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Over the last few decades, existing Partial Differential Equation (PDE)solvers have demonstrated a tremendous success in solving complex, non-linearPDEs. Although accurate, these PDE solvers are computationally costly. With theadvances in Machine Learning (ML) technologies, there has been a significantincrease in the research of using ML to solve PDEs. The goal of this work is todevelop an ML-based PDE solver, that couples important characteristics ofexisting PDE solvers with ML technologies. The two solver characteristics thathave been adopted in this work are: 1) the use of discretization-based schemesto approximate spatio-temporal partial derivatives and 2) the use of iterativealgorithms to solve linearized PDEs in their discrete form. In the presence ofhighly non-linear, coupled PDE solutions, these strategies can be veryimportant in achieving good accuracy, better stability and faster convergence.Our ML-solver, DiscretizationNet, employs a generative CNN-basedencoder-decoder model with PDE variables as both input and output features.During training, the discretization schemes are implemented inside thecomputational graph to enable faster GPU computation of PDE residuals, whichare used to update network weights that result into converged solutions. Anovel iterative capability is implemented during the network training toimprove the stability and convergence of the ML-solver. The ML-Solver isdemonstrated to solve the steady, incompressible Navier-Stokes equations in 3-Dfor several cases such as, lid-driven cavity, flow past a cylinder andconjugate heat transfer.

DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization