Template-Type: ReDIF-Paper 1.0
Title: Estimating initial conditions for dynamical systems with incomplete information
Abstract: In this paper we study the problem of inferring the initial conditions of a dynamical system under incomplete information. Studying several model systems, we infer the latent microstates that best reproduce an observed time series when the observations are sparse, noisy and aggregated under a (possibly) nonlinear observation operator. This is done by minimizing the least-squares distance between the observed time series and a model-simulated time series using gradient-based methods. We validate this method for the Lorenz and Mackey-Glass systems by making out-of-sample predictions. Finally, we analyze the predicting power of our method as a function of the number of observations available. We find a critical transition for the MackeyGlass system, beyond which it can be initialized with arbitrary precision.
Author-Name: Farmer, J. Doyne
Author-Name: Kolic, Blas
Author-Name: Sabuco, Juan
File-URL: https://oms-inet.files.svdcdn.com/production/files/Microstates_Initialization-4-00000002.pdf
File-Format: Application/pdf
File-Function: 
Length: 17 pages
Creation-Date: 2021-09
Handle: RePEc:amz:wpaper:2021-20