Many natural systems, especially biological ones, exhibit complex multivariate nonlinear dynamical behaviors that can be hard to capture by linear autoregressive models. On the other hand, generic nonlinear models such as deep recurrent neural networks often require large amounts of training data, not always available in domains such as brain imaging; also, they often lack interpretability. Domain knowledge about the types of dynamics typically observed in such systems, such as a certain type of dynamical systems models, could complement purely data-driven techniques by providing a good prior. In this work, we consider a class of ordinary differential equation (ODE) models known as van der Pol (VDP) oscil lators and evaluate their ability to capture a low-dimensional representation of neural activity measured by different brain imaging modalities, such as calcium imaging (CaI) and fMRI, in different living organisms: larval zebrafish, rat, and human. We develop a novel and efficient approach to the nontrivial problem of parameters estimation for a network of coupled dynamical systems from multivariate data and demonstrate that the resulting VDP models are both accurate and interpretable, as VDP's coupling matrix reveals anatomically meaningful excitatory and inhibitory interactions across different brain subsystems. VDP outperforms linear autoregressive models (VAR) in terms of both the data fit accuracy and the quality of insight provided by the coupling matrices and often tends to generalize better to unseen data when predicting future brain activity, being comparable to and sometimes better than the recurrent neural networks (LSTMs). Finally, we demonstrate that our (generative) VDP model can also serve as a data-augmentation tool leading to marked improvements in predictive accuracy of recurrent neural networks. Thus, our work contributes to both basic and applied dimensions of neuroimaging: gaining scientific insights and improving brain-based predictive models, an area of potentially high practical importance in clinical diagnosis and neurotechnology.

中文翻译：

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使用耦合的低维非线性振荡器和深度循环网络学习大脑动力学。

许多自然系统，尤其是生物系统，表现出复杂的多元非线性动力学行为，线性自回归模型很难捕捉到这些行为。另一方面，深度循环神经网络等通用非线性模型通常需要大量训练数据，在脑成像等领域并不总是可用；此外，它们通常缺乏可解释性。有关此类系统中通常观察到的动态类型的领域知识，例如某种类型的动态系统模型，可以通过提供良好的先验来补充纯粹的数据驱动技术。在这项工作中，我们考虑了一类称为 van der Pol (VDP) 振荡器的常微分方程 (ODE) 模型，并评估它们捕获由不同脑成像模式测量的神经活动的低维表示的能力，例如钙成像 (CaI) 和 fMRI，在不同的生物体中：幼虫斑马鱼、大鼠和人类。我们开发了一种新颖有效的方法来解决来自多元数据的耦合动力系统网络的参数估计的重要问题，并证明由此产生的 VDP 模型既准确又可解释，因为 VDP 的耦合矩阵揭示了不同解剖学上有意义的兴奋性和抑制性相互作用。大脑子系统。VDP 在数据拟合精度和耦合矩阵提供的洞察质量方面均优于线性自回归模型 (VAR)，并且在预测未来大脑活动时往往倾向于更好地泛化到看不见的数据，可与循环模型相媲美，有时甚至优于循环模型神经网络（LSTM）。最后，我们证明了我们的（生成）VDP 模型也可以作为数据增强工具，从而显着提高循环神经网络的预测准确性。因此，我们的工作对神经影像学的基础和应用层面都有贡献：获得科学见解并改进基于大脑的预测模型，这是一个在临床诊断和神经技术中具有潜在高度实际重要性的领域。