GNet: A scalable and flexible Gaussian process network with nonparametric neurons

We develop GNet, a scalable and flexible Gaussian process network with nonparametric activation functions modeled by Gaussian processes. To reduce computational and storage costs, we introduce the jointly inverse Kalman filter, a fast algorithm together with closed-form expressions of gradients for accelerating model training and predictions without the need to form covariance matrices. Using a unified optimization setting, GNet shows competitive performance across a diverse range of test problems, including predicting nonlinear functions, nonparametric regression of real-world data, and predicting one-body direct correlation functions with high-dimensional inputs in classical density function theory. The strong performance of GNet, accelerated by the jointly inverse Kalman filter, suggests broad applicability to large-scale predictive modeling with substantially reduced computational and storage costs.