Scalable Mechanistic Neural Networks
Keywords: Scientific Machine Learning, Ordinary Differential Equations, Time Series, Dynamical Systems
TL;DR: We introduce a scalable solver for the mechanistic neural networks that reduces time and memory costs from cubic/quadratic to linear in the sequence length, enabling long-horizon scientific modeling of dynamical systems in the neural networks.
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.
Supplementary Material: zip
Primary Area: learning on time series and dynamical systems
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Submission Number: 10522
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