# Event detail

## Statistical Treatment of inverse problems constrained by differential equations-based models with stochastic terms: Neyman Seminar

Seminar: Neyman Seminar | December 4 | 4-5 p.m. | 1011 Evans Hall

Noemi Petra, UC Merced

In this talk, we introduce a statistical treatment of

inverse problems constrained by models with stochastic terms. The

solution of the forward problem is given by a distribution represented

numerically by an ensemble of simulations. The goal is to formulate

the inverse problem, in particular the objective function, to find the

closest forward distribution (i.e., the output of the stochastic

forward problem) that best explains the distribution of the

observations in a certain metric. We use proper scoring rules, a

concept employed in statistical forecast verification, namely energy,

variogram, and hybrid (i.e., combination of the two) scores. We study

the performance of the proposed formulation in the context of two

applications: a coefficient field inversion for subsurface flow

governed by an elliptic partial differential equation with a

stochastic source and a parameter inversion for power grid governed

by differential-algebraic equations. In both cases we show that the

variogram and the hybrid scores produce better parameter inversion

results than does the energy score, whereas the energy score leads to

better probabilistic predictions.

Berkeley, CA 94720, 5106422781

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