Results 131 to 140 of about 2,048 (231)

Fredholm Neural Networks for forward and inverse problems in elliptic PDEs

CoRR
Building on our previous work introducing Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to tackle forward and inverse problems for linear and semi-linear elliptic partial differential equations.
Kyriakos Georgiou, Constantinos I. Siettos, Athanasios N. Yannacopoulos   +2 more
openaire   +2 more sources

A Novel Mixed‐Hybrid, Higher‐Order Accurate Formulation for Kirchhoff–Love Shells

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT This paper presents a novel mixed‐hybrid finite element formulation for Kirchhoff–Love shells, designed to enable the use of standard C0$C^0$‐continuous higher‐order Lagrange elements. This is possible by introducing the components of the moment tensor as a primary unknown alongside the displacement vector, circumventing the need for C1$C^1 ...
Jonas Neumeyer, Thomas‐Peter Fries
wiley   +1 more source

Solving inverse problems for PDEs in terms of Lax-Milgram functional and a generalized collage method

In this paper, we develop a general collage coding framework for inverse problems in partial differential equations (PDEs) with boundary conditions. Although a general PDEs inverse problem can be very complicated, via the Generalized Collage Theorem in ...
Davide La Torre, Ed Vrscay, Herb Kunze
core  

A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains on a hemisphere

, 2018
We prove an isoperimetric inequality for the harmonic mean of the first $N-1$ non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemisphere of $\mathbb{S}^N$
B. Brandolini
core  

On the Performance and Convergence of PINNs for Problems in Linear Elasticity

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT Physics‐informed neural networks (PINNs) have emerged as a promising approach for solving partial differential equations by embedding physical laws directly into the loss function. However, their performance characteristics for problems in computational mechanics remain insufficiently understood.
Dipraj Kadlag, Carolin Birk, Sundararajan Natarajan, Hauke Gravenkamp   +3 more
wiley   +1 more source

Two Scale FE‐FFT‐Based Modeling of Cancellous Bone

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT Osteoporosis is characterized by a loss of volume percentage of cortical bone, which reduces the loading capacity of this organ and increases its likelihood for fractures. The disease has the highest prevalence of any bone disease worldwide, with a particularly high incidence among the elderly.
Mischa Blaszczyk, Christian Gierden, Klaus Hackl, Johanna Waimann   +3 more
wiley   +1 more source

On inverse source problems for space-dependent sources in thermoelasticity

The aim of this contribution is to discuss the results in Maes and Van Bockstal (J Inverse Ill-Posed Prob (5)4, 2022). These uniqueness results deal with inverse source problems of determining a space-dependent load or heat source in thermoelastic ...
Restrepo, JoeleditorUGent0002118425428020039725889749713629620000-0002-2381-733491709ea8-ac8f-11ec-a485-a41a7ef681a6, Maes, FrederickTW060001402509838020032475160000-0002-5742-6112B65FF17E-07B4-11E4-B754-00CA4B2F559A, Chatzakou, MariannaeditorWE168020034354520000-0003-0853-3007b2b75e9a-9309-11ea-a1d1-a1982ee4fe3d, Torebek, BerikboleditorUGent8020031341468710030321020000-0002-2354-237758CB7C6A-654A-11E9-8DA5-0B6A5607D3EF, Ruzhansky, MichaeleditorWE168020029013460000-0001-8633-55708B63EA9E-C5C8-11E8-8987-A2685607D3EF, Van Bockstal, KarelWE160020041042668020008579790000-0002-1898-7611165072B4-F0EE-11E1-A9DE-61C894A0A6B4, Van Bockstal, KareleditorWE160020041042668020008579790000-0002-1898-7611165072B4-F0EE-11E1-A9DE-61C894A0A6B4   +6 more
core  

On MAP Estimates and Source Conditions for Drift Identification in SDEs

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT We consider the inverse problem of identifying the drift in an stochastic differential equation (SDE) from n$n$ observations of its solution at M+1$M+1$ distinct time points. We derive a corresponding maximum a posteriori (MAP) estimate, we prove differentiability properties as well as a so‐called tangential cone condition for the forward ...
Daniel Tenbrinck, Nikolas Uesseler, Philipp Wacker, Benedikt Wirth   +3 more
wiley   +1 more source

AI‐Organized Multiscale Battery Modeling: Linking Structure and Property from Quantum to Device Scales

Small Structures, Volume 7, Issue 6, June 2026.
Multiscale modeling of battery systems combines quantum‐mechanical calculations, atomistic simulations, and mesoscale phase‐field approaches to describe processes spanning from reaction energetics to morphology evolution. Establishing consistent links between these scales remains a key challenge, particularly for the transfer of physical descriptors ...
Shoutong Jin, Ziyuan Wang, Mengke Li, Zeyu Deng   +3 more
wiley   +1 more source

A Neural Operator Emulator for Coastal and Riverine Shallow Water Dynamics

Journal of Geophysical Research: Machine Learning and Computation, Volume 3, Issue 3, June 2026.
Abstract Coastal regions and river floodplains are particularly vulnerable to the impacts of extreme weather events. Accurate real‐time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation.
Peter Rivera‐Casillas, Sourav Dutta, Shukai Cai, Mark Loveland, Kamaljyoti Nath, Khemraj Shukla, Corey Trahan, Jonghyun Lee, Matthew Farthing, Clint Dawson   +9 more
wiley   +1 more source