In this paper, we consider the problem of discovering dynamical system models from noisy data. The presence of noise is known to be a significant problem for symbolic regression algorithms. We combine Gaussian process regression, a nonparametric learning method, with SINDy, a parametric learning approach, to identify nonlinear dynamical systems from data. The key advantages of our proposed approach are its simplicity coupled with the fact that it demonstrates improved robustness properties with noisy data over SINDy. We demonstrate our proposed approach on a Lotka-Volterra model and a unicycle dynamic model in simulation and on an NVIDIA JetRacer system using hardware data. We demonstrate improved performance over SINDy for discovering the system dynamics and predicting future trajectories.

翻译：本文研究从含噪数据中发现动力学系统模型的问题。已知噪声是符号回归算法面临的显著难题。我们将非参数学习方法高斯过程回归与参数化学习方法SINDy相结合，从数据中识别非线性动力学系统。所提方法的关键优势在于其简洁性，同时与SINDy相比，在含噪数据下表现出更强的鲁棒性。我们在Lotka-Volterra模型和单轮车动力学模型上进行了仿真验证，并在NVIDIA JetRacer系统上利用硬件数据进行了实验。结果表明，与SINDy相比，本方法在发现系统动力学和预测未来轨迹方面均展现出更优性能。