# GANs and Closures: Micro-Macro Consistency in Multiscale Modeling

arXiv: https://arxiv.org/abs/2208.10715 · HTML: https://mlsanity.com/paper/2208.10715/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 59 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 9 of 9)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Molecular Latent Space Simulators](https://mlsanity.com/paper/2007.00728/) (2020)
- [Chasing Collective Variables using Autoencoders and biased trajectories](https://mlsanity.com/paper/2104.11061/) (2021)
- [On the Correspondence between Gaussian Processes and Geometric Harmonics](https://mlsanity.com/paper/2110.02296/) (2021)

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

- [Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems](https://mlsanity.com/paper/2312.05715/) (2023)
- [Generative Learning for Slow Manifolds and Bifurcation Diagrams](https://mlsanity.com/paper/2504.20375/) (2025)
- [Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling](https://mlsanity.com/paper/2311.00797/) (2023)
- [Generative Learning of Separatrices](https://mlsanity.com/paper/2608.14743/) (2026)

## Abstract (arXiv)

Sampling the phase space of molecular systems -- and, more generally, of complex systems effectively modeled by stochastic differential equations -- is a crucial modeling step in many fields, from protein folding to materials discovery. These problems are often multiscale in nature: they can be described in terms of low-dimensional effective free energy surfaces parametrized by a small number of "slow" reaction coordinates; the remaining "fast" degrees of freedom populate an equilibrium measure on the reaction coordinate values. Sampling procedures for such problems are used to estimate effective free energy differences as well as ensemble averages with respect to the conditional equilibrium distributions; these latter averages lead to closures for effective reduced dynamic models. Over the years, enhanced sampling techniques coupled with molecular simulation have been developed. An intriguing analogy arises with the field of Machine Learning (ML), where Generative Adversarial Networks can produce high dimensional samples from low dimensional probability distributions. This sample generation returns plausible high dimensional space realizations of a model state, from information about its low-dimensional representation. In this work, we present an approach that couples physics-based simulations and biasing methods for sampling conditional distributions with ML-based conditional generative adversarial networks for the same task. The "coarse descriptors" on which we condition the fine scale realizations can either be known a priori, or learned through nonlinear dimensionality reduction. We suggest that this may bring out the best features of both approaches: we demonstrate that a framework that couples cGANs with physics-based enhanced sampling techniques can improve multiscale SDE dynamical systems sampling, and even shows promise for systems of increasing complexity.