Model validation: A probabilistic formulation

Frequency domain model validation in Wasserstein metric

“…A probabilistic formulation for the time-domain model validation problem was proposed recently [1], [2] by the authors. For both deterministic and stochastic systems, the proposed method uses uncertainty propagation as a construct to perform model validation.…”

“…This was detailed in [1], [2], with p = q = 2. The choice p = 2 is due to the fact that we measure inter-sample distance in Euclidean metric.…”

“…To conclude a model is valid with high probability, its Wasserstein gap trajectory 2 W 2 (t) must lie below user-specified tolerance levels, at all times. A probabilistically robust validation certificate was constructed Abhishek Halder and [1] to guarantee provably correct inference through a finite-sample computation.…”

“…To quantify the distributional closeness between the measured and model-predicted outputs, we used the L 2 Wasserstein distance of order 2, denoted as 2 W 2 , as a metric. It was shown in [1] that unlike pointwise notions of distances on the manifold of probability densities, the Wasserstein distance, originated from the Monge-Kantorovich theory of optimal transport [7], [8], is an integral notion of distance and is a measure of the minimum amount of work needed to convert one distributional shape to the other. It was shown that computation of 2 W 2 is fully non-parametric and it is robust against unequal number of samples, and nonoverlapping supports -situations commonly encountered in nonlinear model validation.…”

Nonlinear filtering with transfer operator

“…Thus, in order to compute the Wasserstein time history, we resort to the LP formulation [22]. At each time, we sample (15) using the MetropolisHastings MCMC technique [27], and solve the LP between the sampled true Benes posterior and particle filter/KLPF posterior, to result the normalized Wasserstein trajectories shown in Fig.…”