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pro vyhledávání: '"Redman, William"'
Koopman operator theory, a data-driven dynamical systems framework, has found significant success in learning models from complex, real-world data sets, enabling state-of-the-art prediction and control. The greater interpretability and lower computat
Externí odkaz:
http://arxiv.org/abs/2311.12615
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep learning ap
Externí odkaz:
http://arxiv.org/abs/2305.09060
Autor:
Redman, William T., Bello-Rivas, Juan M., Fonoberova, Maria, Mohr, Ryan, Kevrekidis, Ioannis G., Mezić, Igor
Study of the nonlinear evolution deep neural network (DNN) parameters undergo during training has uncovered regimes of distinct dynamical behavior. While a detailed understanding of these phenomena has the potential to advance improvements in trainin
Externí odkaz:
http://arxiv.org/abs/2302.09160
Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification and compa
Externí odkaz:
http://arxiv.org/abs/2209.06374
The discovery of sparse subnetworks that are able to perform as well as full models has found broad applied and theoretical interest. While many pruning methods have been developed to this end, the na\"ive approach of removing parameters based on the
Externí odkaz:
http://arxiv.org/abs/2110.14856
Publikováno v:
Proceedings of the 39th International Conference on Machine Learning, PMLR Vol. 162, pp. 18483-18498 (ICML 2022)
Foundational work on the Lottery Ticket Hypothesis has suggested an exciting corollary: winning tickets found in the context of one task can be transferred to similar tasks, possibly even across different architectures. This has generated broad inter
Externí odkaz:
http://arxiv.org/abs/2110.03210
Autor:
Redman, William T.
Koopman mode decomposition and tensor component analysis (also known as CANDECOMP/PARAFAC or canonical polyadic decomposition) are two popular approaches of decomposing high dimensional data sets into low dimensional modes that capture the most relev
Externí odkaz:
http://arxiv.org/abs/2101.00555
Autor:
Dogra, Akshunna S., Redman, William T
Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide variety o
Externí odkaz:
http://arxiv.org/abs/2008.12190
Autor:
Dogra, Akshunna S., Redman, William T
Publikováno v:
Advances in Neural Information Processing Systems 33, 2087-2097 (2020)
Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in making use of t
Externí odkaz:
http://arxiv.org/abs/2006.02361
Autor:
Redman, William T
Publikováno v:
Phys. Rev. E 101, 060104 (2020)
Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $\eta$ and $\delta$, as well as ratios of critical exp
Externí odkaz:
http://arxiv.org/abs/1912.13010