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Title: Scalable Stochastic Programming with Bayesian Hybrid Models
Bayesian hybrid models (BHMs) fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we demonstrate a scalable computational strategy to embed BHMs in an equation-oriented modelling environment. Thus, this paper generalizes stochastic programming, which traditionally focuses on aleatoric uncertainty (as characterized by a probability distribution for uncertainty model parameters) to also consider epistemic uncertainty, i.e., mode-form uncertainty or systematic bias as modelled by the Gaussian process in the BHM. As an illustrative example, we consider ballistic firing using a BHM that includes a simplified glass-box (i.e., equation-oriented) model that neglects air resistance and a Gaussian process model to account for systematic bias (i.e., epistemic or model-form uncertainty) induced from the model simplification. The gravity parameter and the GP hypermeters are inferred from data in a Bayesian framework, yielding a posterior distribution. A novel single-stage stochastic program formulation using the posterior samples and Gaussian quadrature rules is proposed to compute the optimal decisions (e.g., firing angle and velocity) that minimize the expected value of an objective (e.g., distance from a stationary target). PySMO is used to generate expressions for the GP prediction mean and uncertainty in Pyomo, enabling efficient optimization with gradient-based solvers such as Ipopt. A scaling study characterizes the solver time and number of iterations for up to 2,000 samples from the posterior.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ;
Yamashita, Y.; Kano, M.
Date Published:
Journal Name:
Computer aided chemical engineering
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
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