Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning
This work addresses the computational bottleneck of Mechanistic Neural Networks for scientific machine learning tasks involving long temporal sequences.
The authors propose Scalable Mechanistic Neural Network (S-MNN), which reduces computational time and space complexities from cubic and quadratic to linear in sequence length, enabling efficient modeling of long-term dynamics without sacrificing accuracy.
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.