Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

Fuente: arXiv
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Main Authors: Chen, Jiale, Yao, Dingling, Pervez, Adeel, Alistarh, Dan, Locatello, Francesco
Format: Preprint
Published: 2024
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author Chen, Jiale
Yao, Dingling
Pervez, Adeel
Alistarh, Dan
Locatello, Francesco
author_facet Chen, Jiale
Yao, Dingling
Pervez, Adeel
Alistarh, Dan
Locatello, Francesco
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_06074
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning
Chen, Jiale
Yao, Dingling
Pervez, Adeel
Alistarh, Dan
Locatello, Francesco
Machine Learning
Numerical Analysis
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.
title Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning
topic Machine Learning
Numerical Analysis
url https://arxiv.org/abs/2410.06074