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pro vyhledávání: '"sterck"'
Stochastic Reinforcement Learning with Stability Guarantees for Control of Unknown Nonlinear Systems
Designing a stabilizing controller for nonlinear systems is a challenging task, especially for high-dimensional problems with unknown dynamics. Traditional reinforcement learning algorithms applied to stabilization tasks tend to drive the system clos
Externí odkaz:
http://arxiv.org/abs/2409.08382
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned residual ite
Externí odkaz:
http://arxiv.org/abs/2407.03873
When applying nonnegative matrix factorization (NMF), generally the rank parameter is unknown. Such rank in NMF, called the nonnegative rank, is usually estimated heuristically since computing the exact value of it is NP-hard. In this work, we propos
Externí odkaz:
http://arxiv.org/abs/2407.00706
Graph Neural Networks (GNNs) have established themselves as the preferred methodology in a multitude of domains, ranging from computer vision to computational biology, especially in contexts where data inherently conform to graph structures. While ma
Externí odkaz:
http://arxiv.org/abs/2404.03081
We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-oscillatory (WENO) reconstruction
Externí odkaz:
http://arxiv.org/abs/2401.04936
Anderson acceleration (AA) is widely used for accelerating the convergence of an underlying fixed-point iteration $\bm{x}_{k+1} = \bm{q}( \bm{x}_{k} )$, $k = 0, 1, \ldots$, with $\bm{x}_k \in \mathbb{R}^n$, $\bm{q} \colon \mathbb{R}^n \to \mathbb{R}^
Externí odkaz:
http://arxiv.org/abs/2312.04776
Transformer-based models have achieved state-of-the-art performance in many areas. However, the quadratic complexity of self-attention with respect to the input length hinders the applicability of Transformer-based models to long sequences. To addres
Externí odkaz:
http://arxiv.org/abs/2310.11960
Autor:
Cui, Tiangang, De Sterck, Hans, Gilbert, Alexander D., Polishchuk, Stanislav, Scheichl, Robert
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE) discreti
Externí odkaz:
http://arxiv.org/abs/2303.03673