# Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles

arXiv: https://arxiv.org/abs/2205.00286 · HTML: https://mlsanity.com/paper/2205.00286/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 62 references that are in the map.
- First posted on arXiv 30 Apr 2022.

## Builds on (most cited first, 8 of 8)

- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [Identifying Latent Stochastic Differential Equations](https://mlsanity.com/paper/2007.06075/) (2020)
- [Stochastic Physics-Informed Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.01621/) (2021)
- [A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise](https://mlsanity.com/paper/2005.03769/) (2020)
- [Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models](https://mlsanity.com/paper/2008.01915/) (2020)
- [Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas](https://mlsanity.com/paper/2108.12570/) (2021)
- [Data mining when each data point is a network](https://mlsanity.com/paper/1612.02908/) (2016)

## Built on by (most cited first, 5 of 5)

- [Early warning indicators via latent stochastic dynamical systems](https://mlsanity.com/paper/2309.03842/) (2023)
- [Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling](https://mlsanity.com/paper/2311.00797/) (2023)
- [Discovering mesoscopic descriptions of collective movement with neural stochastic modelling](https://mlsanity.com/paper/2303.09906/) (2023)
- [Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example](https://mlsanity.com/paper/2310.19039/) (2023)
- [From Noise to Signal: Unveiling Treatment Effects from Digital Health Data through Pharmacology-Informed Neural-SDE](https://mlsanity.com/paper/2403.03274/) (2024)

## Abstract (arXiv)

We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian Dynamics Simulations. We use Diffusion Maps (a manifold learning algorithm) to identify a set of useful latent observables. In this latent space we identify an eSDE using a deep learning architecture inspired by numerical stochastic integrators and compare it with the traditional Kramers-Moyal expansion estimation. We show that the obtained variables and the learned dynamics accurately encode the physics of the Brownian Dynamic Simulations. We further illustrate that our reduced model captures the dynamics of corresponding experimental data. Our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.