Multi-fidelity classification using Gaussian processes: Accelerating the prediction of large-scale computational models

• Published in: Computer methods in applied mechanics and engineering 2019-12, Vol.357 (C), p.112602, Article 112602
• Main Authors: Sahli Costabal, Francisco, Perdikaris, Paris, Kuhl, Ellen, Hurtado, Daniel E.
• Format: Article
• Language: English
• Subjects: Accuracy; Artificial intelligence; Autoregressive models; Bayesian inference; Cardiac electrophysiology; Classification; Classifiers; Computer simulation; Data-driven modeling; Electrophysiology; Gaussian process; Hamiltonian Monte Carlo; Machine learning; Markov analysis; Markov chains; Monte Carlo simulation; Samplers; Source code; State-of-the-art reviews
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.112602

Machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational models which typically take days to run, thus hindering the potential of machine learning tools. In this work, we present a novel classifier that takes advantage of lower fidelity models and inexpensive approximations to predict the binary output of expensive computer simulations. We postulate an autoregressive model between the different levels of fidelity with Gaussian process priors. We adopt a fully Bayesian treatment for the hyper-parameters and use Markov Chain Monte Carlo samplers. We take advantage of the probabilistic nature of the classifier to implement active learning strategies. We also introduce a sparse approximation to enhance the ability of the multi-fidelity classifier to handle a large amount of low fidelity samples. We test these multi-fidelity classifiers against their single-fidelity counterpart with synthetic data, showing a median computational cost reduction of 23% for a target accuracy of 90%. In an application to cardiac electrophysiology, the multi-fidelity classifier achieves an F1 score, the harmonic mean of precision and recall, of 99.6% compared to 74.1% of a single-fidelity classifier when both are trained with 50 samples. In general, our results show that the multi-fidelity classifiers outperform their single-fidelity counterpart in terms of accuracy in all cases. We envision that this new tool will enable researchers to study classification problems that would otherwise be prohibitively expensive. Source code is available at https://github.com/fsahli/MFclass. •State-of-the-art computational models can take days to run.•We introduce a multi-fidelity classifier to predict the output of expensive models.•We use active learning to maximize the information gained with each sample.•The multi-fidelity classifier outperforms its single-fidelity version in all cases.