Double Diffusion Maps and their Latent Harmonics for scientific computations in latent space

We introduce a data-driven approach to building reduced dynamical models through manifold learning; the latent space is discovered using Diffusion Maps (a learning technique) on time series data. A second round of those coordinates allows approximation models. This enables mapping back full ambient (what called lifting); it also state functions interest in terms coordinates. In our work, we develop and test three different numerical simulation methodologies, either pre-tabulation integration fly or by going forth between space. The results, based approaches, are validated (a) observation Nystr\"om Extension formula, (b) lifting trajectory space, via Latent Harmonics. modeling often involves additional regularization favor certain properties over others, then constructed mostly independently from these properties; here, use same construct map