Results 111 to 120 of about 723 (140)

Solving Implicit Inverse Problems with Homotopy-Based Regularization Path

Advances in Computational Science and Engineering
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions.
Davide Parodi, F. Benvenuto, Sara Garbarino, Michele Piana   +3 more
semanticscholar   +1 more source

Unlearning Noise in PINNs: A Selective Pruning Framework for PDE Inverse Problems

arXiv.org
Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization objective. However,
Yong-Sheng Chen, Yong Chen, Wei Guo, Xinghui Zhong   +3 more
semanticscholar   +1 more source

A Score-based Generative Solver for PDE-constrained Inverse Problems with Complex Priors

arXiv.org
In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters.
Yankun Hong, Harshit Bansal, K. Veroy
semanticscholar   +1 more source

Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles

arXiv.org
Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconstruction of turbulent flow fields from sparse data.
Khemraj Shukla, Zongren Zou, Theo Kaeufer, M. Triantafyllou, G. Karniadakis   +4 more
semanticscholar   +1 more source

Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation

arXiv.org
Inverse problems for stiff parabolic partial differential equations (PDEs), such as the inverse heat conduction problem (IHCP), are severely ill-posed: the forward map rapidly damps high-frequency interior structure before it reaches the boundary.
Tao Zhong, Yixun Hu, Dongzhe Zheng, A. Sood, Christine Allen-Blanchette   +4 more
semanticscholar   +1 more source

On the Numerical Approximation and Optimization Techniques for Solving an Inverse Cauchy Problem of Viscous-Burgers’ Equation

International journal of neutrosophic science
This paper deals with some inverse problems for nonlinear time-dependent PDEs in one spatial dimension, we investigate an inverse Cauchy problem that is settled by the nonlinear viscous Burgers equation.
Mohammed Mohammed, Faris M. Alwan, A. Auad   +2 more
semanticscholar   +1 more source

An iteratively regularized Gauss–Newton–Halley method for solving nonlinear ill-posed problems

Numerische Mathematik, 2015
B. Kaltenbacher
semanticscholar   +2 more sources

Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations

arXiv.org
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering.
Wenrui Hao, Xinliang Liu, Yahong Yang
semanticscholar   +1 more source

Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts

arXiv.org
Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing physics.
Arturo Rodríguez, A. Chattopadhyay, Piyush Kumar, Luis F. Rodriguez, Vinod Kumar   +4 more
semanticscholar   +1 more source

Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems

, 2009
B. Kaltenbacher, F. Schöpfer, T. Schuster   +2 more
semanticscholar   +1 more source