Stochastic Processes as Surrogate Models for Dynamical Systems in Magnetic Confinement Fusion
MCML Authors
Katharina Röck (née Rath)
Dr.
* Former Member
Abstract
Katharina Röck (née Rath)
Dr.
* Former Member
Abstract
This thesis focuses on incorporating domain-specific knowledge into machine learning (ML) models for scientific applications, ensuring they accurately reflect underlying physical systems.<br>The first part introduces physics-consistent Gaussian processes (GPs), embedding physical laws directly into the model. These models address data governed by partial differential equations (PDEs) and Hamiltonian systems, preserving physical properties like symplecticity and enabling faster, long-term simulations. Applications include classifying chaotic trajectories and computing Lyapunov exponents. The second part tackles data scarcity in plasma physics by proposing robust surrogate models for multivariate time series. Using Student-$t$ process regression, these models handle outliers effectively and facilitate data imputation and augmentation, ensuring reliable predictions for multichannel sensor data.<br>This work advances ML approaches for surrogate modeling, chaos analysis, and plasma physics. (Shortened.)
BibTeXKey: Roe24