Results 101 to 110 of about 723 (140)

The Gradient Descent Method for the Convexification to Solve Boundary Value Problems of Quasi-Linear PDEs and a Coefficient Inverse Problem

Journal of Scientific Computing, 2021
We study the global convergence of the gradient descent method of the minimization of strictly convex functionals on an open and bounded set of a Hilbert space.
T. Le, L. Nguyen
semanticscholar   +1 more source

Physics- Informed Neural Networks for Inverse Electromagnetic Problems

IEEE Conference on Electromagnetic Field Computation, 2022
PDE-constrained inverse problems are very common in electromagnetism, just like in other engineering fields. Their ill-posedness (in the sense of Hadamard) makes their solution non-trivial, also taking into account that solving PDEs could be ...
M. Baldan, P. di Barba, D. Lowther
semanticscholar   +1 more source

Schrödingerisation based computationally stable algorithms for ill-posed problems in partial differential equations

arXiv.org
We introduce a simple and stable computational method for ill-posed partial differential equation (PDE) problems. The method is based on Schr\"odingerization, introduced in [S. Jin, N. Liu and Y. Yu, arXiv:2212.13969][S. Jin, N. Liu and Y. Yu, Phys. Rev.
Shi Jin, Nana Liu, Chuwen Ma
semanticscholar   +1 more source

The tangential cone condition for some coefficient identification model problems in parabolic PDEs

arXiv.org, 2019
The tangential condition was introduced in [Hanke et al., 95] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems. In this paper we present a series of time dependent benchmark inverse problems for which we
B. Kaltenbacher, T. Nguyen, O. Scherzer
semanticscholar   +1 more source

The Ill-Posed Foundations of Physics-Informed Neural Networks and Their Finite-Difference Variants

arXiv.org
Physics-informed neural networks based on automatic differentiation (AD-PINNs) and their finite-difference counterparts (FD-PINNs) are widely used for solving partial differential equations (PDEs), yet their analytical properties remain poorly understood.
Andreas Langer
semanticscholar   +1 more source

On a Moment Problem on a Curve Connected with Ill-posed Boundary Value Problems for a PDE and Some Other Problems

2009
This paper is devoted to a connection between ill-posed boundary value problems in a bounded domain for a PDE that isn’t proper elliptic and a new moment problem on a curve that is a generalization of well-known trigonometric moment problem. Some connections with another field of mathematics are given in partial cases of the curve and the equation.
openaire   +1 more source

Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

arXiv.org
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer, Andrew B. Duncan   +3 more
semanticscholar   +1 more source

Graph Neural Regularizers for PDE Inverse Problems

arXiv.org
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme that ...
William Lauga, James Rowbottom, Alexander Denker, Željko Kereta, Moshe Eliasof, C. Schönlieb   +5 more
semanticscholar   +1 more source

A probabilistic approach to spectral analysis of Cauchy-type inverse problems: Convergence and stability analysis

arXiv.org
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study.
I. Cîmpean, Andreea Grecu, Liviu Marin
semanticscholar   +1 more source

Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations

arXiv.org
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying model or ...
Oluwatosin Akande, G. P. Langlois, Akwum Onwunta   +2 more
semanticscholar   +1 more source