Deep Multi-fidelity Gaussian Processes
By Maizar Raissi, G. Em Karniadakis. 2016
66 citations recorded by the source corpus.
We develop a novel multi-fidelity framework that goes far beyond the classical AR(1) Co-kriging scheme of Kennedy and O'Hagan (2000). Our method can handle general discontinuous cross-correlations among systems with different levels of fidelity. A combination of multi-fidelity Gaussian Processes (AR(1) Co-kriging) and deep neural networks enables us to construct a method that is immune to discontinuities. We demonstrate the effectiveness of the new technology using standard benchmark problems designed to resemble the outputs of complicated high- and low-fidelity codes.
Subfields: Artificial Intelligence, Astronomy and Astrophysics, Computational Theory and Mathematics
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
- G. Em Karniadakis
- Maizar Raissi
- Xuhui Meng
- Paris Perdikaris
- Yew-Soon Ong
- Jianfei Cai
- Haitao Liu
- Yibo Yang
In Astronomy and Astrophysics
In Computational Theory and Mathematics
- Xuhui Meng
- G. Em Karniadakis
- Maizar Raissi
- Yew-Soon Ong
- Jianfei Cai
- Haitao Liu
- Paris Perdikaris
- Ferrante Neri
Citations in the corpus
- Hidden physics models: Machine learning of nonlinear partial differential equations (2017, background): “Furthermore, more complex function classes can be accommodated by employing nonlinear warping of the input space to capture discontinuities [49,50].”
- A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems (2019, methodology): “, approximations of discontinuous functions [7], high-dimensional problems [9], and inverse problems with strong nonlinearities (i.”
- Remarks on multi-output Gaussian process regression (2018, background): “, discontinuous problems [52, 100]; (4) sampling strategies for sequential updating of the MOGPs by considering the output correlations and, particularly, the computing ratios between different fidelity levels in asymmetric scenarios [75, 101]; and (5) MOGP-assisted optimization [102, 103] and uncer”