Multi-fidelity Hierarchical Neural Processes
- URL: http://arxiv.org/abs/2206.04872v1
- Date: Fri, 10 Jun 2022 04:54:13 GMT
- Title: Multi-fidelity Hierarchical Neural Processes
- Authors: Dongxia Wu, Matteo Chinazzi, Alessandro Vespignani, Yi-An Ma, Rose Yu
- Abstract summary: Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs.
We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling.
We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation.
- Score: 79.0284780825048
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Science and engineering fields use computer simulation extensively. These
simulations are often run at multiple levels of sophistication to balance
accuracy and efficiency. Multi-fidelity surrogate modeling reduces the
computational cost by fusing different simulation outputs. Cheap data generated
from low-fidelity simulators can be combined with limited high-quality data
generated by an expensive high-fidelity simulator. Existing methods based on
Gaussian processes rely on strong assumptions of the kernel functions and can
hardly scale to high-dimensional settings. We propose Multi-fidelity
Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model
for multi-fidelity surrogate modeling. MF-HNP inherits the flexibility and
scalability of Neural Processes. The latent variables transform the
correlations among different fidelity levels from observations to latent space.
The predictions across fidelities are conditionally independent given the
latent states. It helps alleviate the error propagation issue in existing
methods. MF-HNP is flexible enough to handle non-nested high dimensional data
at different fidelity levels with varying input and output dimensions. We
evaluate MF-HNP on epidemiology and climate modeling tasks, achieving
competitive performance in terms of accuracy and uncertainty estimation. In
contrast to deep Gaussian Processes with only low-dimensional (< 10) tasks, our
method shows great promise for speeding up high-dimensional complex simulations
(over 7000 for epidemiology modeling and 45000 for climate modeling).
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