# Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems

arXiv: https://arxiv.org/abs/2406.04626 · HTML: https://mlsanity.com/paper/2406.04626/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 7 Jun 2024.

## Builds on (most cited first, 3 of 3)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Exact Enforcement of Temporal Continuity in Sequential Physics-Informed Neural Networks](https://mlsanity.com/paper/2403.03223/) (2024)
- [On the Compatibility between Neural Networks and Partial Differential Equations for Physics-informed Learning](https://mlsanity.com/paper/2212.00270/) (2022)

## Built on by (most cited first, 3 of 3)

- [WellPINN: Accurate Well Representation for Transient Fluid Pressure Diffusion in Subsurface Reservoirs with Physics-Informed Neural Networks](https://mlsanity.com/paper/2507.09330/) (2025)
- [Hybrid Quantum-Classical PINNs for Scientific Computing: A Multi-GPU Open-Source Framework](https://mlsanity.com/paper/2604.15645/) (2026)
- [CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Laws](https://mlsanity.com/paper/2607.06587/) (2026)

## Abstract (arXiv)

We present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://dx.doi.org/10.2139/ssrn.4766623), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.