# A deep learning based surrogate model for stochastic simulators

arXiv: https://arxiv.org/abs/2110.13809 · HTML: https://mlsanity.com/paper/2110.13809/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 24 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [Conditional Generative Moment-Matching Networks](https://mlsanity.com/paper/1606.04218/) (2016)
- [A Gaussian process latent force model for joint input-state estimation in linear structural systems](https://mlsanity.com/paper/1904.00093/) (2019)
- [Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions](https://mlsanity.com/paper/1911.09067/) (2019)
- [Emulation of stochastic simulators using generalized lambda models](https://mlsanity.com/paper/2007.00996/) (2020)
- [State estimation with limited sensors -- A deep learning based approach](https://mlsanity.com/paper/2101.11513/) (2021)
- [GrADE: A graph based data-driven solver for time-dependent nonlinear partial differential equations](https://mlsanity.com/paper/2108.10639/) (2021)
- [Emulators for stochastic simulation codes](https://mlsanity.com/paper/1406.6348/) (2014)
- [Stochastic simulators based optimization by Gaussian process metamodels -- Application to maintenance investments planning issues](https://mlsanity.com/paper/1512.07060/) (2015)

## Built on by (most cited first, 6 of 6)

- [Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations](https://mlsanity.com/paper/2209.09750/) (2022)
- [Deep Capsule Encoder-Decoder Network for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2201.07753/) (2022)
- [Enabling scalable clinical interpretation of ML-based phenotypes using real world data](https://mlsanity.com/paper/2208.01607/) (2022)
- [Underwater Soft Fin Flapping Motion with Deep Neural Network Based Surrogate Model](https://mlsanity.com/paper/2502.03135/) (2025)
- [Self-induced stochastic resonance: A physics-informed machine learning approach](https://mlsanity.com/paper/2510.22848/) (2025)
- [CoNBONet: Conformalized Neuroscience-inspired Bayesian Operator Network for Reliability Analysis](https://mlsanity.com/paper/2603.21678/) (2026)

## Abstract (arXiv)

We propose a deep learning-based surrogate model for stochastic simulators. The basic idea is to use generative neural network to approximate the stochastic response. The challenge with such a framework resides in designing the network architecture and selecting loss-function suitable for stochastic response. While we utilize a simple feed-forward neural network, we propose to use conditional maximum mean discrepancy (CMMD) as the loss-function. CMMD exploits the property of reproducing kernel Hilbert space and allows capturing discrepancy between the between the target and the neural network predicted distributions. The proposed approach is mathematically rigorous, in the sense that it makes no assumptions about the probability density function of the response. Performance of the proposed approach is illustrated using four benchmark problems selected from the literature. Results obtained indicate the excellent performance of the proposed approach.