Optimising neural fractional differential equations for performance and efficiency

Publication date
2024-10
Document type
Konferenzbeitrag
Author
Organisational unit
URL
URI
Conference
1st ECAI Workshop on “Machine Learning Meets Differential Equations: From Theory to Applications” (ML-DE Workshop at ECAI 2024) ; Santiago de Compostela, Spain ; October 20th, 2024
Publisher
MLResearchPress
Series or journal
Proceedings of machine learning research
ISSN
Periodical volume
255
Book title
1st ECAI Workshop on “Machine Learning Meets Differential Equations: From Theory to Applications”, 20 October 2024, Santiago de Compostela, Spain
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Neural networks
Cyber-physical systems
Neural ordinary differential equation
Neural Fractional Differential Equation
Benchmark
Abstract
Neural Ordinary Differential Equations (NODEs) are well-established architectures that fit an ODE, modelled by a neural network (NN), to data, effectively modelling complex dynamical systems. Recently, Neural Fractional Differential Equations (NFDEs) were proposed, inspired by NODEs, to incorporate non-integer order differential equations, capturing memory effects and long-range dependencies. In this work, we present an optimised implementation of the NFDE solver, achieving up to 570 times faster computations and up to 79 times higher accuracy. Additionally, the solver supports efficient multidimensional computations and batch processing. Furthermore, we enhance the experimental design to ensure a fair comparison of NODEs and NFDEs by implementing rigorous hyperparameter tuning and using consistent numerical methods. Our results demonstrate that for systems exhibiting fractional dynamics, NFDEs significantly outperform NODEs, particularly in extrapolation tasks on unseen time horizons. Although NODEs can learn fractional dynamics when time is included as a feature to the NN, they encounter difficulties in extrapolation due to reliance on explicit time dependence. The code is available at https://github.com/zimmer-ing/Neural-FDE
Cite as
Bernd Zimmering, Cecília Coelho, Oliver Niggemann Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications", PMLR 255:1-22, 2024
Version
Published version
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Metadata only access