arXiv:2606. 20326v1 Announce Type: new Abstract: We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs).
By Xiang Rao, Yuxuan Shen
arXiv:2609.22189v1 Announce Type: cross
Abstract: The Schrodinger equation in one spatial dimension admits a small set of exactly solvable potentials that serve as natural proving grounds for any new...
By Tariq Mahmood, Waqas Arshad, Bilal Naseer, Alfredo Raya
QGPINNs is a PyTorch-based physics-informed neural network framework for solving nonlocal differential equations on quantum graphs. It approximates the solution on each edge with a neural network and uses a unified graph‑based loss to enforce governing equations, initial, boundary, and vertex transmission conditions, including continuity, Kirchhoff‑Neumann, and Dirichlet conditions. The framework supports multi‑order fractional elliptic problems and time‑fractional evolution equations, incorporates graph‑adapted learning strategies such as soft/hard constraints, dynamic loss balancing, Fourier feature embeddings, and a learnable singularity‑capturing feature, and extends to inverse problems for identifying fractional orders and physical parameters from noisy data, as validated on benchmark and real‑world networks such as the IEEE 14‑bus system and an agricultural drainage network.
By Vaibhav Mehandiratta, Saket Ramchandra
arXiv:2608. 00850v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems.
By Fabio Pereira dos Santos, Renato Portugal, J\'ulio de Castro Vargas Fernandes, Lucas Timotheo Sanches
arXiv:2610. 02084v1 Announce Type: cross Abstract: We study free-boundary problems within a physics-informed framework using Kolmogorov-Arnold network (KAN) approximations.
By Tan Phuong Dong Le
arXiv:2607. 12269v1 Announce Type: new Abstract: We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), a family of parameterised quantum circuits that learn classical dynamics in a structure-preserving manner.
By Dibakar Sigdel