题目：Green's Matching: an Efficient Approach to Parameter Estimation in Complex Dynamic Systems

姓名：王学钦 讲席教授 (中国科学技术大学)

地点：致远楼108室

时间：2024年4月12日 星期五 10:00-11:00

Abstract：

Parameters of differential equations are essential to characterize the intrinsic behaviors of dynamic systems. 

Many scientific challenges are hindered by a lack of computational and statistical efficiency in parameter 

estimation of dynamic systems, especially for complex systems with general-order differential operators, such 

as motion dynamics. Aiming at discovering these dynamic systems behind noisy data, we develop a computationally 

tractable and statistically efficient two-step method called Green’s matching via estimating equations. 

Particularly, we avoid time-consuming numerical integration by the pre-smoothing of trajectories in the estimating 

equations, and the pre-smoothing of curve derivatives is generally not involved in the   estimating equations due 

to the inversion of differential operators by Green’s functions. These appealing features improve both computational 

and statistical efficiency for parameter estimation. We prove that Green’s matching attains statistically optimal 

convergence for general-order systems. While for the other two widely used two-step methods, their estimation biases 

may dominate the estimation errors, resulting in poor convergence rates for high-order systems. We conduct extensive 

simulations to examine the estimation behaviors of two-step methods and other competitive approaches. Our results 

show that Green’s matching outperforms other methods for parameter estimation, which also supports Green’s matching 

in more complicated statistical inferences, such as equation discovery or causal network inference, for general-order 

dynamic systems.

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