  Learning and forecasting stochastic time series is essential in various
scientific fields. However, despite the proposals of nonlinear filters and
deep-learning methods, it remains challenging to capture nonlinear dynamics
from a few noisy samples and predict future trajectories with uncertainty
estimates while maintaining computational efficiency. Here, we propose a fast
algorithm to learn and forecast nonlinear dynamics from noisy time series data.
A key feature of the proposed model is kernel functions applied to projected
lines, enabling fast and efficient capture of nonlinearities in the latent
dynamics. Through empirical case studies and benchmarking, the model
demonstrates its effectiveness in learning and forecasting complex nonlinear
dynamics, offering a valuable tool for researchers and practitioners in time
series analysis.
