Before revision: Deep learning has significantly revolutionized the design of numerical algorithms for solving high-dimensional partial differential equations (PDEs) . Yet the empirical successes of such approaches remains mysterious in theory. In deep learning-based PDE solvers, solving the original PDE is formulated into an expectation minimization problemwith a PDE solution space discretized via deep neural networks .
After revision: Deep learning has significantly revolutionized the design of numerical algorithms for solving high-dimensional partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solutions .