Thema der Dissertation:
Data-Driven Non-Markovian Models for the Analysis and Prediction of Time-Series Data
Data-Driven Non-Markovian Models for the Analysis and Prediction of Time-Series Data
Abstract: We develop and apply generalized Langevin equations (GLEs) for modeling non-Markovian dynamics in discrete time-series data. Emphasizing both theoretical and computational aspects, we investigate how memory effects, non-Gaussian noise, or coupling between multi-dimensional reaction coordinates shape the dynamics of stochastic observables. By combining theoretical foundations with computational techniques, we demonstrate that GLEs can provide a practical and physically grounded framework for analyzing and predicting the dynamics of systems ranging from molecules to weather and financial markets.
We begin by laying out the theoretical foundation of the GLE using the projection operator formalism and introducing numerical tools that enable us to extract memory kernels and noise properties from real, discrete datasets, even when they describe systems out of equilibrium. As a first application, we examine dihedral transitions in butane using molecular dynamics simulations. Here, we directly compare different GLE formulations and demonstrate that including non-Gaussian noise yields significantly better predictions of mean first-passage times than traditional Gaussian-based approaches. This clearly shows that the noise statistics themselves carry valuable information about the underlying dynamics.
Moving beyond molecular systems, we explore how GLEs can be used for time-series forecasting. Using a convolution-based filtering method, we separate slow trends and oscillations from fast fluctuations and model the latter with a GLE. When applied to daily weather data, this approach reveals long-lasting memory effects, while in financial time-series data, memory vanishes quickly, being consistent with the efficient-market hypothesis. In terms of predictive power, our GLE-based forecasts achieve a level comparable to modern recurrent neural networks, but with significantly lower computational cost and parameters that can be interpreted in physical terms.
Finally, we provide a glimpse of where this research is heading: toward multi-dimensional GLEs that capture the coupling between multiple coarse-grained coordinates. Results on pentane dihedral dynamics show strong cross-friction and higher-dimensional confinement between coarse-grained coordinates, pointing toward a richer description of non-Markovian effects in higher-dimensional reaction coordinates.
We begin by laying out the theoretical foundation of the GLE using the projection operator formalism and introducing numerical tools that enable us to extract memory kernels and noise properties from real, discrete datasets, even when they describe systems out of equilibrium. As a first application, we examine dihedral transitions in butane using molecular dynamics simulations. Here, we directly compare different GLE formulations and demonstrate that including non-Gaussian noise yields significantly better predictions of mean first-passage times than traditional Gaussian-based approaches. This clearly shows that the noise statistics themselves carry valuable information about the underlying dynamics.
Moving beyond molecular systems, we explore how GLEs can be used for time-series forecasting. Using a convolution-based filtering method, we separate slow trends and oscillations from fast fluctuations and model the latter with a GLE. When applied to daily weather data, this approach reveals long-lasting memory effects, while in financial time-series data, memory vanishes quickly, being consistent with the efficient-market hypothesis. In terms of predictive power, our GLE-based forecasts achieve a level comparable to modern recurrent neural networks, but with significantly lower computational cost and parameters that can be interpreted in physical terms.
Finally, we provide a glimpse of where this research is heading: toward multi-dimensional GLEs that capture the coupling between multiple coarse-grained coordinates. Results on pentane dihedral dynamics show strong cross-friction and higher-dimensional confinement between coarse-grained coordinates, pointing toward a richer description of non-Markovian effects in higher-dimensional reaction coordinates.
Zeit & Ort
24.09.2025 | 15:00
Hörsaal A (1.3.14)
(Fachbereich Physik, Arnimallee 14, 14195 Berlin)