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A comparative study of NeuralODE and Universal ODE approaches to solving Chandrasekhar White Dwarf equation

arXiv 2410.14998 ↗First posted 19 Oct 2024cs.LG cs.AIcited by 0

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Abstract (arXiv)

In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Chandrasekhar White Dwarf Equation (CWDE). The CWDE is fundamental for understanding the life cycle of a star, and describes the relationship between the density of the white dwarf and its distance from the center. Despite the rise in Scientific Machine Learning frameworks, very less attention has been paid to the systematic applications of the above SciML pillars on astronomy based ODEs. Through robust modeling in the Julia programming language, we show that both Neural ODEs and UDEs can be used effectively for both prediction as well as forecasting of the CWDE. More importantly, we introduce the forecasting breakdown point - the time at which forecasting fails for both Neural ODEs and UDEs. Through a robust hyperparameter optimization testing, we provide insights on the neural network architecture, activation functions and optimizers which provide the best results. This study provides opens a door to investigate the applicability of Scientific Machine Learning frameworks in forecasting tasks for a wide range of scientific domains.

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References · 18

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  3. 2019Augmented Neural ODEscited by 397
  4. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  5. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  6. 2020Dissecting Neural ODEscited by 153
  7. 2019A Differentiable Programming System to Bridge Machine Learning and Scientific Computingcited by 83
  8. 2019On Robustness of Neural Ordinary Differential Equationscited by 83
  9. 2021Stiff Neural Ordinary Differential Equationscited by 78
  10. 2020Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problemscited by 45
  11. 2019DiffEqFlux.jl - A Julia Library for Neural Differential Equationscited by 33
  12. 2020Universal Approximation Property of Neural Ordinary Differential Equationscited by 32
6 more
  1. 2020Universal Battery Performance and Degradation Model for Electric Aircraftcited by 8
  2. 2022Neural networks: solving the chemistry of the interstellar mediumcited by 7
  3. 2021Autonomous Kinetic Modeling of Biomass Pyrolysis using Chemical Reaction Neural Networkscited by 6
  4. 2017A Universal Ordinary Differential Equationcited by 4
  5. 2023Hybridizing Physics and Neural ODEs for Predicting Plasma Inductance Dynamics in Tokamak Fusion Reactorscited by 4
  6. 2020Julia Language in Machine Learning: Algorithms, Applications, and Open Issuescited by 3

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