6 papers
Deep-Koopman-KANDy: Dictionary Discovery for Deep-Koopman Operators with Kolmogorov-Arnold Networks for Dynamics
Kevin Slote, Erik Bollt, Jeremie Fish
Symbolic library -- or Koopman dictionary -- selection is a fundamental challenge in data-driven dynamical systems. Extended Dynamic Mode Decomposition (EDMD), Sparse Identificatio…
CausationEntropy: Pythonic Optimal Causation Entropy
Kevin Slote, Jeremie Fish, Erik Bollt
Optimal Causation Entropy (oCSE) is a robust causal network modeling technique that reveals causal networks from dynamical systems and coupled oscillators, distinguishing direct fr…
On the emergence of numerical instabilities in Next Generation Reservoir Computing
Edmilson Roque dos Santos, Erik Bollt
Next Generation Reservoir Computing (NGRC) is a low-cost machine learning method for forecasting chaotic time series from data. Computational efficiency is crucial for scalable res…
Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs
Gianluca Fabiani, Erik Bollt, Constantinos Siettos +1
We present a linear stability analysis of physics-informed random projection neural networks (PI-RPNNs), for the numerical solution of {the initial value problem (IVP)} of (stiff)…
Locality Blended Next Generation Reservoir Computing For Attention Accuracy
Daniel J. Gauthier, Andrew Pomerance, Erik Bollt
We extend an advanced variation of a machine learning algorithm, next-generation reservoir Computing (NGRC), to forecast the dynamics of the Ikeda map of a chaotic laser. The machi…
Fractal Conditional Correlation Dimension Infers Complex Causal Networks
Ãzge Canlı Usta, Erik M. Bollt
Determining causal inference has become popular in physical and engineering applications. While the problem has immense challenges, it provides a way to model the complex networks…