3 papers
math.NA2025
Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers
Emil Haugen, Alexei Stepanenko, Anders C. Hansen
We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. These verification algorithms compute accurate estimates of …
math.DS2024
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
Matthew J. Colbrook, Igor Mezić, Alexei Stepanenko
Many systems resist analytical modeling, making data-driven inference of dynamics important. Yet data-driven methods can fail to converge or generalize, leaving open a central ques…
math.NA2024
Computing scattering resonances of rough obstacles
Frank Rösler, Alexei Stepanenko
This paper is concerned with the numerical computation of scattering resonances of the Laplacian for Dirichlet obstacles with rough boundary. We prove that under mild geometric ass…