A Dynamic Mode Decomposition Extension for the Forecasting of Parametric Dynamical Systems

Abstract

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a dynamical system as a sum of spatial basis evolving linearly in time, thus enabling a better understanding of the physical phenomena and forecasting of future time instants. In this work we propose an extension of DMD to parameterized dynamical systems, focusing on the future forecasting of the output of interest in a parametric context. Initially all the snapshots -- for different parameters and different time instants -- are projected to a reduced space; then DMD, or one of its variants, is employed to approximate reduced snapshots for future time instants. Exploiting the low dimension of the reduced space the predicted reduced snapshots are then combined using regression techniques, thus enabling the possibility to approximate any untested parametric configuration in future. This paper depicts in detail the algorithmic core of this method; we also present and discuss three test cases for our algorithm: a simple dynamical system with a linear parameter dependency, a heat problem with nonlinear parameter dependency and a fluid dynamics problem with nonlinear parameter dependency.

References in corpus (13)

• Survey of Nearest Neighbor Techniques
• De-Biasing the Dynamic Mode Decomposition for Applied Koopman Spectral Analysis
• Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
• Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems
• Sparse sensing and DMD based identification of flow regimes and bifurcations in complex flows
• Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification
• An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics
• Enhancing CFD predictions in shape design problems by model and parameter space reduction
• On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis
• An efficient computational framework for naval shape design and optimization problems by means of data-driven reduced order modeling techniques
• Projection-based model reduction of dynamical systems using space-time subspace and machine learning

Cited by in corpus (5)

• Reduced Order Modeling with Shallow Recurrent Decoder Networks
• A Comparison of Parametric Dynamic Mode Decomposition Algorithms for Thermal-Hydraulics Applications
• Fast prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition
• On Deep-Learning-Based Closures for Algebraic Surrogate Models of Turbulent Flows
• Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models