55 citations · 61 across the 3 of their papers we have counts for
3 papers
cs.LG2022★ 55 cited
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems
Derick Nganyu Tanyu, Jianfeng Ning, Tom Freudenberg +4
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make…
cs.NE2020
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…
cs.NE2019★ 6 cited
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…