Forecasting N-Body Dynamics: A Comparative Study of Neural Ordinary Differential Equations and Universal Differential Equations

Suriya R S, Prathamesh Dinesh Joshi, Rajat Dandekar, Raj Dandekar, Sreedath Panat

Track: Tiny Paper Track (Page limit: 3-5 pages)

Keywords: Scientific Machine Learning, Neural ODE, Universal ODE

TL;DR: For solving n-body problem, we have experimented with interpretabale Scientific Machine learning models NeuralODEs and UniversalODEs

Abstract:

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 frame-
work. Through robust modelling in the Julia programming
language, our method uses the Scientific ML frameworks:
Neural ordinary differential equations (NODEs) and Univer-
sal differential equations (UDEs) to predict and forecast the
system’s 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%.

Submission Number: 52