# Meshfree Variational Physics Informed Neural Networks (MF-VPINN): an adaptive training strategy

arXiv: https://arxiv.org/abs/2406.19831 · HTML: https://mlsanity.com/paper/2406.19831/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2024.

## Built on by (most cited first, 2 of 2)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities](https://mlsanity.com/paper/2606.18032/) (2026)

## Abstract (arXiv)

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 the 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.