On one- and two-dimensional Poisson equations, finite differences beat physics-informed neural networks in accuracy, and PINNs can reconstruct source terms and coefficients in a forward-inverse setting.
It provides significant applications to physics and engineering, modeling electrostatics, heat conduction, and fluid dynamics among many others
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Development and optimization of physics-informed neural networks for solving partial differential equations
On one- and two-dimensional Poisson equations, finite differences beat physics-informed neural networks in accuracy, and PINNs can reconstruct source terms and coefficients in a forward-inverse setting.