In many real-world applications where the system dynamics has an underlying
interdependency among its variables (such as power grid, economics,
neuroscience, omics networks, environmental ecosystems, and others), one is
often interested in knowing whether the past values of one time series
influences the future of another, known as Granger causality, and the
associated underlying dynamics. This paper introduces a Koopman-inspired
framework that leverages neural networks for data-driven learning of the
Koopman bases, termed NeuroKoopman Dynamic Causal Discovery (NKDCD), for
reliably inferring the Granger causality along with the underlying nonlinear
dynamics. NKDCD employs an autoencoder architecture that lifts the nonlinear
dynamics to a higher dimension using data-learned bases, where the lifted time
series can be reliably modeled linearly. The lifting function, the linear
Granger causality lag matrices, and the projection function (from lifted space
to base space) are all represented as multilayer perceptrons and are all
learned simultaneously in one go. NKDCD also utilizes sparsity-inducing
penalties on the weights of the lag matrices, encouraging the model to select
only the needed causal dependencies within the data. Through extensive testing
on practically applicable datasets, it is shown that the NKDCD outperforms the
existing nonlinear Granger causality discovery approaches.

通过神经网络的数据驱动学习 Koopman 基础知识的 Koopman 灵感框架 (NKDCD)，可可靠地推断 Granger 因果关系以及相关的非线性动力学。