INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities

arXiv:2606.18032 · math.NA, cs.LG, cs.NA, physics.comp-ph · Submitted 2026-06-16 · Read on arXiv

math.NA, cs.LG, cs.NA, physics.comp-ph

Submitted: 2026-06-16

Updated: 2026-06-16

Comments: Preprint version. Under peer review. Code available at: https://github.com/ShayanDodge/INI-VPINN

Journal ref: Journal of Computational Physics, Volume 565, 115328 (2026)

DOI: 10.1016/j.jcp.2026.115328

Code: https://github.com/ShayanDodge/INI-VPINN

Project page: https://shayandodge.github.io

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 26× in this paper · explained in 1 episode
• Loss Function — 9× in this paper · explained in 2 episodes
• Benchmark — 6× in this paper · explained in 2 episodes
• Consistency — 4× in this paper · explained in 3 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Alignment — 3× in this paper · explained in 1 episode
• Finite Element Method — 3× in this paper
• Activation Function — 2× in this paper · explained in 1 episode
• Adaptivity — 2× in this paper · explained in 1 episode
• Inverse Problem — 2× in this paper · explained in 2 episodes
• Neural Tangent Kernel — 2× in this paper
• PDE residual — 2× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 2× in this paper · explained in 6 episodes
• Automatic Differentiation — 1× in this paper
• Computational overhead — 1× in this paper · explained in 2 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Deep Energy Method — 1× in this paper
• Deep Galerkin Method — 1× in this paper
• Fidelity — 1× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Physics Informed Neural Network for Option Pricing
• Variational Physics-Informed Neural Networks For Solving Partial Differential Equations
• VarNet: Variational Neural Networks for the Solution of Partial Differential Equations
• Adam: A Method for Stochastic Optimization

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