Related papers: Algorithmic (Semi-)Conjugacy via Koopman Operator …
Social computation, whether in the form of searches performed by swarms of agents or collective predictions of markets, often supplies remarkably good solutions to complex problems. In many examples, individuals trying to solve a problem…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…
Modern artificial intelligence relies on networks of agents that collect data, process information, and exchange it with neighbors to collaboratively solve optimization and learning problems. This article introduces a novel distributed…
kooplearn is a machine-learning library that implements linear, kernel, and deep-learning estimators of dynamical operators and their spectral decompositions. kooplearn can model both discrete-time evolution operators (Koopman/Transfer) and…
We consider the distributed optimization problem, where a group of agents work together to optimize a common objective by communicating with neighboring agents and performing local computations. For a given algorithm, we use tools from…
The Koopman Operator (KO) takes nonlinear state dynamics and ``lifts'' those dynamics to an infinite-dimensional functional space of observables in which those dynamics are linear. Computational applications typically use a…
Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
We describe an iterative approach to computing long-time semiclassical dynamics in the presence of chaos, which eliminates the need for summing over an exponentially large number of classical paths, and has good convergence properties even…
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical…
The Koopman operator lifts nonlinear dynamical systems into a functional space of observables, where the dynamics are linear. In this paper, we provide three different Koopman representations for hybrid systems. The first is specific to…
For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between…
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…
This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the…