Search Results for author: Sebastian Peitz

Found 14 papers, 6 papers with code

Predicting PDEs Fast and Efficiently with Equivariant Extreme Learning Machines

no code implementations29 Apr 2024 Hans Harder, Sebastian Peitz

We utilize extreme learning machines for the prediction of partial differential equations (PDEs).

On the continuity and smoothness of the value function in reinforcement learning and optimal control

no code implementations21 Mar 2024 Hans Harder, Sebastian Peitz

The value function plays a crucial role as a measure for the cumulative future reward an agent receives in both reinforcement learning and optimal control.

reinforcement-learning

A multiobjective continuation method to compute the regularization path of deep neural networks

1 code implementation23 Aug 2023 Augustina C. Amakor, Konstantin Sonntag, Sebastian Peitz

To overcome this limitation, we present an algorithm that allows for the approximation of the entire Pareto front for the above-mentioned objectives in a very efficient manner for high-dimensional DNNs with millions of parameters.

Multiobjective Optimization

Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems

no code implementations28 Jul 2023 Sebastian Peitz, Hans Harder, Feliks Nüske, Friedrich Philipp, Manuel Schaller, Karl Worthmann

The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems, the main reason being the enormous potential of identifying linear function space representations of nonlinear dynamics from measurements.

Learning a model is paramount for sample efficiency in reinforcement learning control of PDEs

1 code implementation14 Feb 2023 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 partial differential equations (PDEs).

Reinforcement Learning (RL)

Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning

1 code implementation25 Jan 2023 Sebastian Peitz, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, Kunihiko Taira

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).

reinforcement-learning Reinforcement Learning (RL)

Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories

1 code implementation20 Sep 2022 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 learning, state estimation, and control.

Model Predictive Control

Efficient time stepping for numerical integration using reinforcement learning

1 code implementation8 Apr 2021 Michael Dellnitz, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, Karlson Pfannschmidt

While the classical schemes apply very generally and are highly efficient on regular systems, they can behave sub-optimal when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems.

Meta-Learning Numerical Integration +2

On the Universal Transformation of Data-Driven Models to Control Systems

1 code implementation9 Feb 2021 Sebastian Peitz, Katharina Bieker

In other words, surrogate modeling for autonomous systems is much easier than for control systems.

Quantization

On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation

no code implementations14 Dec 2020 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 scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning (e. g., for the training of neural networks).

Model Selection Multiobjective Optimization

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

no code implementations23 Sep 2019 Stefan Klus, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia Clementi, Christof Schütte

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition).

Model Predictive Control

Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions

no code implementations16 May 2018 Stefan Klus, Sebastian Peitz, Ingmar Schuster

Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance operators and have been shown to be closely related to the conditional mean embedding framework developed by the machine learning community.

Time Series Time Series Analysis +1

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