# Generative Quasi-Continuum Modeling of Confined Fluids at the Nanoscale

arXiv: https://arxiv.org/abs/2509.08223 · HTML: https://mlsanity.com/paper/2509.08223/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 91 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [DeScoD-ECG: Deep Score-Based Diffusion Model for ECG Baseline Wander and Noise Removal](https://mlsanity.com/paper/2208.00542/) (2022)
- [Simulate Time-integrated Coarse-grained Molecular Dynamics with Multi-Scale Graph Networks](https://mlsanity.com/paper/2204.10348/) (2022)
- [Stability-Aware Training of Machine Learning Force Fields with Differentiable Boltzmann Estimators](https://mlsanity.com/paper/2402.13984/) (2024)

## Abstract (arXiv)

We present a data-efficient, multiscale framework for predicting the density profiles of confined fluids at the nanoscale. While accurate density estimates require prohibitively long timescales that are inaccessible by ab initio molecular dynamics (AIMD) simulations, machine-learned molecular dynamics (MLMD) offers a scalable alternative, enabling the generation of force predictions at ab initio accuracy with reduced computational cost. However, despite their efficiency, MLMD simulations remain constrained by femtosecond timesteps, which limit their practicality for computing long-time averages needed for accurate density estimation. To address this, we propose a conditional denoising diffusion probabilistic model (DDPM) based quasi-continuum approach that predicts the long-time behavior of force profiles along the confinement direction, conditioned on noisy forces extracted from a limited AIMD dataset. The predicted smooth forces are then linked to continuum theory via the Nernst-Planck equation to reveal the underlying density behavior. We test the framework on water confined between two graphene nanoscale slits and demonstrate that density profiles for channel widths outside of the training domain can be recovered with ab initio accuracy. Compared to AIMD and MLMD simulations, our method achieves orders-of-magnitude speed-up in runtime and requires significantly less training data than prior works.