This workshop addresses the “physical-to-virtual” leg of the Digital Twins (DT) framework, in which observational or experimental data from the physical system is assimilated into a virtual model of its dynamics on a moving time horizon to infer model components (such as initial conditions boundary conditions, material coefficients, source terms). The focus will be on statistical formulations of data assimilation and inverse problems, notably the Bayesian framework, motivated by the critical need to quantify and manage uncertainty in DTs from data to inference to prediction to decisions. Several major challenges that arise in the DT framework will be addressed: (1) the goal-oriented (“fit-for-purpose”) nature of DTs, implying that the inverse solution needs to be accurate with respect to the downstream prediction/control quantities of interest, as opposed to the full parameter or state fields; (2) the real-time nature of DTs (dictated by the time scales of the dynamical system), necessitating fast algorithms for inference; (3) the fact that DTs typically describe complex physical systems (large-scale, multiphysics, multiscale, multirate) with high dimensional parameter/state spaces (often discretizations of infinite dimensional fields), necessitating scalable dimension-independent formulations and algorithms; (4) the need for inference methods that can exploit the sequential nature of the data assimilation/inverse problems; (5) the forward models often will include stochastic forcings, leading to “intractable” likelihoods that must be dealt with; and (6) the crucial task of accounting for model (structural) uncertainty in Bayesian inference remains an open problem in the general setting.
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