ENABLING OPTIMIZATION OF INFINITE-HORIZON PREDICTION THROUGH BIFURCATION DIAGRAMS

Lu, Yizhen

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https://hdl.handle.net/2142/124937 Copy

Description

Title

ENABLING OPTIMIZATION OF INFINITE-HORIZON PREDICTION THROUGH BIFURCATION DIAGRAMS

Author(s)

Lu, Yizhen

Issue Date

2021-05-01

Keyword(s)

Forecasting; Non-linear Dynamics; Infinite-horizon; Parameter Inference; Bifurcation; MAP Estimation

Abstract

This work focuses on predicting the long-term behavior of dynamical systems from very short, noisy trajectories. Traditional techniques often split the problem of forecasting into separate estimation and prediction steps. In that manner, the optimization is done over a surrogate objective rather than the true objective. We propose an alternative representation that shifts the emphasis to the final prediction, rather than the system identification. This thesis will mainly discuss three different methods that can be used for the infinite-horizon prediction. The baseline approach is maximum a posteriori (MAP) estimation of the underlying system parameters and state, followed by a simulation of the selected dynamics. Because the conditional distribution given the trajectory is often not easily differentiable, we apply zero-order optimization techniques to approximate the result. The other techniques begin with the marginalization of the distribution onto the stable nodes in the bifurcation diagram. The first is the application of MAP estimation to the marginalized distribution. The second method is minimum mean square error (MMSE) prediction, which reduces to the weighted average of the set of convergence points. For problems that involve stability detection, MAP estimation and likelihood ratio test (LRT) are performed to predict whether the system is more likely to be stable or not. Our simulations show that the forecasting performance can be improved by reformulating the problem as a distinct estimation problem instead of as an application of system identification. This work suggests a new direction for estimating the limiting behavior of unknown dynamics and may lead to more accurate, yet efficient algorithms in the future.

Type of Resource

text

Language

eng

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