Beyond the Model Limit: Parameter Inference Across Scales

In multiscale studies of emergent phenomena, a common approach is to define a microscopic scale generative model and subsequently, by passing to a diffusion limit, to derive a mesoscopic or macroscopic model via a homogenization argument. Microscopic models are often inherently stochastic, while the diffusion limit model may represent distributions or mean field quantities. A canonical example of this type of limiting process is the classical diffusion equation as a limit of Brownian random motion. Being typically based on ordinary or partial differential equations formalism, large scale models are more amenable to inverse problems, where the model parameters are estimated from indirect observations. Due to the intrinsic ill-posed nature of inverse problems, the estimation of the parameters of large scale models may be itself a significant challenge. In some multiscale investigations, the quantities of primary interest are not those characterizing the large scale model, but rather the parameters of the as...