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math.NA2024★ 102 cited
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations
Nick McGreivy, Ammar Hakim
One of the most promising applications of machine learning (ML) in computational physics is to accelerate the solution of partial differential equations (PDEs). The key objective o…
math.NA2023★ 2 cited
Invariant preservation in machine learned PDE solvers via error correction
Nick McGreivy, Ammar Hakim
Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a sol…