# Data-driven learning of non-autonomous systems

arXiv: https://arxiv.org/abs/2006.02392 · HTML: https://mlsanity.com/paper/2006.02392/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space](https://mlsanity.com/paper/2106.03603/) (2021)
- [Deep Learning of Chaotic Systems from Partially-Observed Data](https://mlsanity.com/paper/2205.08384/) (2022)
- [Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning](https://mlsanity.com/paper/2203.03458/) (2022)
- [Modeling unknown dynamical systems with hidden parameters](https://mlsanity.com/paper/2202.01858/) (2022)
- [Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence](https://mlsanity.com/paper/2206.01807/) (2022)
- [Learning Nonautonomous Systems via Dynamic Mode Decomposition](https://mlsanity.com/paper/2306.15618/) (2023)

## Abstract (arXiv)

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.