Self-learning emulators and eigenvector continuation

Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed enable new studies of fundamental science as well more potential applications. In this work we discuss solving a system constraint equations efficiently using self-learning emulator. A emulator is an active learning protocol be used any faithfully reproduces the exact solution at selected training points. The key ingredient fast estimate error becomes progressively accurate improved, corrected machine learning. We illustrate three examples. first uses cubic spline interpolation to find transcendental equation variable coefficients. second example compares reduced basis method solutions parameterized differential equation. third eigenvector continuation eigenvectors eigenvalues large Hamiltonian matrix depends on several control parameters.