In many digital twin (DT) applications, the complexity of the forward models, the high dimensionality of the inference parameter and decision variable spaces, the need for real-time response, and the imperative of accounting for uncertainties all conspire to make the underlying inverse and optimal control problems intractable using high fidelity forward models. Surrogates and reduced order models (ROMs) can make these tasks tractable, provided they are sufficiently accurate and can be constructed with sufficiently few forward model solves.
Specific challenges arising in the DT setting and that will be addressed in this workshop include: (1) The surrogates/ROMs need not represent the full spatiotemporal system dynamics well, but only the control objectives and data assimilation observables—how this “goal-orientation” is best done remains a challenge; (2) since DTs typically evolve the dynamics over long time periods, there is a need to make ROMs structure preserving (e.g., energy conserving); (3) Neural network representations have shown much promise as surrogates in high dimensions, but work remains to be done to provide guarantees of their trustworthiness, particularly in the few data regime; (4) the surrogates/ROMs must be parametric with respect to not just state space, but also control variable space and uncertain parameter space, since the DT framework executes data assimilation and control problems repeatedly over a moving horizon; (5) many methods for surrogates rely on an intrinsically low-dimensional map from parameters to outputs of interest, and for ROMs an intrinsically low-dimensional solution manifold, yet linear subspaces may not capture this low-dimensionality efficiently for certain classes of problems (e.g., high frequency wave propagation, advection-dominated flow and transport); and (6) using surrogates trained on samples of high-fidelity input–output maps and not their Jacobians can result in poor approximation of gradients, leading to inaccurate solutions of optimization problems underlying data assimilation and optimal control.
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