# Physics-Informed Neural Networks with Architectural Physics Embedding for Large-Scale Wave Field Reconstruction

arXiv: https://arxiv.org/abs/2603.02231 · HTML: https://mlsanity.com/paper/2603.02231/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [NeRF2: Neural Radio-Frequency Radiance Fields](https://mlsanity.com/paper/2305.06118/) (2023)
- [RF-3DGS: Wireless Channel Modeling with Radio Radiance Field and 3D Gaussian Splatting](https://mlsanity.com/paper/2411.19420/) (2024)
- [Quantum deep field: data-driven wave function, electron density generation, and atomization energy prediction and extrapolation with machine learning](https://mlsanity.com/paper/2011.07923/) (2020)
- [Physics Embedded Machine Learning for Electromagnetic Data Imaging](https://mlsanity.com/paper/2207.12607/) (2022)
- [Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features](https://mlsanity.com/paper/2510.19399/) (2025)
- [Gabor-Enhanced Physics-Informed Neural Networks for Fast Simulations of Acoustic Wavefields](https://mlsanity.com/paper/2502.17134/) (2025)
- [Deep, data-driven modeling of room acoustics: literature review and research perspectives](https://mlsanity.com/paper/2504.16289/) (2025)

## Built on by (most cited first, 1 of 1)

- [Physics-Informed Domain-Invariant Feature Learning with Autoencoder-Driven Gaussian Clustering for Robust Non-line-of-Sight Scenarios](https://mlsanity.com/paper/2607.02537/) (2026)

## Abstract (arXiv)

Large-scale wave field reconstruction requires precise solutions but faces challenges with computational efficiency and accuracy. The physics-based numerical methods like Finite Element Method (FEM) provide high accuracy but struggle with large-scale or high-frequency problems due to prohibitive computational costs. Pure data-driven approaches excel in speed but often lack sufficient labeled data for complex scenarios. Physics-informed neural networks (PINNs) integrate physical principles into machine learning models, offering a promising solution by bridging these gaps. However, standard PINNs embed physical principles only in loss functions, leading to slow convergence, optimization instability, and spectral bias, limiting their ability for large-scale wave field reconstruction. This work introduces architectural physics embedded (PE)-PINN, which integrates additional physical guidance directly into the neural network architecture beyond Helmholtz equations and boundary conditions in loss functions. Specifically, a new envelope transformation layer is designed to mitigate spectral bias with kernels parameterized by source properties, material interfaces, and wave physics. Experiments demonstrate that PE-PINN achieves more than 10 times speedup in convergence compared to standard PINNs and several orders of magnitude reduction in memory usage compared to FEM. This breakthrough enables high-fidelity modeling for large-scale 2D/3D electromagnetic wave reconstruction involving reflections, refractions, and diffractions in room-scale domains, readily applicable to wireless communications, sensing, room acoustics, and other fields requiring large-scale wave field analysis.