To reduce carbon emissions, electrical power systems are Outside of the power systems community, novel machine increasingly incorporating renewable generation resources into learning techniques for partial differential equations (PDEs) the energy mix. These resources are often dependent on have been used to efficiently learn evolution equations for weather inputs and, as a result, they behave stochastically PDFs of system states. We refer to such equations as PDF in the short and long terms, posing planning and operational equations, and unlike the FPE [9], many are unclosed.

Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order model (ROM) of an advection-dominated partial differential equation. This is motivated by the fact that the nonlinear term is the most expensive component of a successful ROM. For our approach, we utilize a Galerkin projection to isolate the linear and the transient components of the dynamical system and then use discrete empirical interpolation to generate training data for supervised learning. We note that the numerical time-advancement and linear-term computation of the system ensures a greater preservation of physics than does a process that is fully modeled. Our results show that the proposed framework recovers transient dynamics accurately without nonlinear term computations in full-order space and represents a cost-effective alternative to solely equation-based ROMs.