# Physics-Incorporated Convolutional Recurrent Neural Networks for Source Identification and Forecasting of Dynamical Systems

arXiv: https://arxiv.org/abs/2004.06243 · HTML: https://mlsanity.com/paper/2004.06243/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2020.

## Built on by (most cited first, 12 of 12)

- [State-space models are accurate and efficient neural operators for dynamical systems](https://mlsanity.com/paper/2409.03231/) (2024)
- [Discovering Sparse Interpretable Dynamics from Partial Observations](https://mlsanity.com/paper/2107.10879/) (2021)
- [Physics guided neural networks for modelling of non-linear dynamics](https://mlsanity.com/paper/2205.06858/) (2022)
- [Robust Hybrid Learning With Expert Augmentation](https://mlsanity.com/paper/2202.03881/) (2022)
- [Higher-order Spatio-temporal Physics-incorporated Graph Neural Network for Multivariate Time Series Imputation](https://mlsanity.com/paper/2405.10995/) (2024)
- [A general reduced-order neural operator for spatio-temporal predictive learning on complex spatial domains](https://mlsanity.com/paper/2409.05508/) (2024)
- [FluidFormer: Transformer with Continuous Convolution for Particle-based Fluid Simulation](https://mlsanity.com/paper/2508.01537/) (2025)
- [Learning Point Processes using Recurrent Graph Network](https://mlsanity.com/paper/2208.05736/) (2022)
- [Physics-aware deep learning framework for linear elasticity](https://mlsanity.com/paper/2302.09668/) (2023)
- [STONet: A Neural-Operator-Driven Spatio-temporal Network](https://mlsanity.com/paper/2204.08414/) (2022)
- [A Pioneering Neural Network Method for Efficient and Robust Fluid Simulation](https://mlsanity.com/paper/2412.10748/) (2024)
- [Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamics](https://mlsanity.com/paper/2203.08655/) (2022)

## Abstract (arXiv)

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown external sources. In such cases, developing a purely analytical model becomes very difficult and data-driven modeling can be of assistance. In this paper, we present a hybrid framework combining physics-based numerical models with deep learning for source identification and forecasting of spatio-temporal dynamical systems with unobservable time-varying external sources. We formulate our model PhICNet as a convolutional recurrent neural network (RNN) which is end-to-end trainable for spatio-temporal evolution prediction of dynamical systems and learns the source behavior as an internal state of the RNN. Experimental results show that the proposed model can forecast the dynamics for a relatively long time and identify the sources as well.