274 citations · 1k across the 43 of their papers we have counts for
43 papers
Toward an Energy-Optimized Operation of Data Centers Located in Wind Farms Using Reinforcement Learning
Jan Stenner, Alexander Kilian, Sebastian Peitz +1
This paper studies Reinforcement Learning as an online controller for curtailment-aware workload shifting in wind-turbine-integrated high-performance computing (HPC) data centers.…
Bayesian Transfer Operators in Reproducing Kernel Hilbert Spaces
Septimus Boshoff, Sebastian Peitz, Stefan Klus
The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has bee…
Invariance of Gaussian RKHSs under Koopman operators of stochastic differential equations with constant matrix coefficients
Friedrich Philipp, Manuel Schaller, Karl Worthmann +2
We consider the Koopman operator semigroup associated with stochastic differential equations of the form with constant matrices and…
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
Konstantin Sonntag, Bennet Gebken, Georg Müller +2
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spa…
Variance representations and convergence rates for data-driven approximations of Koopman operators
Friedrich M. Philipp, Manuel Schaller, Septimus Boshoff +3
We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; b…
Error analysis of kernel EDMD for prediction and control in the Koopman framework
Friedrich Philipp, Manuel Schaller, Karl Worthmann +2
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is…
Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
Marco Bernreuther, Michael Dellnitz, Bennet Gebken +4
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimizati…
A multiobjective continuation method to compute the regularization path of deep neural networks
Augustina C. Amakor, Konstantin Sonntag, Sebastian Peitz
Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of rel…
Equivariance and partial observations in Koopman operator theory for partial differential equations
Sebastian Peitz, Hans Harder, Feliks Nüske +3
The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying line…
Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping
Konstantin Sonntag, Sebastian Peitz
We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping.…
Learning a model is paramount for sample efficiency in reinforcement learning control of PDEs
Stefan Werner, Sebastian Peitz
The goal of this paper is to make a strong point for the usage of dynamical models when using reinforcement learning (RL) for feedback control of dynamical systems governed by part…
Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning
Sebastian Peitz, Jan Stenner, Vikas Chidananda +3
We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical syste…
Error bounds for kernel-based approximations of the Koopman operator
Friedrich Philipp, Manuel Schaller, Karl Worthmann +2
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation…
Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories
Samuel E. Otto, Sebastian Peitz, Clarence W. Rowley
Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature l…
Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients
Manuel Berkemeier, Sebastian Peitz
In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogat…
Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-like Systems
Konstantin Sonntag, Sebastian Peitz
We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To th…
Towards reliable data-based optimal and predictive control using extended DMD
Manuel Schaller, Karl Worthmann, Friedrich Philipp +2
While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates…
Koopman analysis of quantum systems
Stefan Klus, Feliks Nüske, Sebastian Peitz
Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology.…
On the structure of regularization paths for piecewise differentiable regularization terms
Bennet Gebken, Katharina Bieker, Sebastian Peitz
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity.…
Finite-data error bounds for Koopman-based prediction and control
Feliks Nüske, Sebastian Peitz, Friedrich Philipp +2
The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems, e.g., via extended dynamic mode decomposition. Despite its popularit…
Efficient time stepping for numerical integration using reinforcement learning
Michael Dellnitz, Eyke Hüllermeier, Marvin Lücke +4
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamic…
Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models
Manuel Berkemeier, Sebastian Peitz
We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive…
On the Universal Transformation of Data-Driven Models to Control Systems
Sebastian Peitz, Katharina Bieker
The advances in data science and machine learning have resulted in significant improvements regarding the modeling and simulation of nonlinear dynamical systems. It is nowadays pos…
On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation
Katharina Bieker, Bennet Gebken, Sebastian Peitz
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scienti…