Papers › Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

8 Oct 2024arXiv:2410.06074archive 2025-07-28

Jiale Chen, Dingling Yao, Adeel Pervez, Dan Alistarh, Francesco Locatello

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.

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