论文标题
在不确定性下，用于稳健系统识别的贝叶斯差分编程
Bayesian differential programming for robust systems identification under uncertainty
论文作者
论文摘要
本文介绍了一个机器学习框架，用于贝叶斯系统识别非线性动力学系统的嘈杂，稀疏和不规则观察结果。所提出的方法利用了可区分编程中的最新发展，通过普通的微分方程求解器传播梯度信息，并使用哈密顿蒙特卡洛（Monte Carlo）对未知模型参数进行贝叶斯推断。这使我们能够在具有量化的不确定性的合理模型上有效地推断后验分布，而使用稀疏性先验的使用者则可以发现基本的潜在动力学的可解释和偏见的表示。提出了一系列数值研究，以证明所提出的方法的有效性，包括非线性振荡器，捕食者 - 捕集系统，混乱动力学和系统生物学。总的来说，我们的发现提出了一个新颖，灵活且健壮的工作流程，以在不确定性下进行数据驱动的模型发现。
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. This allows us to efficiently infer 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, chaotic dynamics and systems biology. Taken all together, our findings put forth a novel, flexible and robust workflow for data-driven model discovery under uncertainty.
