Deep learning to discover and predict dynamics on an inertial manifold
Alec J. Linot, Michael D. Graham
Abstract
A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM) and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.
Topics & Concepts
AttractorChaoticNonlinear systemArtificial neural networkDimensionality reductionInertial frame of referenceInvariant manifoldManifold (fluid mechanics)Computer scienceStatistical physicsDimension (graph theory)Nonlinear dimensionality reductionApplied mathematicsArtificial intelligenceMathematicsAlgorithmMathematical analysisClassical mechanicsPhysicsPure mathematicsQuantum mechanicsMechanical engineeringEngineeringModel Reduction and Neural NetworksMeteorological Phenomena and SimulationsNeural Networks and Applications