将神经网络计算复杂度从立方降至线性，实现长期动态高效建模。
Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning
- 重构机制神经网络，使计算时间和空间复杂度均变为线性。
- 在长序列上保持原模型精度，计算资源减少显著。
- 适合需要高效建模复杂系统动力学的研究者使用。
我们提出可扩展的机制神经网络（S-MNN），一种专为涉及长时序序列的科学机器学习应用设计的增强型神经网络框架。通过对原始机制神经网络（MNN）（Pervez等，2024）进行重构，我们将计算时间复杂度从与序列长度的立方关系降低至线性，空间复杂度从二次降至线性。这一显著改进使得在不牺牲精度或可解释性的前提下，高效建模长期动态成为可能。大量实验表明，S-MNN 在精度上与原始 MNN 保持一致，同时大幅降低计算资源消耗。因此，S-MNN 可直接替代原始 MNN 应用于各类场景，为复杂动力系统中整合机制瓶颈提供实用高效的工具。源代码可在 https://github.com/IST-DASLab/ScalableMNN 获取。
原文摘要 · Abstract (English)
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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