# Vanishing Stacked-Residual PINN for State Reconstruction of Hyperbolic Systems

arXiv: https://arxiv.org/abs/2503.14222 · HTML: https://mlsanity.com/paper/2503.14222/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2025.

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

- [Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features](https://mlsanity.com/paper/2510.19399/) (2025)
- [Curriculum-Learned Vanishing Stacked Residual PINNs for Hyperbolic PDE State Reconstruction](https://mlsanity.com/paper/2602.06996/) (2026)
- [Scientific Knowledge-Guided Machine Learning for Vessel Power Prediction: A Comparative Study](https://mlsanity.com/paper/2602.18403/) (2026)

## Abstract (arXiv)

In a more connected world, modeling multi-agent systems with hyperbolic partial differential equations (PDEs) offers a compact, physics-consistent description of collective dynamics. However, classical control tools need adaptation for these complex systems. Physics-informed neural networks (PINNs) provide a powerful framework to fix this issue by inferring solutions to PDEs by embedding governing equations into the neural network. A major limitation of original PINNs is their inability to capture steep gradients and discontinuities in hyperbolic PDEs. To tackle this problem, we propose a stacked residual PINN method enhanced with a vanishing viscosity mechanism. Initially, a basic PINN with a small viscosity coefficient provides a stable, low-fidelity solution. Residual correction blocks with learnable scaling parameters then iteratively refine this solution, progressively decreasing the viscosity coefficient to transition from parabolic to hyperbolic PDEs. Applying this method to traffic state reconstruction improved results by an order of magnitude in relative L2 error, demonstrating its potential to accurately estimate solutions where original PINNs struggle with instability and low fidelity.