Results 41 to 50 of about 35,710 (245)
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs [PDF]
Inverse Problems, 2019 We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the model that exist
K. Koval, A. Alexanderian, G. Stadler
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Machine Learning: Science and Technology, 2023 We present novel approximates of variational losses, being applicable for the training of physics-informed neural networks (PINNs). The formulations reflect classic Sobolev space theory for partial differential equations (PDEs) and their weak ...
Juan-Esteban Suarez Cardona +1 more
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Mathematics, 2023 Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws.
Zhixiang Liu +4 more
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The Cauchy problem for the Pavlov equation [PDF]
, 2014 Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature.
Grinevich, P. G., Santini, P. M., Wu, D.
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Solving inverse-PDE problems with physics-aware neural networks [PDF]
Journal of Computational Physics, 2021 39 pages, 17 ...
Frederic Gibou +3 more
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The General Fractional Derivative and Related Fractional Differential Equations
Mathematics, 2020 In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
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Entropy, 2023 Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has ...
Kuo Sun, Xinlong Feng
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International Journal of Mathematics and Mathematical Sciences, 2014 Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction
Nemat Dalir
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Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization [PDF]
Inverse Problems, 2023 Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse ...
Tucker Hartland +4 more
semanticscholar +1 more source
Variational Autoencoding of PDE Inverse Problems
, 2020 Specifying a governing physical model in the presence of missing physics and recovering its parameters are two intertwined and fundamental problems in science. Modern machine learning allows one to circumvent these, via emulators and surrogates, but in doing so disregards prior knowledge and physical laws that are especially important for small data ...
Tait, Daniel J., Damoulas, Theodoros
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