The problem of estimating model parameters from data representing near-equilibrium patterns in PDEs is considered. This problem is formulated as an optimization problem by determining the nearest state on a manifold of equilibria. Algorithms to solve this optimization problem are proposed, by first regularizing the problem and using explicit search directions on the tangent space of the equilibrium manifold. Some rigorous results on local converge are obtained. Several examples of pattern forming systems are used to test the proposed methodology. Comparisons to synthetic data are made showing the ability of obtaining excellent estimates even when significant noise is present.

考虑了从表示PDE中接近平衡模式的数据估计模型参数的问题。通过确定平衡流形上的最近状态，将此问题表述为优化问题。通过首先对问题进行正则化并在平衡流形的切线空间上使用显式搜索方向，提出了解决此优化问题的算法。在局部收敛上获得了一些严格的结果。图案形成系统的几个示例用于测试所提出的方法。与合成数据进行了比较，显示出即使存在很大的噪声也能获得出色的估计。