A Computational Study of Optimal Transport Problems Using Generalized Frobenius-Perron Operators

We propose a new perspective by connecting continuous optimal transport problems to the newly defined concept of generalized Frobenius-Perron operators. Based on this formulation, we numerically construct transport mappings that approximately satisfy the required constraint, thereby transforming the original variational problem into a tractable numerical optimization task. Here the optimal transport mapping is approximated by using either linear or cubic splines. Experimental results demonstrate that the proposed method can effectively approximate the true optimal transport mapping with some accuracy.