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math.DS2025
When is a System Discoverable from Data? Discovery Requires Chaos
Zakhar Shumaylov, Peter Zaika, Philipp Scholl +3
The deep learning revolution has enabled major AI advances in physical sciences, particularly in discovering dynamical systems from observational data. Yet the reliability of learn…
cs.LG2025
Generalized Lie Symmetries in Physics-Informed Neural Operators
Amy Xiang Wang, Zakhar Shumaylov, Peter Zaika +2
Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated…