Koopman operator dynamical models: Learning, analysis and control

Bevanda, Petar; Sosnowski, Stefan; Hirche, Sandra

doi:10.1016/j.arcontrol.2021.09.002

Cited by 89 publications

(29 citation statements)

References 115 publications

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“…While we are able to program a single RC at multiple operating points that are far apart, the linearization is a prominent limitation. Future extensions would use more advanced dynamical approximations into the bilinear regime using Volterra kernels [49] or Koopman composition operators [50] to better capture nonlinear behaviors.…”

Section: Discussionmentioning

confidence: 99%

A Neural Programming Language for the Reservoir Computer

Kim¹,

Bassett²

2022

Preprint

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From logical reasoning to mental simulation, biological and artificial neural systems possess an incredible capacity for computation. Such neural computers offer a fundamentally novel computing paradigm by representing data continuously and processing information in a natively parallel and distributed manner. To harness this computation, prior work has developed extensive training techniques to understand existing neural networks. However, the lack of a concrete and low-level programming language for neural networks precludes us from taking full advantage of a neural computing framework. Here, we provide such a programming language using reservoir computinga simple recurrent neural network-and close the gap between how we conceptualize and implement neural computers and silicon computers. By decomposing the reservoir's internal representation and dynamics into a symbolic basis of its inputs, we define a low-level neural machine code that we use to program the reservoir to solve complex equations and store chaotic dynamical systems as random access memory (dRAM). Using this representation, we provide a fully distributed neural implementation of software virtualization and logical circuits, and even program a playable game of pong inside of a reservoir computer. Taken together, we define a concrete, practical, and fully generalizable implementation of neural computation.

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Section: Discussionmentioning

confidence: 99%

A Neural Programming Language for the Reservoir Computer

Kim¹,

Bassett²

2022

Preprint

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“…where g and f are observables of the input and the output (Bevanda et al, 2021;Korda & Mezić, 2018;Narasingam & Kwon, 2019;Wu & Noé, 2019). This system achieves high adaptability to different control processes by using the action and rainfall as the input, and has thus been used in this study.…”

Section: Step 4: Structure Identification and Parameter Estimation Ba...mentioning

confidence: 99%

Flooding and Overflow Mitigation Using Deep Reinforcement Learning Based on Koopman Operator of Urban Drainage Systems

Tian

Liao

Zhang

et al. 2022

Water Resources Research

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“…These are infinite-dimensional operators that allow to handle nonlinear systems through a globally linear representation. See [111] for a detailed survey of data-driven representations of Koopman operators for dynamical systems and for their applications to control.…”

Section: Probabilistic Design Of Policies Through the Lenses Of Problemmentioning

confidence: 99%

Probabilistic design of optimal sequential decision-making algorithms in learning and control

Emiland¹,

Russo²

2022

Preprint

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This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that combines a problem formulation and a set of resolution methods. The formulation consists of an infinite-dimensional optimization problem. The methods come from approaches to search optimal solutions in the space of probability functions. Through the lenses of this overarching framework we revisit popular learning and control algorithms, showing that these naturally arise from suitable variations on the formulation mixed with different resolution methods. A running example, for which we make the code available, complements the survey. Finally, a number of challenges arising from the survey are also outlined.

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Koopman operator dynamical models: Learning, analysis and control

Cited by 89 publications

References 115 publications

A Neural Programming Language for the Reservoir Computer

A Neural Programming Language for the Reservoir Computer

Flooding and Overflow Mitigation Using Deep Reinforcement Learning Based on Koopman Operator of Urban Drainage Systems

Probabilistic design of optimal sequential decision-making algorithms in learning and control

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