On generalized residue network for deep learning of unknown dynamical systems
This work addresses the challenge of modeling complex dynamical systems for researchers in computational science and engineering, but it is incremental as it builds upon existing ResNet methods.
The authors tackled the problem of learning unknown dynamical systems by proposing a generalized ResNet framework that corrects existing coarse models or creates them from data, achieving higher prediction accuracy than standard ResNet, as demonstrated in numerical examples including chaotic systems.
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.