2 research outputs found
Learning and Optimization with Bayesian Hybrid Models
Bayesian hybrid models fuse physics-based insights with machine learning
constructs to correct for systematic bias. In this paper, we compare Bayesian
hybrid models against physics-based glass-box and Gaussian process black-box
surrogate models. We consider ballistic firing as an illustrative case study
for a Bayesian decision-making workflow. First, Bayesian calibration is
performed to estimate model parameters. We then use the posterior distribution
from Bayesian analysis to compute optimal firing conditions to hit a target via
a single-stage stochastic program. The case study demonstrates the ability of
Bayesian hybrid models to overcome systematic bias from missing physics with
less data than the pure machine learning approach. Ultimately, we argue
Bayesian hybrid models are an emerging paradigm for data-informed
decision-making under parametric and epistemic uncertainty.Comment: Submitted to 2020 American Control Conferenc
GPdoemd: a Python package for design of experiments for model discrimination
Model discrimination identifies a mathematical model that usefully explains
and predicts a given system's behaviour. Researchers will often have several
models, i.e. hypotheses, about an underlying system mechanism, but insufficient
experimental data to discriminate between the models, i.e. discard inaccurate
models. Given rival mathematical models and an initial experimental data set,
optimal design of experiments suggests maximally informative experimental
observations that maximise a design criterion weighted by prediction
uncertainty. The model uncertainty requires gradients, which may not be readily
available for black-box models. This paper (i) proposes a new design criterion
using the Jensen-R\'enyi divergence, and (ii) develops a novel method replacing
black-box models with Gaussian process surrogates. Using the surrogates, we
marginalise out the model parameters with approximate inference. Results show
these contributions working well for both classical and new test instances. We
also (iii) introduce and discuss GPdoemd, the open-source implementation of the
Gaussian process surrogate method