NeuroKoopman Dynamic Causal Discovery

TL;DR

NeuroKoopman Dynamic Causal Discovery (NKDCD) introduces a neural network-based framework that uses Koopman theory to reliably infer nonlinear Granger causality and underlying dynamics from time series data.

Contribution

This paper presents a novel neural network architecture that learns Koopman bases for causal discovery, combining autoencoders with sparsity penalties for effective nonlinear Granger causality inference.

Findings

NKDCD outperforms existing nonlinear causality methods.

The framework reliably identifies causal dependencies in complex datasets.

It effectively models nonlinear dynamics through learned linear representations.

Abstract

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.