Field dynamics inference via spectral density estimation
Abstract
Stochastic differential equations are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to solve, e.g., when modeling Brownian motion. In some cases, the equations governing the dynamics of a physical system on macroscopic scales occur to be unknown since they typically cannot be deduced from general principles. In this work, we describe how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process. Furthermore, we show how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field. Generally, inverse problems like these can be tackled with the help of Information Field Theory. For now, we restrict to linear and autonomous processes. To demonstrate its applicability, we employ our reconstruction algorithm on a timeseries and spatiotemporal processes.
 Publication:

Physical Review E
 Pub Date:
 November 2017
 DOI:
 10.1103/PhysRevE.96.052104
 arXiv:
 arXiv:1708.05250
 Bibcode:
 2017PhRvE..96e2104F
 Keywords:

 Statistics  Methodology;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 12 pages, 9 figures