Data-Driven Discovery of Coarse-Grained Equations

Joseph Bakarji 1, Daniel M. Tartakovsky 1 Department of Energy Resources Engineering, Stanford University, 367 Panama Mall, Stanford, 94305 CA, USAAbstract A general method for learning probability density function (PDF) equations based on Monte Carlo simulations of random fields is proposed. Sparse linear regression is used to discover the relevant terms of a partial differential equation of the distribution. The various properties of PDF equations, like smoothness and conservation, makes them very well adapted to equation learning methods. The results show a promising direction for data-driven discovery of coarse-grained equations in general. Introduction Probabilistic models have proven to be essential in various fields of science and technology for optimizing predictability under epistemic and model uncertainty.