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physics.comp-ph2026
Data-driven reconstruction of dynamical systems using Takens' Theorem, manifold learning, and universal function approximators
Maximilian Topel, Andrew L. Ferguson
Embedding theorems can be used to provide theoretical guarantees about the relation between low-dimensional observations of a system and its full-dimensional state and dynamics. Su…
physics.comp-ph2026
Kolmogorov-Sinai entropies identify optimal observables for prediction and dynamics reconstruction in chaotic systems
Maximilian Topel
Choosing the optimal observable to model dynamical systems for which we do not know the driving equations is nearly always an ad hoc art. Takens' Delay Embedding Theorem guarantees…
physics.comp-ph2020★ 9 cited
Reconstruction of Protein Structures from Single-Molecule Time Series
Maximilian Topel, Andrew L. Ferguson
Single-molecule experimental techniques track the real-time dynamics of molecules by recording a small number of experimental observables. Following these observables provides a co…