Unlocking Simulators: From Screening to Fingerprints via Sensitivity Analysis

Overview

Abstract 

Simulators are computer codes nowadays ubiquitous to the analysis of complex physical systems. The premise of this work is to view a simulator as a black-box, mathematically represented by a function that one wishes to analyze only on the basis of information on its inputs and outputs. Performing experiments by running a simulator at specific input configurations and/or experimental settings helps infer insights about underlying processes and behaviors of the complex physical system it represents. In this context, the concept of sensitivity analysis (SA) is central. Broadly speaking, SA consists in characterizing both qualitatively and quantitatively the relationship between inputs and outputs of a given simulator via sensitivity measures.

In this talk, I first take you through SA taxonomy. I present how simulators are analyzed with an emphasis on so-called global methods. I elaborate on how these can be carried out using a probabilistic approach leading to Probabilistic Sensitivity Analysis (PSA). Second, I describe a framework to assess the challenges imposed by heavy simulators, characterized mainly by the curse of dimensionality and computational cost, which make sensitivity measures computationally prohibitive and impractical. This framework relies on the construction of a statistical emulator as a fast surrogate to the simulator. I give special care to the presentation and spatial visualization of the sensitivity measures with an estimate of modeling uncertainty. Furthermore, I introduce the notion of fingerprints, defined as characteristic modes extracted from the variation of the sensitivity measures. Finally, I present recent developments towards a novel framework connecting SA and PSA for dynamical systems, extending the notion of fingerprints to characterize the evolution of physical structures.

Applications of SA include initial condition sensitivity, dominant factors selection, environmental factor detection, engineering design, risk assessment, and uncertainty quantification. Here, I illustrate four main ones for (i) screening parameters via a model described by ODEs, (ii) selecting dominant factors via an oil reservoir simulator, (iii) gaining knowledge on mechanisms and processes via a paleoclimate application, and (iv) characterizing the evolution of physical structures via the Elder problem, a classical density-driven groundwater flow benchmark.