Forecasting N-Body Dynamics: A Comparative Study of Neural Ordinary Differential Equations and Universal Differential Equations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912786438684672 |
|---|---|
| author | S, Suriya R Joshi, Prathamesh Dinesh Dandekar, Rajat Dandekar, Raj Panat, Sreedath |
| author_facet | S, Suriya R Joshi, Prathamesh Dinesh Dandekar, Rajat Dandekar, Raj Panat, Sreedath |
| contents | The n body problem, fundamental to astrophysics, simulates the motion of n bodies acting under the effect of their own mutual gravitational interactions. Traditional machine learning models that are used for predicting and forecasting trajectories are often data intensive black box models, which ignore the physical laws, thereby lacking interpretability. Whereas Scientific Machine Learning ( Scientific ML ) directly embeds the known physical laws into the machine learning framework. Through robust modelling in the Julia programming language, our method uses the Scientific ML frameworks: Neural ordinary differential equations (NODEs) and Universal differential equations (UDEs) to predict and forecast the system dynamics. In addition, an essential component of our analysis involves determining the forecasting breakdown point, which is the smallest possible amount of training data our models need to predict future, unseen data accurately. We employ synthetically created noisy data to simulate real-world observational limitations. Our findings indicate that the UDE model is much more data efficient, needing only 20% of data for a correct forecast, whereas the Neural ODE requires 90%. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forecasting N-Body Dynamics: A Comparative Study of Neural Ordinary Differential Equations and Universal Differential Equations S, Suriya R Joshi, Prathamesh Dinesh Dandekar, Rajat Dandekar, Raj Panat, Sreedath Machine Learning Artificial Intelligence Computational Physics The n body problem, fundamental to astrophysics, simulates the motion of n bodies acting under the effect of their own mutual gravitational interactions. Traditional machine learning models that are used for predicting and forecasting trajectories are often data intensive black box models, which ignore the physical laws, thereby lacking interpretability. Whereas Scientific Machine Learning ( Scientific ML ) directly embeds the known physical laws into the machine learning framework. Through robust modelling in the Julia programming language, our method uses the Scientific ML frameworks: Neural ordinary differential equations (NODEs) and Universal differential equations (UDEs) to predict and forecast the system dynamics. In addition, an essential component of our analysis involves determining the forecasting breakdown point, which is the smallest possible amount of training data our models need to predict future, unseen data accurately. We employ synthetically created noisy data to simulate real-world observational limitations. Our findings indicate that the UDE model is much more data efficient, needing only 20% of data for a correct forecast, whereas the Neural ODE requires 90%. |
| title | Forecasting N-Body Dynamics: A Comparative Study of Neural Ordinary Differential Equations and Universal Differential Equations |
| topic | Machine Learning Artificial Intelligence Computational Physics |
| url | https://arxiv.org/abs/2512.20643 |