Discovery of Low-Dimensional Generative Models for Complex Dynamical Systems
This thesis presents a data-driven framework for discovering low-dimensional generative models of complex systems by using a library of normal-form equations to identify both observable dynamics and hidden control variables directly from time-series data.
Overview
Systems in nature are inherently complex, consisting of numerous interacting components operating across multiple spatial and temporal scales (e.g., neuroscience, climate, genomics, ecology). While these fields generate ever-larger volumes of data, the underlying dynamical principles often remain hidden when first-principles equations are unavailable. This thesis develops a data-driven framework to discover low-dimensional generative models - built from normal-form “building blocks” of nonlinear dynamics - that include both observables and inferred hidden control variables. We demonstrate that:
- Minimal libraries of normal forms can reconstruct the evolution of complex dynamics.
- Hidden bifurcation control variables mediating regime transitions can be inferred solely from time-series data.
- Structured model discovery reduces ill-posedness, but full scalability remains an open challenge.
This work has been presented at SIAM DS 2021, ICSB 2022 & 2023, and received a best-poster award at EMBL Theory & Concepts 2025.
Presenters
Brief Biography
Juan Pablo Muñoz Díaz is a Ph.D. candidate under the supervision of Prof. Jesper Tegnér (KAUST), co-supervised by Dr. Narsis Kiani (karolinska institutet). His research merges machine learning and bifurcation theory to uncover hidden variables in nonlinear biological systems. He has conducted collaborative research at the University of Cambridge and presented at leading international conferences, including the International Conference on Systems Biology and the SIAM Conference on Dynamical Systems.
