We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a statistical inference framework that enables the end-to-end training of surrogate models on paired input-output observations that may be stochastic in nature, originate from different information sources of variable fidelity, or be corrupted by complex noise processes. The resulting surrogates can accommodate high-dimensional inputs and outputs and are able to return predictions with quantified uncertainty. The effectiveness our approach is demonstrated through a series of canonical studies, including the regression of noisy data, multi-fidelity modeling of stochastic processes, and uncertainty propagation in high-dimensional dynamical systems.
This paper was published on Computational Mechanics.
- Yibo, Yang, and Paris Perdikaris. "Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems.", Computational Mechanics, volume 64, pages417–434(2019).
For the high dimensional Burgers example, the data is too large that we are not able to provide here, but you can find them in: https://drive.google.com/file/d/1n4a5Bivt6INq2xHSlVByZaJn-lB0mImK/view?usp=sharing
@Article{Yang2019,
author="Yang, Yibo
and Perdikaris, Paris",
title="Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems",
journal="Computational Mechanics",
year="2019",
month="May",
day="21",
abstract="We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a statistical inference framework that enables the end-to-end training of surrogate models on paired input--output observations that may be stochastic in nature, originate from different information sources of variable fidelity, or be corrupted by complex noise processes. The resulting surrogates can accommodate high-dimensional inputs and outputs and are able to return predictions with quantified uncertainty. The effectiveness our approach is demonstrated through a series of canonical studies, including the regression of noisy data, multi-fidelity modeling of stochastic processes, and uncertainty propagation in high-dimensional dynamical systems.",
issn="1432-0924",
doi="10.1007/s00466-019-01718-y",
url="https://doi.org/10.1007/s00466-019-01718-y"
}