Parametric Gaussian process regression for big data

By Maizar Raissi, Hessam Babaee, G. Em Karniadakis. 2017

41 citations recorded by the source corpus.

This work introduces the concept of parametric Gaussian processes (PGP), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. The resulting framework is capable of encoding massive amount of data into a small number of “hypothetical” data points. Moreover, parametric Gaussian processes are well aware of their imperfections and are capable of properly quantifying the uncertainty in their predictions associated with such limitations. The effectiveness of the proposed approach is demonstrated using three illustrative examples, including one with simulated data, a benchmark with dataset in the airline industry with approximately 6 million records, and spatio-temporal sea surface temperature maps in Massachusetts and Cape Cod Bays and Stellwagen Bank for the year 2015.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering

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. Paris Perdikaris
3. Maizar Raissi
4. Mamikon A. Gulian
5. Zhicheng Wang
6. Yibo Yang
7. Liu Yang
8. Michael S. Triantafyllou

In Computational Theory and Mathematics

1. G. Em Karniadakis
2. Paris Perdikaris
3. Maizar Raissi
4. Zhicheng Wang
5. Michael S. Triantafyllou
6. Mamikon A. Gulian
7. Yibo Yang
8. Xuhui Meng

In Control and Systems Engineering

1. G. Em Karniadakis
2. Maizar Raissi
3. Paris Perdikaris
4. Mamikon A. Gulian
5. Michael S. Triantafyllou
6. Zhicheng Wang
7. Ameya Dilip Jagtap
8. Xuhui Meng

Citations in the corpus

• Hidden physics models: Machine learning of nonlinear partial differential equations (2017, methodology): “However, ideas such as recursive Kalman updates [69], variational inference [55], and parametric Gaussian processes [56] can be used to address this limitation.”
• Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations (2017, background): “A large body of recent literature has been devoted to overcoming this scalability shortcoming, and some prevalent approaches can be found in [13, 23, 32].”
• Machine Learning of Space-Fractional Differential Equations (2018, background): “In this regard, remedies proposed in [12, 22] may be worth exploring.”
• Deep learning of vortex-induced vibrations (2018, methodology): “This choice is motivated by modern techniques for solving forward and inverse problems involving partial differential equations, where the unknown solution is approximated either by a neural network [5–7, 39, 40] or a Gaussian process [8, 9, 12, 13, 41–43].”