This workshop addresses the “virtual-to-physical” leg of the DT framework, in which the updated model is used as a basis for optimal control of the physical system or otherwise informs decisions. As with the data assimilation/inverse problem leg of DTs, quantify- ing uncertainties is crucial. This manifests as forward models that are characterized by random parameters, leading to optimal control problems that take the form of stochastic optimization problems that are governed by (usually PDE) models with random parameters. Specific challenges include: (1) when the random parameters are high dimensional (as in discretizations of infinite dimensional fields), and the models are sufficiently complex, solution of PDE-constrained stochastic optimization problems with conventional algorithms becomes prohibitive; (2) for critical societal problems, the objective of the optimization problem must be risk averse, rather than the risk neutral; while risk measures that quantify tail risk are available, they typically lead to non-differentiable objective functions when discretized, complicating the use of efficient optimization methods; (3) the real-time nature of DTs presents enormous challenges for optimal control of systems described by PDEs; (4) the sequential nature of the control problems can be exploited to construct algorithms that are dynamically adaptive; and (5) the sensors/observations themselves can be controlled as the physical system evolves, to better learn about the state/parameters of the system; this leads to an outer optimization problem (for control of the observing system) wrapped around a coupled data assimilation/optimal control problem, a daunting task.
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