Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

TL;DR

This paper introduces a probabilistic deep learning framework for creating surrogate models that handle stochastic, high-dimensional, and multi-fidelity systems, providing uncertainty quantification and end-to-end training.

Contribution

It proposes a novel variational inference-based approach for training deep surrogate models on diverse, noisy, and multi-source data, advancing the capabilities of data-driven stochastic modeling.

Findings

Effective in regression of noisy data

Successful multi-fidelity modeling of stochastic processes

Accurate uncertainty propagation in high-dimensional systems

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.