Optimal-transport flow matching for stochastic model updating: a comparison with transitional MCMC-based Bayesian updating
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Deep generative models have attracted considerable attention as inference engines for stochastic model updating. Among these deep generative models, conditional flow matching offers a particularly efficient formulation, in which a continuous transport map from a latent distribution to the posterior is learned by regression against optimal-transport probability paths, avoiding both the invertibility constraints of normalising flows and the iterative denoising of diffusion models. However, its performance in engineering model updating has not been examined against an established baseline such as the Bayesian updating framework under controlled conditions. In this work, conditional flow matching is therefore assessed against the Bayesian model updating approach with transitional Markov chain Monte Carlo, in which the Bhattacharyya distance provides the approximate likelihood for the Bayesian approach. The two methods are assessed with respect to posterior fidelity, evaluated by statistical distances against the known ground truth and computational expenditure in model evaluations, with the offline training budget reported separately from the inference cost of each subsequent conditioning. A 3-DOF spring–mass system with uncertain stiffness parameters serves as the benchmark. Since the calibrated posterior constitutes the input description upon which subsequent reliability assessment depends, the accuracy and the marginal cost of the updating step both bear directly on reliability computations. In addition, the amortised nature of the learned transport map is discussed in this work, as it permits the posterior to be re-evaluated under new observations at negligible cost, which is a property of practical relevance to reliability assessment under sequentially acquired monitoring data.
