Learning Nonautonomous Systems via Dynamic Mode Decomposition

• URL: http://arxiv.org/abs/2306.15618v1
• Date: Tue, 27 Jun 2023 16:58:26 GMT
• Title: Learning Nonautonomous Systems via Dynamic Mode Decomposition
• Authors: Hannah Lu and Daniel M. Tartakovsky
• Abstract summary: We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD) To circumvent the difficulty of approximating the time-dependent Koopman operators for nonautonomous systems, a modified system is employed as an approximation to the original nonautonomous system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the difficulty of approximating the time-dependent Koopman operators for nonautonomous systems, a modified system derived from local parameterization of the external time-dependent inputs is employed as an approximation to the original nonautonomous system. The modified system comprises a sequence of local parametric systems, which can be well approximated by a parametric surrogate model using our previously proposed framework for dimension reduction and interpolation in parameter space (DRIPS). The offline step of DRIPS relies on DMD to build a linear surrogate model, endowed with reduced-order bases (ROBs), for the observables mapped from training data. Then the offline step constructs a sequence of iterative parametric surrogate models from interpolations on suitable manifolds, where the target/test parameter points are specified by the local parameterization of the test external time-dependent inputs. We present a number of numerical examples to demonstrate the robustness of our method and compare its performance with deep neural networks in the same settings.

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