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cs.NE2021
Adaptive neural domain refinement for solving time-dependent differential equations
Toni Schneidereit, Michael Breuß
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution do…
cs.NE2021
Collocation Polynomial Neural Forms and Domain Fragmentation for solving Initial Value Problems
Toni Schneidereit, Michael Breuß
Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial so…
cs.NE2020
Computational characteristics of feedforward neural networks for solving a stiff differential equation
Toni Schneidereit, Michael Breuß
Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issue…