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Time-dependent Partial Differential Equations with given initial conditionsare considered in this paper. New differentiation techniques of the unknownsolution with respect to time variable are proposed. It is shown that theproposed techniques allow to generate accurate higher order derivativessimultaneously for a set of spatial points. The calculated derivatives can thenbe used for data-driven solution in different ways. An application for PhysicsInformed Neural Networks by the well-known DeepXDE software solution in Pythonunder Tensorflow background framework has been presented for three real-lifePDEs: Burgers', Allen-Cahn and Schrodinger equations.

High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks