Design of Dynamic Experiments for Black-Box Model Discrimination

• URL: http://arxiv.org/abs/2102.03782v1
• Date: Sun, 7 Feb 2021 11:34:39 GMT
• Title: Design of Dynamic Experiments for Black-Box Model Discrimination
• Authors: Simon Olofsson and Eduardo S. Schultz and Adel Mhamdi and Alexander Mitsos and Marc Peter Deisenroth and Ruth Misener
• Abstract summary: Consider a dynamic model discrimination setting where we wish to chose: (i) what is the best mechanistic, time-varying model and (ii) what are the best model parameter estimates. For rival mechanistic models where we have access to gradient information, we extend existing methods to incorporate a wider range of problem uncertainty. We replace these black-box models with Gaussian process surrogate models and thereby extend the model discrimination setting to additionally incorporate rival black-box model.
• Score: 72.2414939419588
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Diverse domains of science and engineering require and use mechanistic mathematical models, e.g. systems of differential algebraic equations. Such models often contain uncertain parameters to be estimated from data. Consider a dynamic model discrimination setting where we wish to chose: (i) what is the best mechanistic, time-varying model and (ii) what are the best model parameter estimates. These tasks are often termed model discrimination/selection/validation/verification. Typically, several rival mechanistic models can explain data, so we incorporate available data and also run new experiments to gather more data. Design of dynamic experiments for model discrimination helps optimally collect data. For rival mechanistic models where we have access to gradient information, we extend existing methods to incorporate a wider range of problem uncertainty and show that our proposed approach is equivalent to historical approaches when limiting the types of considered uncertainty. We also consider rival mechanistic models as dynamic black boxes that we can evaluate, e.g. by running legacy code, but where gradient or other advanced information is unavailable. We replace these black-box models with Gaussian process surrogate models and thereby extend the model discrimination setting to additionally incorporate rival black-box model. We also explore the consequences of using Gaussian process surrogates to approximate gradient-based methods.

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