Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation
Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation
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DOI：
10.1016/j.jcp.2024.112994
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发表时间：
2024-04-11
影响因子：
4.1
通讯作者：
Li，Wuchen
中科院分区：
文献类型：
--
作者：
Fu，Guosheng;Osher，Stanley;Li，Wuchen
我们设计并计算了一类反应扩散系统的最优控制问题。它们形成了与多密度反应扩散系统相关的平均场控制问题。为了在数值上解决所提出的最优控制问题，我们首先采用高阶有限元方法对时空域进行离散化，然后采用增广拉格朗日方法（ALG2）求解最优控制问题。数值例子，包括高斯分布和图像密度之间的广义最优输运和平均场控制问题，证明了所提出的建模和计算方法对涉及反应扩散方程/系统的平均场控制问题的有效性。
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we first apply high-order finite element methods to discretize the space-time domain and then solve the optimal control problem using augmented Lagrangian methods (ALG2). Numerical examples, including generalized optimal transport and mean field control problems between Gaussian distributions and image densities, demonstrate the effectiveness of the proposed modeling and computational methods for mean field control problems involving reaction-diffusion equations/systems.