A numerical algorithm for the solution of an inverse coefficient problem for nonstationary, nonlinear production-destruction type model is proposed and tested on an example of the Lorenz’63 system. With an ensemble of adjoint problem solutions, the inverse problem is transformed into a quasi-linear matrix problem and solved with Newton-type algorithm. Two different ways of the adjoint ensemble construction are compared. In the first one, a trigonometric basis is used. In the second one in situ measurements are taken into account. Local convergence properties of the algorithm are studied numerically to find out when the use of more data can lead to the degradation of the reconstruction results.

中文翻译：

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生产-破坏模型的伴随问题解集合的系数识别算法的数值研究

提出了一种求解非平稳，非线性生产-破坏型模型反系数问题的数值算法，并以Lorenz'63系统为例进行了测试。在伴随问题解的集合中，逆问题被转化为准线性矩阵问题，并用牛顿型算法求解。比较了两种不同的伴随合奏结构。在第一个中，使用了三角学基础。在第二个中，考虑了原位测量。对算法的局部收敛性进行了数值研究，以找出何时使用更多数据会导致重建结果下降。