Quantized EDMD predictor estimates converge, as data grows, to a regularized least-squares solution of the unquantized problem, with finite-data errors of order ϵ.
On the Effect of Quantization on Dynamic Mode Decomposition
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abstract
Dynamic Mode Decomposition (DMD) is a widely used data-driven algorithm for estimating the Koopman Operator.This paper investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental connection between estimates of the operator obtained from unquantized data and those from quantized data. Furthermore, using the law of large numbers, we demonstrate that, under a large data regime, the quantized estimate can be considered a regularized version of the unquantized estimate. This key theoretical finding paves the way to accurately recover the unquantized estimate from quantized data. We also explore the relationship between the two estimates in the finite data regime. The theory is validated through repeated numerical experiments conducted on three different dynamical systems.
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Koopman Meets Limited Bandwidth: Effect of Quantization on Data-Driven Linear Prediction and Control of Nonlinear Systems
Quantized EDMD predictor estimates converge, as data grows, to a regularized least-squares solution of the unquantized problem, with finite-data errors of order ϵ.