论文标题
部分可观测时空混沌系统的无模型预测
SINDy for delay-differential equations: application to model bacterial zinc response
论文作者
论文摘要
我们扩展了Brunton等人开发的非线性动力学（Sindy）稀疏识别的数据驱动方法。纳特。学院。 SCI USA 113（2016）延迟微分方程（DDES）。这是通过首先应用Sindy进行固定延迟，然后在延迟时间内优化重建的Sindy模型的误差来实现的。我们从玩具延迟微分方程中的嘈杂的简短数据集上测试了Sindy-Delay方法，并显示出极好的一致性。然后，我们将该方法应用于细菌（\ it铜绿假单胞菌）中基因表达的实验数据，以受锌的影响。衍生的信德模型表明，锌浓度的增加主要影响时间延迟，而不是控制锌出口机制的不同试剂之间相互作用的强度。
We extend the data-driven method of Sparse Identification of Nonlinear Dynamics (SINDy) developed by Brunton et al, Proc. Natl. Acad. Sci USA 113 (2016) to the case of delay differential equations (DDEs). This is achieved in a bilevel optimization procedure by first applying SINDy for fixed delay and then subsequently optimizing the error of the reconstructed SINDy model over delay times. We test the SINDy-delay method on a noisy short data set from a toy delay differential equation and show excellent agreement. We then apply the method to experimental data of gene expressions in the bacterium {\it Pseudomonas aeruginosa} subject to the influence of zinc. The derived SINDy model suggests that the increase of zinc concentration mainly affects the time delay and not the strengths of the interactions between the different agents controlling the zinc export mechanism.
