while not Singularity:
            year += 1

The neural ordinary differential equation (Neural ODE) is a novel machine learning architecture whose weights are smooth functions of the continuous depth. We apply the Neural ODE to holographic QCD by regarding the weight functions as a bulk metric, and train the machine with lattice QCD data of chiral condensate at finite temperature. The machine finds consistent bulk geometry at various values of temperature and discovers the emergent black hole horizon in the holographic bulk automatically. The holographic Wilson loops calculated with the emergent machine-learned bulk spacetime have consistent temperature dependence of confinement and Debye-screening behavior. In machine learning models with physically interpretable weights, the Neural ODE frees us from discretization artifact leading to difficult ingenuity of hyperparameters, and improves numerical accuracy to make the model more trustworthy.

Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts, explicit data collection is expensive and learning algorithms must be data-efficient to be feasible. This suggests using additional qualitative information about the system, which is often available from prior experiments or domain knowledge. In this paper, we propose an approach to learning the vector field of differential equations using sparse Gaussian Processes that allows us to combine data and additional structural information, like Lie Group symmetries and fixed points, as well as known input transformations. We show that this combination improves extrapolation performance and long-term behaviour significantly, while also reducing the computational cost.