# Deep neural network based adaptive learning for switched systems

arXiv: https://arxiv.org/abs/2207.04623 · HTML: https://mlsanity.com/paper/2207.04623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Extracting Sparse High-Dimensional Dynamics from Limited Data](https://mlsanity.com/paper/1707.08528/) (2017)
- [Machine Learning for Prediction with Missing Dynamics](https://mlsanity.com/paper/1910.05861/) (2019)
- [Learning reduced systems via deep neural networks with memory](https://mlsanity.com/paper/2003.09451/) (2020)
- [Revealing hidden dynamics from time-series data by ODENet](https://mlsanity.com/paper/2005.04849/) (2020)

## Abstract (arXiv)

In this paper, we present a deep neural network based adaptive learning (DNN-AL) approach for switched systems. Currently, deep neural network based methods are actively developed for learning governing equations in unknown dynamic systems, but their efficiency can degenerate for switching systems, where structural changes exist at discrete time instants. In this new DNN-AL strategy, observed datasets are adaptively decomposed into subsets, such that no structural changes within each subset. During the adaptive procedures, DNNs are hierarchically constructed, and unknown switching time instants are gradually identified. Especially, network parameters at previous iteration steps are reused to initialize networks for the later iteration steps, which gives efficient training procedures for the DNNs. For the DNNs obtained through our DNN-AL, bounds of the prediction error are established. Numerical studies are conducted to demonstrate the efficiency of DNN-AL.