# A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problems

arXiv: https://arxiv.org/abs/2301.09926 · HTML: https://mlsanity.com/paper/2301.09926/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 58 references that are in the map.
- First posted on arXiv 24 Jan 2023.

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

- [Show, Attend and Tell: Neural Image Caption Generation with Visual Attention](https://mlsanity.com/paper/1502.03044/) (2015)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Understanding LSTM -- a tutorial into Long Short-Term Memory Recurrent Neural Networks](https://mlsanity.com/paper/1909.09586/) (2019)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [A C-LSTM Neural Network for Text Classification](https://mlsanity.com/paper/1511.08630/) (2015)
- [Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems](https://mlsanity.com/paper/1808.01346/) (2018)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows](https://mlsanity.com/paper/1907.09909/) (2019)
- [Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models](https://mlsanity.com/paper/2201.10215/) (2022)
- [Theoretical Analysis of the k-Means Algorithm - A Survey](https://mlsanity.com/paper/1602.08254/) (2016)
- [Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method](https://mlsanity.com/paper/2203.00360/) (2022)
- [Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural Networks](https://mlsanity.com/paper/1904.06965/) (2019)

## Built on by (most cited first, 1 of 1)

- [Generative Adversarial Reduced Order Modelling](https://mlsanity.com/paper/2305.15881/) (2023)

## Abstract (arXiv)

Parametric time-dependent systems are of a crucial importance in modeling real phenomena, often characterized by non-linear behaviors too. Those solutions are typically difficult to generalize in a sufficiently wide parameter space while counting on limited computational resources available. As such, we present a general two-stages deep learning framework able to perform that generalization with low computational effort in time. It consists in a separated training of two pipe-lined predictive models. At first, a certain number of independent neural networks are trained with data-sets taken from different subsets of the parameter space. Successively, a second predictive model is specialized to properly combine the first-stage guesses and compute the right predictions. Promising results are obtained applying the framework to incompressible Navier-Stokes equations in a cavity (Rayleigh-Bernard cavity), obtaining a 97% reduction in the computational time comparing with its numerical resolution for a new value of the Grashof number.