Learning on dynamic statistical manifolds

05/07/2020
by   Francesca Boso, et al.
0

Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data assimilation, remain an open challenge. That is due to nonlinearity of governing equations, whose solutions are highly non-Gaussian and often discontinuous. To ameliorate these issues in a computationally efficient way, we use the method of distributions, which here takes the form of a deterministic equation for spatiotemporal evolution of the cumulative distribution function (CDF) of the random system state, as a means of forward uncertainty propagation. Uncertainty reduction is achieved by recasting the standard loss function, i.e., discrepancy between observations and model predictions, in distributional terms. This step exploits the equivalence between minimization of the square error discrepancy and the Kullback-Leibler divergence. The loss function is regularized by adding a Lagrangian constraint enforcing fulfillment of the CDF equation. Minimization is performed sequentially, progressively updating the parameters of the CDF equation as more measurements are assimilated.

READ FULL TEXT
research
12/20/2019

Parameter identification in uncertain scalar conservation laws discretized with the discontinuous stochastic Galerkin Scheme

We study an identification problem which estimates the parameters of the...
research
06/23/2021

Lagrangian dual framework for conservative neural network solutions of kinetic equations

In this paper, we propose a novel conservative formulation for solving k...
research
01/13/2020

Considering discrepancy when calibrating a mechanistic electrophysiology model

Uncertainty quantification (UQ) is a vital step in using mathematical mo...
research
05/09/2021

Probabilistic forecast of multiphase transport under viscous and buoyancy forces in heterogeneous porous media

In this study, we develop a probabilistic approach to map the parametric...
research
08/23/2020

Sparse approximation of data-driven Polynomial Chaos expansions: an induced sampling approach

One of the open problems in the field of forward uncertainty quantificat...
research
01/22/2020

Bayesian design for minimising uncertainty in spatial processes

Model-based geostatistical design involves the selection of locations to...
research
08/17/2022

Towards Learning in Grey Spatiotemporal Systems: A Prophet to Non-consecutive Spatiotemporal Dynamics

Spatiotemporal forecasting is an imperative topic in data science due to...

Please sign up or login with your details

Forgot password? Click here to reset