# HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systems

arXiv: https://arxiv.org/abs/1806.07439 · HTML: https://mlsanity.com/paper/1806.07439/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2018.

## Built on by (most cited first, 21 of 21)

- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers](https://mlsanity.com/paper/2207.11417/) (2022)
- [PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems](https://mlsanity.com/paper/2505.12882/) (2025)
- [A Review of Physics-based Machine Learning in Civil Engineering](https://mlsanity.com/paper/2110.04600/) (2021)
- [Physics-informed Deep Super-resolution for Spatiotemporal Data](https://mlsanity.com/paper/2208.01462/) (2022)
- [Hard Encoding of Physics for Learning Spatiotemporal Dynamics](https://mlsanity.com/paper/2105.00557/) (2021)
- [Physics-Infused Fuzzy Generative Adversarial Network for Robust Failure Prognosis](https://mlsanity.com/paper/2206.07762/) (2022)
- [Hybrid Modeling Design Patterns](https://mlsanity.com/paper/2401.00033/) (2023)
- [Wave-Informed Matrix Factorization with Global Optimality Guarantees](https://mlsanity.com/paper/2107.09144/) (2021)
- [Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction](https://mlsanity.com/paper/2202.11432/) (2022)
- [Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach](https://mlsanity.com/paper/2206.04791/) (2022)
- [Complementing Brightness Constancy with Deep Networks for Optical Flow Prediction](https://mlsanity.com/paper/2207.03790/) (2022)
- [Physics-integrated generative modeling using attentive planar normalizing flow based variational autoencoder](https://mlsanity.com/paper/2404.12267/) (2024)
- [Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression](https://mlsanity.com/paper/2607.00257/) (2026)
- [Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamics](https://mlsanity.com/paper/2203.08655/) (2022)
- [Phy-Taylor: Physics-Model-Based Deep Neural Networks](https://mlsanity.com/paper/2209.13511/) (2022)
- [Wave Physics-informed Matrix Factorizations](https://mlsanity.com/paper/2312.13584/) (2023)

## Abstract (arXiv)

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for autonomous operation. In this paper, we present HybridNet, a framework that integrates data-driven deep learning and model-driven computation to reliably predict spatiotemporal evolution of a dynamical systems even with in-exact knowledge of their parameters. A data-driven deep neural network (DNN) with Convolutional LSTM (ConvLSTM) as the backbone is employed to predict the time-varying evolution of the external forces/perturbations. On the other hand, the model-driven computation is performed using Cellular Neural Network (CeNN), a neuro-inspired algorithm to model dynamical systems defined by coupled partial differential equations (PDEs). CeNN converts the intricate numerical computation into a series of convolution operations, enabling a trainable PDE solver. With a feedback control loop, HybridNet can learn the physical parameters governing the system's dynamics in real-time, and accordingly adapt the computation models to enhance prediction accuracy for time-evolving dynamical systems. The experimental results on two dynamical systems, namely, heat convection-diffusion system, and fluid dynamical system, demonstrate that the HybridNet produces higher accuracy than the state-of-the-art deep learning based approach.