This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj.

中文翻译：

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不确定性下鲁棒系统识别的贝叶斯差分编程


本文提出了一种机器学习框架，用于从非线性动力系统的噪声、稀疏和不规则观测中识别贝叶斯系统。所提出的方法利用可微分编程的最新发展，通过常微分方程求解器传播梯度信息，并使用哈密顿蒙特卡罗采样对未知模型参数进行贝叶斯推理。这允许在具有量化不确定性的合理模型上有效地推断后验分布，而使用稀疏性促进先验可以发现潜在动态的可解释和简约的表示。一系列数值研究证明了所提出方法的有效性，包括非线性振荡器、捕食者-猎物系统和系统生物学的例子。总而言之，我们的研究结果为不确定性下的数据驱动模型发现提出了灵活而强大的工作流程。本文附带的所有代码和数据均可在 https://bit.ly/34FOJMj 上获取。