2 papers
cs.LG2026
Learn and Verify: A Framework for Rigorous Verification of Physics-Informed Neural Networks
Kazuaki Tanaka, Kohei Yatabe
The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as…
math.NA2026
A Green's Function-Based Enclosure Framework for Poisson's Equation and Generalized Sub- and Super-Solutions
Kazuaki Tanaka, Ryoga Iwanami, Kaname Matsue +1
This paper presents a novel framework for enclosing solutions of Poisson's equation based on generalized sub- and super-solutions constructed using fundamental solutions. The conve…