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

arXiv: https://arxiv.org/abs/1901.04878 · HTML: https://mlsanity.com/paper/1901.04878/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2019.

## Built on by (most cited first, 18 of 18)

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- [A Genetic Algorithm with Tree-structured Mutation for Hyperparameter Optimisation of Graph Neural Networks](https://mlsanity.com/paper/2102.11995/) (2021)
- [Deep Capsule Encoder-Decoder Network for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2201.07753/) (2022)
- [Dimensionality reduction can be used as a surrogate model for high-dimensional forward uncertainty quantification](https://mlsanity.com/paper/2402.04582/) (2024)
- [Conditional deep generative models as surrogates for spatial field solution reconstruction with quantified uncertainty in Structural Health Monitoring applications](https://mlsanity.com/paper/2302.08329/) (2023)
- [Prediction of liquid fuel properties using machine learning models with Gaussian processes and probabilistic conditional generative learning](https://mlsanity.com/paper/2110.09360/) (2021)
- [MF-GLaM: A multifidelity stochastic emulator using generalized lambda models](https://mlsanity.com/paper/2507.10303/) (2025)
- [PHASE: Physics-Integrated, Heterogeneity-Aware Surrogates for Scientific Simulations](https://mlsanity.com/paper/2509.23453/) (2025)

## Abstract (arXiv)

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.