Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets

By Paris Perdikaris, Daniele Venturi, G. Em Karniadakis. 2016

81 citations recorded by the source corpus.

We develop a framework for multifidelity information fusion and predictive inference in high-dimensional input spaces and in the presence of massive data sets. Hence, we tackle simultaneously the “big N" problem for big data and the curse of dimensionality in multivariate parametric problems. The proposed methodology establishes a new paradigm for constructing response surfaces of high-dimensional stochastic dynamical systems, simultaneously accounting for multifidelity in physical models as well as multifidelity in probability space. Scaling to high dimensions is achieved by data-driven dimensionality reduction techniques based on hierarchical functional decompositions and a graph-theoretic approach for encoding custom autocorrelation structure in Gaussian process priors. Multifidelity information fusion is facilitated through stochastic autoregressive schemes and frequency-domain machine learning algorithms that scale linearly with the data. Taking together these new developments leads to linear complex...

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. G. Em Karniadakis
2. Yibo Yang
3. Paris Perdikaris
4. Guofei Pang
5. Ellen Kuhl
6. Maizar Raissi
7. F. Sahli Costabal
8. Daniel E. Hurtado

In Computational Theory and Mathematics

1. Yibo Yang
2. Paris Perdikaris
3. G. Em Karniadakis
4. Ellen Kuhl
5. Yew-Soon Ong
6. Jianfei Cai
7. Haitao Liu
8. F. Sahli Costabal

In Statistics and Probability

1. G. Em Karniadakis
2. Paris Perdikaris
3. Yibo Yang
4. Ellen Kuhl
5. F. Sahli Costabal
6. Guofei Pang
7. Yew-Soon Ong
8. K. Matsuno

Citations in the corpus

• Adversarial Uncertainty Quantification in Physics-Informed Neural Networks (2018, background): “However, despite the fact that much progress has been made over the last two decades, the most popular methods for scientific computing under uncertainty, such as polynomial chaos expansions [17, 18, 19], sparse grid quadratures [20, 21], multi-level/multi-fidelity Monte Carlo sampling [22, 23], pro”
• Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification (2019, methodology): “We integrate these results into a surrogate model using multi-fidelity Gaussian process regression [50].”
• Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization (2017, background): “Several studies [18,19,14] have been devoted to reducing the training computational cost.”
• Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models (2019, methodology): “This approach has been widely used [26] and has been extended for efficiency [18] and to accommodate large data-sets [29].”
• Remarks on multi-output Gaussian process regression (2018, methodology): “For example, we can devote to (1) effective MOGPs that utilize positive transfer while avoid negative transfer across outputs [48, 62]; (2) efficient MOGPs that handle “Big data” with numerous training points in high dimensions [42, 77]; (3) non-stationary MOGPs that handle, e.”