  In this paper we introduce a Meshfree Variational Physics Informed Neural
Network. It is a Variational Physics Informed Neural Network that does not
require the generation of a triangulation of the entire domain and that can be
trained with an adaptive set of test functions. In order to generate the test
space we exploit an a posteriori error indicator and add test functions only
where the error is higher. Four training strategies are proposed and compared.
Numerical results show that the accuracy is higher than the one of a
Variational Physics Informed Neural Network trained with the same number of
test functions but defined on a quasi-uniform mesh.
