3 papers
math.NA2026
Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds
Gustav Conradie, Nicolas Boullé, Jean-Christophe Loiseau +2
Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature space…
math.DS2025
Weighted Birkhoff Averages Accelerate Data-Driven Methods
Maria Bou-Sakr-El-Tayar, Jason J. Bramburger, Matthew J. Colbrook
Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages c…
cs.LG2025
Noisy PDE Training Requires Bigger PINNs
Sebastien Andre-Sloan, Anirbit Mukherjee, Matthew Colbrook
Physics-Informed Neural Networks (PINNs) are increasingly used to approximate solutions of partial differential equations (PDEs), particularly in high dimensions. In real-world set…