Koffi Ognandon Ayena | Searcharxiv

arXiv2026

1D Convection-Diffusion in Porous Media: A Unified Solution from Bounded Domain to Half-Space

We present an analytical solution for 1D atmospheric pollutant dispersion in a bounded domain. Using coordinate transformation and spectral decomposition, we obtain a Fourier series solution for time-dependent wind velocity. For constant wind, Laplace inversion yields dual representations via residue calculus and Poisson summation. The solution extends to semi-infinite domains, recovering classical error-function profiles.

math.AP↗

arXiv2026

Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction

Variational quantum circuits (VQCs) are parameterized quantum circuits optimized classically. We propose a hybrid variational quantum circuit (HVQC) extending VQCs with a classical affine post-measurement layer, enabling vector-valued regression without the linear overhead of independent scalar circuits. Theoretically, we show that elementary one-and two-qubit circuits can approximate quadratic functions and products via data re-uploading and entanglement, providing the foundations of the full architecture. Experimentally, on two synthetic image reconstruction datasets and the Friedman1 benchmark (40,568 test samples), our HVQC matches Gaussian Process Regression and outperforms XGBoost and Random Forest. An ablation study confirms that both quantum and classical components are essential, and results highlight the central role of the feature map in hybrid quantum-classical models.

cs.LG↗