PICS Colloquium with Daniel Tartakovsky: Information Theory of Multiscale Simulations

We present an information-theoretic approach for integration of multi-resolution data into multiscale simulations.  Fine-scale information can comprise observational data and/or simulation results related to both system states and system parameters. It is aggregated into its coarse-scale representation by setting a probabilistic equivalence between the two scales, with parameters that are determined via minimization of observables error and mutual information across scales. The same quantities facilitate the use of coarse-scale data to constrain compatible fine-scale distributions. In the second part of this talk, we leverage the information-geometric properties of the statistical manifold to reduce predictive uncertainty via data assimilation. Specifically, we exploit the information-geometric structures induced by two discrepancy metrics, the Kullback-Leibler divergence and the Wasserstein distance, which explicitly yield natural gradient descent. The use of a deep neural network as a surrogate model for MD enables automatic differentiation, further accelerating optimization. The manifold’s geometry is quantified without sampling, yielding an accurate approximation of the gradient descent direction. Our numerical experiments demonstrate that accounting for the manifold’s geometry significantly reduces the computational cost of data assimilation by both facilitating the calculation of gradients and reducing the number of required iterations.