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

Abstract

We report that 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%more » 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. Finally, 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.« less

Authors:

Costabal, Francisco Sahli ^[1]; Perdikaris, Paris  ^[2];

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Kuhl, Ellen ^[3]; Hurtado, Daniel E. ^[1]

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+ Show Author Affiliations

1. Pontificia Universidad Católica de Chile, Santiago (Chile). Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences; Millennium Nucleus for Cardiovascular Magnetic Resonance (Chile)
2. Univ. of Pennsylvania, Philadelphia, PA (United States)
3. Stanford Univ., CA (United States)

Publication Date:

Fri Aug 30 00:00:00 EDT 2019

Research Org.:

Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:

1595796

Alternate Identifier(s):

OSTI ID: 1564273

Grant/Contract Number:  

SC0019116

Resource Type:

Accepted Manuscript

Journal Name:

Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:

Journal Volume: 357; Journal Issue: C; Related Information: https://github.com/fsahli/MFclass; Journal ID: ISSN 0045-7825

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; Machine learning; Bayesian inference; Hamiltonian Monte Carlo; Data-driven modeling; Cardiac electrophysiology