The Newton Scheme for Deep Learning

TL;DR

This paper introduces the Newton Scheme (NS), a physics-based neural network leveraging Newton's Law to recognize force patterns and predict trajectories with minimal error, reducing computational costs compared to traditional data-driven methods.

Contribution

The paper proposes a novel Newton physics-based neural network that uses fundamental mechanics for pattern recognition and trajectory prediction, offering a more efficient alternative to data-intensive models.

Findings

NS accurately predicts trajectories with nearly zero error.

NS outperforms TCN, GRU, and FIND-PDE in physical pattern recognition.

The method demonstrates applications in free-falling, pendulum, and curved trajectories.

Abstract

We introduce a neural network (NN) strictly governed by Newton's Law, with the nature required basis functions derived from the fundamental classic mechanics. Then, by classifying the training model as a quick procedure of 'force pattern' recognition, we developed the Newton physics-based NS scheme. Once the force pattern is confirmed, the neuro network simply does the checking of the 'pattern stability' instead of the continuous fitting by computational resource consuming big data-driven processing. In the given physics's law system, once the field is confirmed, the mathematics bases for the force field description actually are not diverged but denumerable, which can save the function representations from the exhaustible available mathematics bases. In this work, we endorsed Newton's Law into the deep learning technology and proposed Newton Scheme (NS). Under NS, the user first identifies the path pattern, like the constant acceleration movement.The object recognition technology first loads mass information, then, the NS finds the matched physical pattern and describe and predict the trajectory of the movements with nearly zero error. We compare the major contribution of this NS with the TCN, GRU and other physics inspired 'FIND-PDE' methods to demonstrate fundamental and extended applications of how the NS works for the free-falling, pendulum and curve soccer balls.The NS methodology provides more opportunity for the future deep learning advances.