# Deep Multiscale Model Learning

arXiv: https://arxiv.org/abs/1806.04830 · HTML: https://mlsanity.com/paper/1806.04830/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2018.

## Built on by (most cited first, 8 of 8)

- [DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method](https://mlsanity.com/paper/2111.01356/) (2021)
- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [Adaptive deep density approximation for stochastic dynamical systems](https://mlsanity.com/paper/2405.02810/) (2024)
- [Multiscale Training of Convolutional Neural Networks](https://mlsanity.com/paper/2501.12739/) (2025)
- [AMS-Net: Adaptive Multiscale Sparse Neural Network with Interpretable Basis Expansion for Multiphase Flow Problems](https://mlsanity.com/paper/2207.11735/) (2022)
- [A variational neural network approach for glacier modelling with nonlinear rheology](https://mlsanity.com/paper/2209.02088/) (2022)
- [Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations](https://mlsanity.com/paper/2506.10636/) (2025)
- [Learning-based Multi-continuum Model for Multiscale Flow Problems](https://mlsanity.com/paper/2403.14084/) (2024)

## Abstract (arXiv)

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts combined with local multiscale model reduction methodologies to predict flow dynamics. Using reduced-order model concepts is important for constructing robust deep learning architectures since the reduced-order models provide fewer degrees of freedom. Flow dynamics can be thought of as multi-layer networks. More precisely, the solution (e.g., pressures and saturations) at the time instant n+1 depends on the solution at the time instant n and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous model reduction concepts to define unknowns and connections for each layer. In each layer, our reduced-order models will provide a forward map, which will be modified ("trained") using available data. It is critical to use reduced-order models for this purpose, which will identify the regions of influence and the appropriate number of variables. Because of the lack of available data, the training will be supplemented with computational data as needed and the interpolation between data-rich and data-deficient models. We will also use deep learning algorithms to train the elements of the reduced model discrete system. We will present main ingredients of our approach and numerical results. Numerical results show that using deep learning and multiscale models, we can improve the forward models, which are conditioned to the available data.