基于最优扰动正则化方法的一维薛定谔方程参数辨识OA
Parameter identification for one-dimensional Schrödinger equation based on optimal perturbation regularization method
研究基于边界控制和边界观测的一维薛定谔方程的参数辨识.首先,借助逆谱理论以及Ingham-Beurling定理证明了系数的可辨识性,且辨识所需观测时间可以任意短;然后,基于最优扰动正则化方法,给出了重构系统未知系数的算法;最后,通过数值仿真验证了辨识算法的有效性.
The parameter identification of one-dimensional Schrödinger equation through boundary control and boundary ob-servation is studied.Firstly,the identifiability of the diffusion coefficient is proven by virtue of inverse spectral theory and In-gham-Beurling theorem.It should be noted that the required observation time for identification can be arbitrarily short.Subse-quently,based on the optimal perturbation regularization method,an algorithm is presented to reconstruct the unknown pa-rameter of the Schrödinger equation.Finally,the effectiveness of the identification algorithm is validated through some nu-merical simulations.
包春莹;赵志学
天津师范大学数学科学学院,天津 300387||天津师范大学数学与交叉科学研究院,天津 300387天津师范大学数学科学学院,天津 300387||天津师范大学数学与交叉科学研究院,天津 300387
数理科学
薛定谔方程参数辨识逆谱理论最优扰动正则化
Schrödinger equationparameter identificationinverse spectral theoryoptimal perturbation regularization method
《天津师范大学学报（自然科学版）》 2026 (1)
1-5,5
国家自然科学基金资助项目(12326327,11901433).
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