A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities
Authors: Shayan Dodge, Alessandro Formisano, Sami Barmada
Journal: Journal of Computational Physics (JCP)
DOI: 10.1016/j.jcp.2026.115328
Links: ScienceDirect ·arXiv ·ResearchGate
The INI-VPINN paper is published in the Journal of Computational Physics (JCP).
This repository hosts the public INI-VPINN implementation and will be expanded progressively with the benchmark cases presented in the work.
The first public release, v1.0.0, provides the homogeneous T-shaped benchmark with:
- the complete INI-VPINN training notebook;
- operator-guided element-wise test-function selection;
- FEM reference data and validation;
- prediction and error-history outputs;
- publication-ready comparison and convergence plots.
The main notebook is:
INI_VPINN_v1.0.0_Homogeneous.ipynb
The repository will be extended with additional INI-VPINN cases, including:
- Non-homogeneous domain benchmarks;
- Poisson-equation benchmarks;
- Non-Rectangular geometries.
These examples are currently being prepared and will be published in future versions of this repository.
Thank you for your interest in INI-VPINN.
The first clean and documented implementation is now available through the v1.0.0. Additional examples and benchmark configurations will be added progressively to support reproducibility and broader use of the method.
For the mathematical formulation, weak-form derivation, implicit treatment of Neumann/interface conditions, and benchmark definitions, readers are strongly encouraged to read the paper.
- Paper: https://doi.org/10.1016/j.jcp.2026.115328
- Repository: https://github.com/ShayanDodge/INI-VPINN
If INI-VPINN is useful for your work, please ⭐ star this repository and cite the paper. This helps others discover the project and supports future releases.
Thank you for your interest and patience!
Shayan Dodge