# AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs

arXiv: https://arxiv.org/abs/1902.08480 · HTML: https://mlsanity.com/paper/1902.08480/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics](https://mlsanity.com/paper/2302.03663/) (2023)
- [Monte Carlo Simulation of SDEs using GANs](https://mlsanity.com/paper/2104.01437/) (2021)
- [Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models](https://mlsanity.com/paper/2106.11609/) (2021)

## Abstract (arXiv)

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.