ISOKANN: Invariant subspaces of Koopman operators learned by a neural network
Robert Julian Rabben, Sourav Ray, Marcus Weber
Abstract
The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural network.
Topics & Concepts
Linear subspaceInvariant (physics)Operator (biology)Artificial neural networkExploitComputer scienceMathematicsAlgebra over a fieldApplied mathematicsArtificial intelligencePure mathematicsRepressorMathematical physicsComputer securityChemistryBiochemistryTranscription factorGeneModel Reduction and Neural NetworksGaussian Processes and Bayesian InferenceNeural Networks and Applications