Latent Neural Operator for Solving Forward and Inverse PDE Problems
Advances in Neural Information Processing Systems 37Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original geometric space, leading to high computational costs when the number of sample points is large.
Wang, Tian, Wang, Chuang
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PDE-aware deep learning for inverse problems in cardiac electrophysiology: datasets
, 2021 Riccardo Tenderini +3 more
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Inverse problems for infinite-dimensional transport PDEs on Wasserstein space
We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been extensively and intensively studied, their corresponding inverse problems--which aim to reconstruct unknown operators,
Liu, Hongyu +2 more
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Solving forward and inverse problems in a non-linear 3D PDE via an asymptotic expansion based approach [PDF]
, 2022 Dmitrii Chaikovskii, Ye Zhang
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PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem
, 2015 Lili Chang +3 more
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On Qualitative Experimental Design for PDE Parameter Identification Inverse Problems [PDF]
Der Erfolg der Rekonstruktion eines Modellparameters aus indirekten experimentellen Messungen durch Lösen des inversen Problems hängt ma{\ss}geblich von der Qualität der zur Verfügung stehenden Daten ab. Ziel der Versuchsplanung ist daher die Auswahl von geeigneten experimentellen Setups, die für diese Aufgabe informative Daten erzeugen.
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Stability for an inverse problem for a two-speed hyperbolic PDE in one space dimension [PDF]
, 2009 Rakesh Rakesh, Paul Sacks
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Stability for a formally determined inverse problem for a hyperbolic PDE with space and time dependent coefficients [PDF]
, 2020 Venky Krishnan +2 more
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Asymptotic Expansion Regularization for Inverse Source Problems in Two-Dimensional Singularly Perturbed Nonlinear Parabolic PDEs [PDF]
, 2023 Dmitrii Chaikovskii +2 more
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