Data-driven discovery and extrapolation of parameterized pattern-forming dynamics
Zachary G. Nicolaou, Guanyu Huo, Y. M. Chen, Steven L. Brunton, J. Nathan Kutz
Abstract
A new machine-learning framework enables the discovery of governing equations in pattern-forming systems parameterized by external driving conditions. The resulting data-driven models reveal effective nonlinear corrections to classical perturbation theory, enabling extrapolation including the prediction of bifurcations far from the conditions used in training.
Topics & Concepts
ExtrapolationParameterized complexityNonlinear systemComputer scienceNonlinear dynamical systemsPerturbation (astronomy)Dynamical systems theoryDynamics (music)Machine learningAlgorithmArtificial intelligenceMathematicsPhysicsMathematical analysisAcousticsQuantum mechanicsModel Reduction and Neural NetworksNonlinear Dynamics and Pattern FormationNeural Networks and Reservoir Computing