90 citations · 289 across the 32 of their papers we have counts for
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Physics-Based Deep Neural Networks for Beam Dynamics in Charged Particle Accelerators
Andrei Ivanov, Ilya Agapov
This paper presents a novel approach for constructing neural networks which model charged particle beam dynamics. In our approach, the Taylor maps arising in the representation of…
Physics-based polynomial neural networks for one-shot learning of dynamical systems from one or a few samples
Andrei Ivanov, Uwe Iben, Anna Golovkina
This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the d…
Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning
Andrei Ivanov, Anna Golovkina, Uwe Iben
The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possi…
Matrix Lie Maps and Neural Networks for Solving Differential Equations
Andrei Ivanov, Sergei Andrianov
The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of…