PreprintCC BY 4.0arXiv
Multiple Nonlinear Waves by (Quantum) Neural Networks: Checking the AI supremacy
Abstract
To test the potential of so-called quantum physics-informed neural network (QPINN) technology for solving evolutionary partial differential equations, we consider the problem of multiple wave propagation in a weakly nonlinear medium described by the Korteweg-de Vries equation with periodic boundary conditions. Although this problem is solvable analytically, high-genus solutions could represent a rather challenging testbed for numerical methods. Therefore, our idea is to test whether a QPINN is sufficiently mature for application in this context by providing a set of indicators of merit and performing several numerical experiments.
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BibTeX
@misc{martina2026multiple,
title = {{Multiple Nonlinear Waves by (Quantum) Neural Networks: Checking the AI supremacy}},
author = {Luigi Martina and Riccardo Caricato and Riccardo Della Torre},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29894},
eprint = {2608.29894},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29894},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multiple Nonlinear Waves by (Quantum) Neural Networks: Checking the AI supremacy
AU - Luigi Martina
AU - Riccardo Caricato
AU - Riccardo Della Torre
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29894
UR - https://arxiv.org/abs/2608.29894
AB - To test the potential of so-called quantum physics-informed neural network (QPINN) technology for solving evolutionary partial differential equations, we consider the problem of multiple wave propagation in a weakly nonlinear medium described by the Korteweg-de Vries equation with periodic boundary conditions. Although this problem is solvable analytically, high-genus solutions could represent a rather challenging testbed for numerical methods. Therefore, our idea is to test whether a QPINN is sufficiently mature for application in this context by providing a set of indicators of merit and performing several numerical experiments.
ER -