Classification with Runge-Kutta networks and feature space augmentation

DOI10.3934/jcd.2021018zbMath1481.65106arXiv2104.02369OpenAlexW3210957872MaRDI QIDQ2063032

Axel Kröner, Elisa Giesecke

Publication date: 10 January 2022

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.02369

zbMATH Keywords

deep learningaugmented neural ODEspoint and image classificationRunge-Kutta networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Uses Software

• PyTorch
• GitHub
• torchdiffeq
• ANODEs

Cites Work

• Symplectic Runge-Kutta and related methods: Recent results
• Runge-Kutta methods in optimal control and the transformed adjoint system
• Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations
• Deep learning as optimal control problems: models and numerical methods
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A proposal on machine learning via dynamical systems
• Symplectic Runge--Kutta Schemes for Adjoint Equations, Automatic Differentiation, Optimal Control, and More
• Structure-preserving deep learning
• Deep Learning: An Introduction for Applied Mathematicians