtap, Ameya D., Karniadakis, George Em

“…•Construction and implementation of new domain-decomposition based parallel algorithm is proposed for cPINNs and XPINNs methods.•The proposed algorithm adds…”
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Weak adversarial networks for high-dimensional partial differential equations Autor Zang, Yaohua, Bao, Gang, Ye, Xiaojing, Zhou, Haomin

“…•Parametrize weak solution and test function as deep neural networks for high-dim PDEs.•Applicable to general nonlinear initial value boundary problems in…”
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PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network Autor Long, Zichao, Lu, Yiping, Dong, Bin

“…Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and…”
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A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems Autor Meng, Xuhui, Karniadakis, George Em

“…•The present method can learn both linear and nonlinear correlations between the low- and high-fidelity data adaptively.•The present method can infer the…”
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A physics-informed diffusion model for high-fidelity flow field reconstruction Autor Shu, Dule, Li, Zijie, Barati Farimani, Amir

“…Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity…”
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Hidden physics models: Machine learning of nonlinear partial differential equations Autor Raissi, Maziar, Karniadakis, George Em

“…While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new…”
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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Autor Zhang, Dongkun, Lu, Lu, Guo, Ling, Karniadakis, George Em

“…Physics-informed neural networks (PINNs) have recently emerged as an alternative way of numerically solving partial differential equations (PDEs) without the…”
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What is the fractional Laplacian? A comparative review with new results Autor Lischke, Anna, Pang, Guofei, Gulian, Mamikon, Song, Fangying, Glusa, Christian, Zheng, Xiaoning, Mao, Zhiping, Cai, Wei, Meerschaert, Mark M., Ainsworth, Mark, Karniadakis, George Em

“…The fractional Laplacian in Rd, which we write as (−Δ)α/2 with α∈(0,2), has multiple equivalent characterizations. Moreover, in bounded domains, boundary…”
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