# Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics

arXiv: https://arxiv.org/abs/1912.11114 · HTML: https://mlsanity.com/paper/1912.11114/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2019.

## Built on by (most cited first, 30 of 45)

- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Fast PDE-constrained optimization via self-supervised operator learning](https://mlsanity.com/paper/2110.13297/) (2021)
- [RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator](https://mlsanity.com/paper/2302.09808/) (2023)
- [Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning](https://mlsanity.com/paper/2302.06186/) (2023)
- [Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems](https://mlsanity.com/paper/2109.09510/) (2021)
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- [Nonlinear proper orthogonal decomposition for convection-dominated flows](https://mlsanity.com/paper/2110.08295/) (2021)
- [Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity](https://mlsanity.com/paper/2208.00246/) (2022)
- [Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models](https://mlsanity.com/paper/2201.10215/) (2022)
- [Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convection](https://mlsanity.com/paper/2202.13129/) (2022)
- [Deep hybrid model with satellite imagery: how to combine demand modeling and computer vision for behavior analysis?](https://mlsanity.com/paper/2303.04204/) (2023)
- [DUE: A Deep Learning Framework and Library for Modeling Unknown Equations](https://mlsanity.com/paper/2504.10373/) (2025)
- [Predicting waves in fluids with deep neural network](https://mlsanity.com/paper/2201.06628/) (2022)
- [Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method](https://mlsanity.com/paper/2203.00360/) (2022)
- [Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows](https://mlsanity.com/paper/2210.15799/) (2022)
- [textitFastSVD-ML-ROM: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications](https://mlsanity.com/paper/2207.11842/) (2022)
- [An Energy-Efficient Reconfigurable Autoencoder Implementation on FPGA](https://mlsanity.com/paper/2301.07050/) (2023)
- [Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19](https://mlsanity.com/paper/2105.07729/) (2021)
- [Reduced-order modeling of unsteady fluid flow using neural network ensembles](https://mlsanity.com/paper/2402.05372/) (2024)
- [An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes](https://mlsanity.com/paper/2202.06170/) (2022)
- [AI-enhanced iterative solvers for accelerating the solution of large scale parametrized systems](https://mlsanity.com/paper/2207.02543/) (2022)
- [An Implicit GNN Solver for Poisson-like problems](https://mlsanity.com/paper/2302.10891/) (2023)
- [Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2307.06816/) (2023)
- [A general reduced-order neural operator for spatio-temporal predictive learning on complex spatial domains](https://mlsanity.com/paper/2409.05508/) (2024)
- [Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models](https://mlsanity.com/paper/2410.13376/) (2024)
- [TAEN: A Model-Constrained Tikhonov Autoencoder Network for Forward and Inverse Problems](https://mlsanity.com/paper/2412.07010/) (2024)
- [A surrogate model for topology optimisation of elastic structures via parametric autoencoders](https://mlsanity.com/paper/2507.22539/) (2025)
- [Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challenges](https://mlsanity.com/paper/2602.11378/) (2026)
- [Discretization-independent surrogate modeling over complex geometries using hypernetworks and implicit representations](https://mlsanity.com/paper/2109.07018/) (2021)

## Abstract (arXiv)

A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state of a system of interest in a parametric setting. A convolutional autoencoder is used as the top level to encode the high dimensional input data along spatial dimensions into a sequence of latent variables. A temporal convolutional autoencoder (TCAE) serves as the second level, which further encodes the output sequence from the first level along the temporal dimension, and outputs a set of latent variables that encapsulate the spatio-temporal evolution of the dynamics. The use of dilated temporal convolutions grows the receptive field exponentially with network depth, allowing for efficient processing of long temporal sequences typical of scientific computations. A fully-connected network is used as the third level to learn the mapping between these latent variables and the global parameters from training data, and predict them for new parameters. For future state predictions, the second level uses a temporal convolutional network to predict subsequent steps of the output sequence from the top level. Latent variables at the bottom-most level are decoded to obtain the dynamics in physical space at new global parameters and/or at a future time. Predictive capabilities are evaluated on a range of problems involving discontinuities, wave propagation, strong transients, and coherent structures. The sensitivity of the results to different modeling choices is assessed. The results suggest that given adequate data and careful training, effective data-driven predictive models can be constructed. Perspectives are provided on the present approach and its place in the landscape of model reduction.