5 papers
Optimization of randomized neural networks for transfer operator approximation
Mohammad Tabish, Stefan Klus
RaNNDy is a randomized neural network architecture for the data-driven approximation of transfer operators associated with complex dynamical systems. The weights and biases of the…
Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Stefan Klus, Feliks Nüske, Patrick GelÃ
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspir…
Learning graphons from data: Random walks, transfer operators, and spectral clustering
Stefan Klus, Jason J. Bramburger
Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying sto…
How deep is your network? Deep vs. shallow learning of transfer operators
Mohammad Tabish, Benedict Leimkuhler, Stefan Klus
We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the n…
Learning dynamical systems from data: Gradient-based dictionary optimization
Mohammad Tabish, Neil K. Chada, Stefan Klus
The Koopman operator plays a crucial role in analyzing the global behavior of dynamical systems. Existing data-driven methods for approximating the Koopman operator or discovering…