The finite element neural network method to simulate two dimensional partial differential equations and perform parameter identification [PDF]
Scientific ReportsNeural networks (NNs) have received growing interest in engineering due to their ability to assimilate high-dimensional data and provide accurate approximations for complex systems.
Mohammed Abda +7 more
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Bayesian bilevel operator learning with low-rank adaptation for efficient uncertainty quantification of PDE inverse problems [PDF]
Nature CommunicationsUncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability ...
Ray Zirui Zhang +3 more
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QEKI: A Quantum–Classical Framework for Efficient Bayesian Inversion of PDEs [PDF]
EntropySolving Bayesian inverse problems efficiently stands as a major bottleneck in scientific computing. Although Bayesian Physics-Informed Neural Networks (B-PINNs) have introduced a robust way to quantify uncertainty, the high-dimensional parameter spaces ...
Jiawei Yong, Sihai Tang
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Going with the flow to solve for symmetry-driven PDE dynamics with physics-informed neural networks [PDF]
Nature CommunicationsWe address a computational framework that integrates symmetry reduction into Physics-Informed Neural Networks (PINNs) for analysing symmetry-driven dynamics in nonlinear partial differential equations (PDEs).
Michail E. Kavousanakis +5 more
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Mathematics, 2023 Physics-informed neural networks (PINNs) provide a new approach to solving partial differential equations (PDEs), while the properties of coupled physical laws present potential in surrogate modeling.
Meijun Zhou, Gang Mei, Nengxiong Xu
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Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps [PDF]
, 2013 Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities ...
Dolean Maini, Victorita +5 more
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Қарағанды университетінің хабаршысы. Математика сериясы, 2022 Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity.
M.J. Huntul, I. Tekin
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PINNs algorithm and its application in geotechnical engineering
Yantu gongcheng xuebao, 2021 The physical information neural networks (PINNs) algorithm, a new mesh-free algorithm, uses the automatic differential method to embed the partial differential equation directly into the neural networks so as to realize the intelligent solution of the ...
LAN Peng 1, LI Hai-chao 1, YE Xin-yu 1, ZHANG Sheng 1, SHENG Dai-chao 1, 2
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A deep neural network approach for parameterized PDEs and Bayesian inverse problems
Machine Learning: Science and Technology, 2023 We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems.
Harbir Antil +3 more
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Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs [PDF]
, 2021 Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique continuation ...
Mishra, Siddhartha +3 more
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