Reconstruction of stochastic nonlinear dynamical models from trajectory measurements

Dmitri G. Luchinsky; Vadim N. Smelyanskiy; Marko Millonas; Peter V. E. McClintock

doi:10.1117/12.610457

23 May 2005 Reconstruction of stochastic nonlinear dynamical models from trajectory measurements (Invited Paper)

Dmitri G. Luchinsky, Vadim N. Smelyanskiy, Marko Millonas, Peter V. E. McClintock

Proceedings Volume 5845, Noise in Complex Systems and Stochastic Dynamics III; (2005) https://doi.org/10.1117/12.610457
Event: SPIE Third International Symposium on Fluctuations and Noise, 2005, Austin, Texas, United States

Abstract

We consider the following general problem of applied stochastic nonlinear dynamics. We observe a time series of signals y(t) = y(t₀+hn) corrupted by noise. The actual state and the nonlinear vector field of the dynamical system is not known. The question is how and with what accuracy can we determine x(t) and functional form of f(x). In this talk we discuss a novel approach to the solution of this problem based on the application of the path-integral approach to the full Bayesian inference. We demonstrate a reconstruction of a dynamical state of a system from corrupted by noise measurements. Next we reconstruct the corresponding nonlinear vector field. The emphasis are on the theoretical analysis. The results are compared with the results of earlier research.

Citation Download Citation

Dmitri G. Luchinsky, Vadim N. Smelyanskiy, Marko Millonas, and Peter V. E. McClintock "Reconstruction of stochastic nonlinear dynamical models from trajectory measurements (Invited Paper)", Proc. SPIE 5845, Noise in Complex Systems and Stochastic Dynamics III, (23 May 2005); https://doi.org/10.1117/12.610457

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