The given work proposes a novel approach for solving inverse problems in machine learning leveraging Physics-Guided Neural Networks (PGNNs). This method incorporates domain knowledge through an additional inverse problem, leading to significant improvements in model performance and accuracy.
(Національний університет "Києво-Могилянська академія", 2025) Kravchuk, Oleg; Kriukova, Galyna
The Moore-Penrose pseudo-inverse is a foundational concept in modern numerical linear algebra, offering a principled approach to solving ill-posed and inconsistent systems arising in machine learning and other fields. This paper explores the pseudo-inverse from five distinct perspectives — axiomatic, variational, regularization, spectral, and algebraic graph theory — highlighting its theoretical depth and practical relevance across disciplines such as machine learning, signal processing, and network analysis.