From the 1 of 4 linked papers with an AI index.
4 papers
Lie Meets Network Dynamics: Exact Macroscopic Reductions (Finite Systems)
Erik Andreas Martens, Sanjay Dharmavaram
The paper develops a Lie‑Scheffers based framework that exactly reduces high‑dimensional network dynamical systems to a low‑dimensional macroscopic system, independent of network s…
Stable equilibria in the Lotka-Volterra equations
Magnus Aspenberg, Erik Martens, Kristofer Wollein Waldetoft
We consider the Lotka-Volterra system and provide necessary conditions for an equilibrium to be stable. Our results naturally complement earlier fundamental results by N. Adachi, Y…
Next-Generation Reservoir Computing for Dynamical Inference
Rok Cestnik, Erik A. Martens
We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom n…
Exact Dimensional Reduction for Quasi-Linear ODE Ensembles
Felix Augustsson, Erik Andreas Martens, Rok Cestnik
We present an exact dimensional reduction for high-dimensional dynamical systems composed of identical dynamical units governed by quasi-linear ordinary differential equations…