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This manuscript introduces a regression-type formulation for approximatingthe Perron-Frobenius Operator by relying on distributional snapshots of data.These snapshots may represent densities of particles. The Wasserstein metric isleveraged to define a suitable functional optimization in the space ofdistributions. The formulation allows seeking suitable dynamics so as tointerpolate the distributional flow in function space. A first-order necessarycondition for optimality is derived and utilized to construct a gradient flowapproximating algorithm. The framework is exemplied with numerical simulations.

Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric