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

arXiv 1912.11114 ↗First posted 23 Dec 2019physics.comp-ph cs.LG physics.flu-dyncited by 45

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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.

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

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Citing papers per year: 2021: 7; 2022: 13; 2023: 7; 2024: 4; 2025: 6; 2026: 8.

45 papers.

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  9. 2022Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticitycited by 11
  10. 2022Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order modelscited by 10
  11. 2022Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convectioncited by 10
  12. 2023Deep hybrid model with satellite imagery: how to combine demand modeling and computer vision for behavior analysis?cited by 8
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  4. 2022Adaptive physics-informed neural operator for coarse-grained non-equilibrium flowscited by 7
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  7. 2021Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19cited by 4
  8. 2024Reduced-order modeling of unsteady fluid flow using neural network ensemblescited by 4
  9. 2022An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipescited by 3
  10. 2022AI-enhanced iterative solvers for accelerating the solution of large scale parametrized systemscited by 3
  11. 2023An Implicit GNN Solver for Poisson-like problemscited by 3
  12. 2023Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencodercited by 3
  13. 2024A general reduced-order neural operator for spatio-temporal predictive learning on complex spatial domainscited by 3
  14. 2024Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate modelscited by 3
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  16. 2025A surrogate model for topology optimisation of elastic structures via parametric autoencoderscited by 3
  17. 2026Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challengescited by 3
  18. 2021Discretization-independent surrogate modeling over complex geometries using hypernetworks and implicit representationscited by 2
  19. 2021Emulation of greenhouse-gas sensitivities using variational autoencoderscited by 2
  20. 2025Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flowscited by 2
  21. 2025A discrete physics-informed training for projection-based reduced order models with neural networkscited by 2
  22. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  23. 2022Deep Convolutional Architectures for Extrapolative Forecast in Time-dependent Flow Problemscited by 1
  24. 2023A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problemscited by 1
  25. 2025Predicting Wave Dynamics using Deep Learning with Multistep Integration Inspired Attention and Physics-Based Loss Decompositioncited by 1
  26. 2026Nonlinear model reduction for transport-dominated problemscited by 1
  27. 2022Assessment of convolutional recurrent autoencoder network for learning wave propagationcited by 0
  28. 2025Attention-Enhanced Convolutional Autoencoder and Structured Delay Embeddings for Weather Predictioncited by 0
  29. 2026Data-driven stochastic reduced-order modeling of parametrized dynamical systemscited by 0
  30. 2026Scalable Gaussian process modeling of parametrized spatio-temporal fieldscited by 0
  31. 2026Informationally Compressive Anonymization: Non-Degrading Sensitive Input Protection for Privacy-Preserving Supervised Machine Learningcited by 0
  32. 2026Variational Parameter Calibration with Physics-Aware Latent-Space Surrogatescited by 0
  33. 2026HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networkscited by 0