# Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations

arXiv: https://arxiv.org/abs/2202.12358 · HTML: https://mlsanity.com/paper/2202.12358/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework](https://mlsanity.com/paper/2012.07938/) (2020)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems](https://mlsanity.com/paper/1904.05417/) (2019)
- [Lat-Net: Compressing Lattice Boltzmann Flow Simulations using Deep Neural Networks](https://mlsanity.com/paper/1705.09036/) (2017)

## Built on by (most cited first, 7 of 7)

- [Dual Cone Gradient Descent for Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2409.18426/) (2024)
- [RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network](https://mlsanity.com/paper/2212.02861/) (2022)
- [Quantum Recurrent Neural Networks with Encoder-Decoder for Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2502.13370/) (2025)
- [Hamiltonian Neural Networks approach to fuzzball geodesics](https://mlsanity.com/paper/2502.20881/) (2025)
- [BO-SA-PINNs: Self-adaptive physics-informed neural networks based on Bayesian optimization for automatically designing PDE solvers](https://mlsanity.com/paper/2504.09804/) (2025)
- [A comprehensive analysis of PINNs: Variants, Applications, and Challenges](https://mlsanity.com/paper/2505.22761/) (2025)
- [CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations](https://mlsanity.com/paper/2610.04405/) (2026)

## Abstract (arXiv)

Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to their architectural nature. In this work, we present a novel physics-informed framework for solving time-dependent partial differential equations. Using only the governing differential equations and problem initial and boundary conditions, we generate a latent representation of the problem's spatio-temporal dynamics. Our model utilizes discrete cosine transforms to encode spatial frequencies and recurrent neural networks to process the time evolution. This efficiently and flexibly produces a compressed representation which is used for additional conditioning of physics-informed models. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations. Our proposed model achieves state-of-the-art performance on the Taylor-Green vortex relative to other physics-informed baseline models.