Solving inverse problems in physics by optimizing a discrete loss: Fast and accurate learning without neural networks. [PDF]
PNAS NexusKarnakov P, Litvinov S, Koumoutsakos P.
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A symbolic dataset for large language models to solve second kind Fredholm integral equations. [PDF]
Sci DataDana Mazraeh H +3 more
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Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells. [PDF]
PLoS Comput BiolSrivastava S +9 more
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Variational State-Dependent Inverse Problems in PDE-Constrained Optimization: A Survey of Contemporary Computational Methods and Applications [PDF]
Vladislav Bukshtynov
openalex
Multi-level physics informed deep learning for solving partial differential equations in computational structural mechanics. [PDF]
Commun EngHe W, Li J, Kong X, Deng L.
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Solving the Richards infiltration equation by coupling physics-informed neural networks with Hydrus-1D. [PDF]
Sci RepLi Y, Sun Q, Fu Y, Wei J.
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Goal-oriented optimal sensor placement for PDE-constrained inverse problems
Mattuschka, Marco +2 more
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Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
Computer Methods in Applied Mechanics and EngineeringDiffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems.
Agnimitra Dasgupta +6 more
semanticscholar +3 more sources
Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems
arXiv.orgInverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach.
S. Cho, Hwijae Son
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