TY  - GEN
A1  - Brenner, Manuel Benjamin
CY  - Heidelberg
Y1  - 2024///
ID  - heidok35092
N2  - Dynamical systems (DS) theory provides a rich framework to model dynamic processes across science and engineering. However, traditional scientific model building is often laborious and struggles with the complexities of real-world DS. Advances in machine learning (ML) have led to the development of automated, data-driven techniques for approximating governing equations from time series, called Dynamical Systems Reconstruction (DSR). Yet, these approaches often struggle with real-world systems characterized by chaos, noise, non-Gaussian and multimodal observations, or multistability. The black-box nature of many ML models further complicates their analysis even if they describe the data well. This thesis introduces novel methods for inferring interpretable DSR models from challenging empirical time series. This includes several recurrent neural network models and training algorithms, tailored to extracting low-dimensional and tractable DSR models, and a flexible framework for DSR from multimodal and non-Gaussian observations. It further introduces a hierarchical inference framework, an analysis pipeline for a class of piecewise linear DSR models, and a novel pruning approach that yields interpretable network topologies. Extensive comparisons to state-of-the-art DSR algorithms illustrate the significant advancements made by the proposed methods, promising applications in physics, neuroscience, and beyond.
TI  - Learning Interpretable Dynamical Systems Models from Multimodal Empirical Time Series
AV  - public
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/35092/
ER  -