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pro vyhledávání: '"Peitz, Sebastian"'
We consider the Koopman operator semigroup $(K^t)_{t\ge 0}$ associated with stochastic differential equations of the form $dX_t = AX_t\,dt + B\,dW_t$ with constant matrices $A$ and $B$ and Brownian motion $W_t$. We prove that the reproducing kernel H
Externí odkaz:
http://arxiv.org/abs/2405.14429
Recently, there has been an increasing interest in exploring the application of multiobjective optimization (MOO) in machine learning (ML). The interest is driven by the numerous situations in real-life applications where multiple objectives need to
Externí odkaz:
http://arxiv.org/abs/2405.01480
We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in
Externí odkaz:
http://arxiv.org/abs/2404.18530
On the continuity and smoothness of the value function in reinforcement learning and optimal control
Autor:
Harder, Hans, Peitz, Sebastian
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. It is therefore of interest to study how similar the values of neighboring states are, i.e., t
Externí odkaz:
http://arxiv.org/abs/2403.14432
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in
Externí odkaz:
http://arxiv.org/abs/2402.06376
Autor:
Philipp, Friedrich M., Schaller, Manuel, Boshoff, Septimus, Peitz, Sebastian, Nüske, Feliks, Worthmann, Karl
We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d. and ergodic sampling under non-restrictive assumptions.
Externí odkaz:
http://arxiv.org/abs/2402.02494
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 linear and encompasses full information on the (expected stochastic) d
Externí odkaz:
http://arxiv.org/abs/2312.10460
The prediction of photon echoes is a crucial technique for gaining an understanding of optical quantum systems. However, it requires a large number of simulations with varying parameters and/or input pulses, which renders numerical studies expensive.
Externí odkaz:
http://arxiv.org/abs/2310.16578
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 relevant features), and robustness. For linear models, it is well known t
Externí odkaz:
http://arxiv.org/abs/2308.12044
Autor:
Bernreuther, Marco, Dellnitz, Michael, Gebken, Bennet, Müller, Georg, Peitz, Sebastian, Sonntag, Konstantin, Volkwein, Stefan
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set
Externí odkaz:
http://arxiv.org/abs/2308.01113