Results 71 to 80 of about 85,369,012 (181)

Sparsity‐Driven Source Localization in Tomographic Sensing Applications

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT Hyperspectral standoff detection systems such as Focal Plane Array (FPA) Fourier Transform Infrared (FTIR) spectrometers provide high spatial resolution in detecting airborne chemical contaminants that are invisible to the human eye but potentially hazardous. When two such systems are operated simultaneously with a suitable opening angle, they
Marco Mattuschka, Noah An der Lan, Stefanie Schröder, Arne Ficks, Max von Danwitz, Alexander Popp   +5 more
wiley   +1 more source

Reconstruction of instantaneous flow fields from transient velocity snapshots using physics-informed neural networks (Applications to pulsatile blood flow behind a stenosis)

Journal of Biomechanical Science and Engineering
Physics-informed neural networks (PINNs) offer a promising framework by embedding partial differential equations (PDEs) into the loss function together with measurement data, making them well-suited for inverse problems.
Kakeru UEDA, Hiro WAKIMURA, Satoshi II
doaj   +1 more source

Gradient Flows on Sparse Representations for PDE‐Regularized Inverse Problems

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT In this short paper, we summarize the theory of Atomic Gradient Flows (AGF) introduced in (Amend, Carioni and Zemas, arxiv:2603.25675, 2026), which provides a framework to construct gradient flows on sparse representations for convex regularized optimization problems.
Christian Amend, Marcello Carioni
wiley   +1 more source

Hierarchical matrix approximations of hessians arising in inverse problems governed by PDEs [PDF]

, 2019
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for Newton solution of deterministic inverse problems, as well as Markov chain
Keyes, David E., Ambartsumyan, Ilona, Boukaram, Wajih Halim, Bui-Thanh, Tan, Boukaram, Wagih Halim, Turkiyyah, George M., Ghattas, Omar, Turkiyyah, George, Stadler, Georg, Ghattas, Omar N., Zampini, Stefano   +10 more
core   +1 more source

A General Method for the Solution of Inverse Problems in Transport Phenomena

Chemical Engineering Transactions, 2015
The typical inverse problems in transport phenomena are given by partial differential equations with unknown boundary conditions, which are to be estimated from measurements corresponding to solutions of the PDEs or of their gradients.
M. Vocciante, A. Reverberi, V. Dovi
doaj   +1 more source

On Switching Times Optimization and Second‐Order Sufficient Conditions for Optimal Bang‐Bang Boundary Control of the Heat Equation

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT We consider optimal control of the heat equation where the control variable appears linearly as a boundary control. We establish switching times optimization for bang–bang controls with multiple switching times. Particularly, representations of variational derivatives of the state and the cost w.r.t. switching times are given.
Georg Vossen
wiley   +1 more source

Poisson inverse problems [PDF]

, 2006
In this paper we focus on nonparametric estimators in inverse problems for Poisson processes involving the use of wavelet decompositions. Adopting an adaptive wavelet Galerkin discretization, we find that our method combines the well-known theoretical ...
Antoniadis, Anestis, Bigot, Jérémie
core   +1 more source

Four Decades of Research at the MADE Site and Beyond: Advancing the Understanding and Modeling of Solute Transport in Heterogeneous Media

Reviews of Geophysics, Volume 64, Issue 4, December 2026.
Abstract Spatial heterogeneity, manifested as strong variability in hydraulic conductivity (K) within geological formations, exerts a fundamental control on groundwater flow and solute transport. Because K can vary over multiple orders of magnitude in complex three‐dimensional patterns, predicting contaminant plume migration remains a long‐standing ...
Zhilin Guo, Maosheng Yin, Peiyao Dong, Yong Zhang, Kewei Chen, Graham Fogg, Brian Berkowitz, Marco Dentz, Chunmiao Zheng   +8 more
wiley   +1 more source

Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems [PDF]

, 2012
In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we study two inverse problems for stochastic parabolic equations.
Lü, Q., Lü Q.
core   +1 more source

Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$

Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.
Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson, Janne Nurminen, Mikko Salo   +2 more
wiley   +1 more source