用线性编码器替代非线性编码器，大幅降低模型降阶训练成本。
Leveraging time and parameters for nonlinear model reduction methods
- 将原系统扩展后，可用线性编码器替代非线性编码器
- 训练参数量减半，精度基本不变
- 适合处理波动或输运主导的复杂问题
本文研究缓慢衰减柯尔莫戈洛夫 $n$-宽度问题的模型降阶方法，如某些波状或输运主导的问题。为突破柯尔莫戈洛夫障碍，常采用基于自编码器的非线性投影。这类自编码器包含非线性编码器和解码器，需耗费大量计算资源训练超参数以保证降阶系统的逼近质量。本文提出通过扩展待降阶系统及其训练数据，可将非线性编码器替换为线性编码器，几乎减少一半需训练的超参数数量，且不损失精度。
原文摘要 · Abstract (English)
In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear projections are used, which are often realized numerically using autoencoders. These autoencoders generally consist of a nonlinear encoder and a nonlinear decoder and involve costly training of the hyperparameters to obtain a good approximation quality of the reduced system. To facilitate the training process, we show that extending the to-be-reduced system and its corresponding training data makes it possible to replace the nonlinear encoder with a linear encoder without sacrificing accuracy, thus roughly halving the number of hyperparameters to be trained.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。