#partial differential equations
37 papers match
Data-free neural PDE solvers based on Graph Neural Networks and weak forms
Mikel M. Iparraguirre, Iciar Alfaro, David Gonzalez +1
The paper introduces a neural network that solves partial differential equations without any training data by using a graph neural network and the weak form of the equations, compu…
Numerical Spectrum Linking: Identification of Governing PDE via Koopman-Chebyshev Approximation with Resampling
Phonepaserth Sisaykeo, Shogo Muramatsu
The paper presents a numerical framework that uses Chebyshev spectral representations of Koopman operators to identify governing partial differential equations directly from observ…
Log-Concavity and Level-Set Horoconvexity of the First Eigenfunction on Horoconvex Domains in the Hyperbolic Plane
Xianzhe Dai, John M. Ennis, Xuan Hien Nguyen +1
The paper proves that the first Dirichlet eigenfunction on any bounded smooth horoconvex domain in the hyperbolic plane is log‑concave, i.e., the Hessian of its negative logarithm…
EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks
Peng Yin, Kai Li, Yifan Zhang +1
EvoPINN is an agentic framework that uses a large language model to automatically generate and verify executable algorithms for physics-informed neural networks, improving the accu…
Dynamic sliding and rolling friction models for viscoelastic contact pairs
Luigi Romano
The paper develops mathematical models for sliding and rolling friction between viscoelastic bodies, deriving a system of PDEs that describe frictional forces, bristle deformations…
Quasi-Monte Carlo for Bayesian design of experiment problems governed by parametric PDEs
Vesa Kaarnioja, Claudia Schillings
The paper studies Bayesian optimal experimental design for PDE-governed inverse problems, deriving regularity estimates and analyzing quasi‑Monte Carlo integration using full and s…