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An operator preconditioning perspective on training in physics-informed machine learning
(2023)SAM Research ReportIn this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize resid uals connected to partial differential equations (PDEs). Our key result is that the difficulty in training these models is closely related to the conditioning of a specific differential operator. This operator, in turn, is associated to the Hermi tian square of the differential operator ...Report