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Uncertainty Quantification in Dynamics Operator Models

Type: Guided Research / Master's Thesis

Prerequisites:

• Knowledge in machine learning/ statistics or dynamical systems
• Good coding skills in Python and a deep learning framework (preferably JAX)

Description:

Recently, operator models for dynamical systems have gained attention in the control community. Methods like Dynamic Mode Decomposition and its extensions are easy to use and, due to the linearity of the operator models, lead to favorable computational properties in downstream algorithms. Yet a fundamental issue of current approaches and theory is the lack of readily usable uncertainty quantification of predictions. This limits the application when distributional predictions are needed and prohibits the use of popular optimization techniques.

During the the course of this project you will investigate ways to understand and extend the state-of-the-art by deriving means to uncertainty quantification and implementing them in Python.

References:

Gaussian Processes and Reproducing Kernels: Connections and Equivalences

Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces

Neural conditional probability for uncertainty quantification

Active Learning in Dynamical Systems

Type: Guided Research / Hiwi / Master's Thesis

Prerequisites:

• Knowledge in machine learning/ statistics or dynamical systems
• Good coding skills in Python and a linear algebra and numerics framework (preferably JAX)

Description:

Within the ALeSCo consortium an intersectional project is P6: Benchmarks for Active Learning in Systems and Control. Within this project we are developing a benchmark for active learning algorithms in dynamical systems. There are multiple subtasks that can be tackled in the course of a research project or thesis. These include deriving principled assessment metrics, designing and implementing a benchmark architecture and environments, as well as implementing and evaluating experimental and state-of-the-art active learning algorithms.

References:

Active learning in robotics: A review of control principles

ALeSCo Research Unit

DeepMind Control Gym

Representation Learning for Dynamical Systems

Type: Guided Research / Hiwi / Master's Thesis

Prerequisites:

• Knowledge in machine learning or dynamical systems
• Good coding skills in Python and a linear algebra and numerics framework (preferably JAX)

Description:

Linear operator learning methods offer a valuable tool for various tasks in systems and control, such as forecasting and optimal control problems. Learning linear operators leads to convex optimization problems for solving optimal control. Consequently, improving the representation spaces of linear operators is expected to contribute to the development of modern optimal control pipelines. Recent advances in learning representations for dynamical systems demonstrated that tailored representations can drastically improve predictive performance. Yet, it is still an open question how to learn representations for controlled models. The goal of this thesis is to get familiar with operator models for dynamical systems and extend them to systems with an additional exogenous inputs.

References:

Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces

Operator SVD with Neural Networks via Nested Low-Rank Approximation