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Stochastic Spatio-Temporal processes are prevalent across domains rangingfrom modeling of plasma to the turbulence in fluids to the wave function ofquantum systems. This letter studies a measure-theoretic description of suchsystems by describing them as evolutionary processes on Hilbert spaces, and indoing so, derives a framework for spatio-temporal manipulation from fundamentalthermodynamic principles. This approach yields a variational optimizationframework for controlling stochastic fields. The resulting scheme is applicableto a wide class of spatio-temporal processes and can be used for optimizingparameterized control policies. Our simulated experiments explore theapplication of two forms of this approach on four stochastic spatio-temporalprocesses, with results that suggest new perspectives and directions forstudying stochastic control problems for spatio-temporal systems.

Leveraging Stochasticity for Open Loop and Model Predictive Control of Complex Fluid Systems