Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

TL;DR

The paper introduces S-MNN, a scalable neural network framework for scientific modeling of long sequences, reducing computational costs while maintaining accuracy and interpretability.

Contribution

It reformulates the original MNN to achieve linear complexity, enabling efficient long-term dynamics modeling in neural networks.

Findings

S-MNN matches original MNN accuracy in experiments.

S-MNN reduces computational time and space complexity.

Source code is publicly available at the provided GitHub URL.

Abstract

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems. Source code is available at https://github.com/IST-DASLab/ScalableMNN.