Data-driven prediction of multistable systems from sparse measurements

We develop a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements system are feasible. Our method predicts behavior an observed by quantifying its proximity states in precomputed library data. To quantify this proximity, we introduce sparsity-promoting metric-learning (SPML) optimization, which learns metric directly from The optimization problem is designed so that resulting optimal satisfies two important properties: (i) It compatible with library, and (ii) computable measurements. prove proposed SPML convex, minimizer non-degenerate, it equivariant respect scaling constraints. demonstrate application systems: reaction-diffusion equation, arising pattern formation, has four asymptotically stable steady FitzHugh-Nagumo model states. Classifications equation initial conditions two-point 95% accuracy moderate number labeled data used. For FitzHugh-Nagumo, one-point 90% accuracy. learned also determines where need be made ensure accurate predictions.