Rectified sigmoid (hard sigmoid) activation is reported to cut PINN solution errors by about an order of magnitude on two ODE benchmarks, but the result may be an interpolation artifact because the paper never discloses the source of the initialization data.
Separable Physics-Informed Neural Networks for the solution of elasticity problems
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abstract
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing that this method has a significantly higher convergence rate and accuracy than the vanilla physics-informed neural networks (PINN) and even SPINN based on a system of partial differential equations (PDEs). In addition, using the SPINN in the framework of DEM approach it is possible to solve problems of the linear theory of elasticity on complex geometries, which is unachievable with the help of PINNs in frames of partial differential equations. Considered problems are very close to the industrial problems in terms of geometry, loading, and material parameters.
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About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks
Rectified sigmoid (hard sigmoid) activation is reported to cut PINN solution errors by about an order of magnitude on two ODE benchmarks, but the result may be an interpolation artifact because the paper never discloses the source of the initialization data.