# On generalized residue network for deep learning of unknown dynamical systems

arXiv: https://arxiv.org/abs/2002.02528 · HTML: https://mlsanity.com/paper/2002.02528/

## Key facts

- Cited by 16 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 23 Jan 2020.

## Built on by (most cited first, 16 of 16)

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- [Accelerating hydrodynamic simulations of urban drainage systems with physics-guided machine learning](https://mlsanity.com/paper/2206.01538/) (2022)
- [Deep learning for model correction of dynamical systems with data scarcity](https://mlsanity.com/paper/2410.17913/) (2024)
- [Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence](https://mlsanity.com/paper/2206.01807/) (2022)
- [Hard-constraint physics-residual networks for hydrogen crossover prediction and high-pressure extrapolation in PEM water electrolysis](https://mlsanity.com/paper/2511.05879/) (2025)
- [Unsupervised Legendre-Galerkin Neural Network for Singularly Perturbed Partial Differential Equations](https://mlsanity.com/paper/2207.10241/) (2022)
- [Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems](https://mlsanity.com/paper/2304.07485/) (2023)
- [Data-Driven Modeling and Correction of Vehicle Dynamics](https://mlsanity.com/paper/2512.00289/) (2025)
- [Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamics](https://mlsanity.com/paper/2608.16084/) (2026)

## Abstract (arXiv)

We present a general numerical approach for learning unknown dynamical systems using deep neural networks (DNNs). Our method is built upon recent studies that identified the residue network (ResNet) as an effective neural network structure. In this paper, we present a generalized ResNet framework and broadly define residue as the discrepancy between observation data and prediction made by another model, which can be an existing coarse model or reduced-order model. In this case, the generalized ResNet serves as a model correction to the existing model and recovers the unresolved dynamics. When an existing coarse model is not available, we present numerical strategies for fast creation of coarse models, to be used in conjunction with the generalized ResNet. These coarse models are constructed using the same data set and thus do not require additional resources. The generalized ResNet is capable of learning the underlying unknown equations and producing predictions with accuracy higher than the standard ResNet structure. This is demonstrated via several numerical examples, including long-term prediction of a chaotic system.