Author

I. A. Velikorechanin

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Open access Oct 2026

From Numerical Schemes to Neural Network Architectures: A Physics-Informed Framework for Differential Equations

Physics-informed neural networks usually incorporate differential equations primarily through the loss function, while the neural architecture itself is selected independently of the underlying numerical structure. This work develops a scheme-induced approach in which an analytically modified numerical method defines t...

Tatiana V. Lazovskaya, Dmitriy Tarkhov, I. Velikorechanin et al. · Machine Learning and Knowled... · 0 citations

Open access Sep 2026

Embedding Physics-Informed Neural Networks into Numerical Schemes for Modeling Dynamical Systems

Context and relevance. Physics-Informed Neural Networks (PINNs) are considered a promising tool for mathematical modeling of dynamical systems described by differential equations. However, classical PINN approaches require repeated computation of high-order derivatives, which leads to significant computational costs an...

I. Velikorechanin, T. Lazovskaya, D. A. Tarkhov · Modelling and Data Analysis · 0 citations