Results 101 to 110 of about 2,057 (240)

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

, 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  

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

Inductive Differential Constraint Method: Symbolic Regression‐Based Partial Differential Equation Regularization for Fatigue Crack Growth Prediction

International Journal for Numerical Methods in Engineering, Volume 127, Issue 15, 15 August 2026.
ABSTRACT This study introduces the inductive differential constraint method (IDCM), a data‐informed structural regularization framework that enhances neural network predictions under data‐scarce regimes by enforcing invariant differential structures extracted from simulation data.
Rekisei Ozawa, Yoshitaka Wada
wiley   +1 more source

On inverse source problems for space-dependent sources in thermoelasticity [PDF]

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  

BiLO: Bilevel Local Operator Learning for PDE Inverse Problems

Journal of Computational Physics
Abstract We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters.
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub   +3 more
openaire   +2 more sources

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Exact Solutions of Linear Multiple Delay Partial Differential Equations

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 14282-14291, August 2026.
ABSTRACT This paper develops an analytical framework for linear differential equations with multiple discrete delays. A new function, referred to as the multiple‐delay exponential function, is introduced, and some of its fundamental properties are established.
Stuart‐James M. Burney
wiley   +1 more source

High-Order Integral Equation Methods for Diffraction Problems Involving Screens and Apertures [PDF]

, 2012
This thesis presents a novel approach for the numerical solution of problems of diffraction by infinitely thin screens and apertures. The new methodology relies on combination of weighted versions of the classical operators associated with the Dirichlet ...
Lintner, Stéphane Karl
core   +1 more source

Efficient Tensor Completion Algorithms for Highly Oscillatory Operators

Numerical Linear Algebra with Applications, Volume 33, Issue 4, August 2026.
ABSTRACT We address the problem of recovering highly oscillatory operators, represented as n×n$$ n\times n $$ matrices with a fixed set of observed entries. Given that these matrices can be well compressed by butterfly matrix decomposition of L=𝒪(logn) levels requiring only O(nlogn)$$ O\left(n\log n\right) $$ degrees of freedom, we propose a novel ...
Navjot Singh, Edgar Solomonik, Xiaoye Sherry Li, Yang Liu   +3 more
wiley   +1 more source

Jacobian-AIME: A Local and Functional Approach to Interpreting Nonlinear Maps for Physics-Informed Neural Networks

IEEE Access
We propose Jacobian-AIME, a novel explanation framework for Physics-Informed Neural Networks (PINNs). PINNs map coordinates to physical fields governed by PDEs.
Kosuke Yano, Takafumi Nakanishi, Soichiro Ikuno   +2 more
doaj   +1 more source