Let's do the time-warp-attend: Learning topological invariants of dynamical systems

arXiv:2312.09234v3 Announce Type: replace
Abstract: Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation …

abstract arxiv behavior circuits cs.lg math.ds networks parameters series stat.ml struggle systems threshold type