# Multiresolution Convolutional Autoencoders

arXiv: https://arxiv.org/abs/2004.04946 · HTML: https://mlsanity.com/paper/2004.04946/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2020.

## Built on by (most cited first, 10 of 10)

- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer](https://mlsanity.com/paper/2512.20399/) (2025)
- [Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks](https://mlsanity.com/paper/2308.01602/) (2023)
- [Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulations](https://mlsanity.com/paper/2311.05961/) (2023)
- [Semantic Multi-Resolution Communications](https://mlsanity.com/paper/2308.11604/) (2023)
- [RefreshNet: Learning Multiscale Dynamics through Hierarchical Refreshing](https://mlsanity.com/paper/2401.13282/) (2024)
- [MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equations](https://mlsanity.com/paper/2209.03151/) (2022)
- [Multi-Hierarchical Surrogate Learning for Structural Dynamical Crash Simulations Using Graph Convolutional Neural Networks](https://mlsanity.com/paper/2402.09234/) (2024)
- [Optimized Dynamic Mode Decomposition for Reconstruction and Forecasting of Atmospheric Chemistry Data](https://mlsanity.com/paper/2404.12396/) (2024)
- [Graph Lineages and Skeletal Graph Products](https://mlsanity.com/paper/2508.00197/) (2025)

## Abstract (arXiv)

We propose a multi-resolution convolutional autoencoder (MrCAE) architecture that integrates and leverages three highly successful mathematical architectures: (i) multigrid methods, (ii) convolutional autoencoders and (iii) transfer learning. The method provides an adaptive, hierarchical architecture that capitalizes on a progressive training approach for multiscale spatio-temporal data. This framework allows for inputs across multiple scales: starting from a compact (small number of weights) network architecture and low-resolution data, our network progressively deepens and widens itself in a principled manner to encode new information in the higher resolution data based on its current performance of reconstruction. Basic transfer learning techniques are applied to ensure information learned from previous training steps can be rapidly transferred to the larger network. As a result, the network can dynamically capture different scaled features at different depths of the network. The performance gains of this adaptive multiscale architecture are illustrated through a sequence of numerical experiments on synthetic examples and real-world spatial-temporal data.