2 papers
math.DS2026
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
Matthew J. Colbrook, Igor MeziÄ, 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.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 …