Convolutional-sparse-coded Dynamic Mode Decomposition and Its Application to River State Estimation

Kaneko, Y.; Muramatsu, Shogo; Yasuda, Hiroyasu; Hayasaka, K.; Otake, Yu; Ono, Shunsuke; Yukawa, Masahiro

doi:10.1109/icassp.2019.8683848

Cited by 9 publications

(5 citation statements)

References 23 publications

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“…to identify an approximate Koopman operator for the state space model (22) as a solution to the identification of the NAR model (8).…”

Section: Discussionmentioning

confidence: 99%

“…We prove the existence of a Koopman operator for this model in Proposition 2. Proposition 2: If the function f (x) in the NAR model ( 8) is analytic, then a Koopman operator exists for ( 16) and (22).…”

Section: Dynamic Mode Decomposition Of Nonlinear Autoregressive Modelsmentioning

confidence: 99%

“…Since the existence of a Koopman operator has been proved for the model (22) in Proposition 2, we construct a state inclusive dictionary of observables…”

Section: Dynamic Mode Decomposition Of Nonlinear Autoregressive Modelsmentioning

confidence: 99%

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Prediction of fitness in bacteria with causal jump dynamic mode decomposition

Balakrishnan¹,

Hasnain²,

Boddupalli³

et al. 2020

Preprint

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In this paper, we consider the problem of learning a predictive model for population cell growth dynamics as a function of the media conditions. We first introduce a generic data-driven framework for training operator-theoretic models to predict cell growth rate. We then introduce the experimental design and data generated in this study, namely growth curves of Pseudomonas putida as a function of casein and glucose concentrations. We use a data driven approach for model identification, specifically the nonlinear autoregressive (NAR) model to represent the dynamics. We show theoretically that Hankel DMD can be used to obtain a solution of the NAR model. We show that it identifies a constrained NAR model and to obtain a more general solution, we define a causal state space system using 1-step, 2-step,..., τ -step predictors of the NAR model and identify a Koopman operator for this model using extended dynamic mode decomposition. The hybrid scheme we call causal-jump dynamic mode decomposition, which we illustrate on a growth profile or fitness prediction challenge as a function of different input growth conditions. We show that our model is able to recapitulate training growth curve data with 96.6% accuracy and predict test growth curve data with 91% accuracy.

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“…to identify an approximate Koopman operator for the state space model (22) as a solution to the identification of the NAR model (8).…”

Section: Discussionmentioning

confidence: 99%

Section: Dynamic Mode Decomposition Of Nonlinear Autoregressive Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Prediction of fitness in bacteria with causal jump dynamic mode decomposition

Balakrishnan¹,

Hasnain²,

Boddupalli³

et al. 2020

Preprint

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“…The extended DMD (EDMD) has found a lot of applications for modeling autonomous systems such as cart pole system and voltage dynamics in a rudimentary model of power grids [14,15]. In [16], we introduce to adopt convolutional dictionary to EDMD to derive a time evolution formula of river bed shape development. The convolutional approach, which we refer to as convolutional-sparse-coded DMD (CSC-DMD), is developed for data on regular grids.…”

Section: Introductionmentioning

confidence: 99%

Sparse-Coded Dynamic Mode Decomposition on Graph for Prediction of River Water Level Distribution

Arai

Muramatsu

Yasuda

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This work proposes a method for estimating dynamics on graph by using dynamic mode decomposition (DMD) and sparse approximation with graph filter banks (GFBs). The motivation of introducing DMD on graph is to predict multi-point river water levels for forecasting river flood and giving proper evacuation warnings. The proposed method represents a spatio-temporal variation of physical quantities on a graph as a time-evolution equation. Specifically, water level observation data available on the Internet is collected by web scraping. As well, the graph structure is defined based on numerical river information published by Ministry of Land, Infrastructure, Transport and Tourism (MILT) of Japan and the graph is used to construct GFBs for analyzing and synthesizing the water level data. GFBs work in combination with a sparse approximation algorithm for feature extraction of water level distribution. The features are exploited to derive the time-evolution equation through the extended DMD (EDMD) framework. The time-evolution equation is applied to predict river water level distribution. In order to verify the significance of the proposed method, the river water level prediction is conducted for real web-scraped data. The performance evaluation shows the superiority to the normal DMD approach.

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“…The classical approach to solve this problem is to use dynamic mode decomposition (DMD) [67]. More recently, variations on DMD involve approximating observable functions with a broad set of dictionary functions (E-DMD) [68,69], which can be generated using deep learning [70][71][72][73], by casting the learning problem, as a robust optimization problem to handle sparse data [74,75] or to treat heterogeneously sampled data [76,77]. The power of Koopman operators lies in their ability to capture the underlying modes that drive the system [78][79][80], directly from data.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Sensor Fusion on Data-Driven Learning of Koopman Operators

Balakrishnan,

Hasnain,

Egbert

et al. 2021

Preprint

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Dictionary methods for system identification typically rely on one set of measurements to learn governing dynamics of a system. In this paper, we investigate how fusion of output measurements with state measurements affects the dictionary selection process in Koopman operator learning problems. While prior methods use dynamical conjugacy to show a direct link between Koopman eigenfunctions in two distinct data spaces (measurement channels), we explore the specific case where output measurements are nonlinear, non-invertible functions of the system state. This setup reflects the measurement constraints of many classes of physical systems, e.g., biological measurement data, where one type of measurement does not directly transform to another. We propose output constrained Koopman operators (OC-KOs) as a new framework to fuse two measurement sets. We show that OC-KOs are effective for sensor fusion by proving that when learning a Koopman operator, output measurement functions serve to constrain the space of potential Koopman observables and their eigenfunctions. Further, low-dimensional output measurements can be embedded to inform selection of Koopman dictionary functions for high-dimensional models. We propose two algorithms to identify OC-KO representations directly from data: a direct optimization method that uses state and output data simultaneously and a sequential optimization method. We prove a theorem to show that the solution spaces of the two optimization problems are equivalent. We illustrate these findings with a theoretical example and two numerical simulations.

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Convolutional-sparse-coded Dynamic Mode Decomposition and Its Application to River State Estimation

Cited by 9 publications

References 23 publications

Prediction of fitness in bacteria with causal jump dynamic mode decomposition

Prediction of fitness in bacteria with causal jump dynamic mode decomposition

Sparse-Coded Dynamic Mode Decomposition on Graph for Prediction of River Water Level Distribution

The Effect of Sensor Fusion on Data-Driven Learning of Koopman Operators

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