发表机构
German Aerospace Center (DLR); Technische Universität Ilmenau（德国航空航天中心（DLR）; 伊尔默瑙工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于复指数函数的周期激活函数，通过同时传递正弦和余弦输出，在稀疏速度数据重构瑞利-贝纳德对流温度场中显著提升质量并降低计算成本。
AI 中文摘要
已有研究表明，在物理信息神经网络的广泛应用中，使用周期激活函数的架构相较于单调激活函数更具优势。本文研究了一种使用复指数函数、生成正弦和余弦输出对作为激活函数的网络架构。将其与可比较的正弦激活多层感知机进行对比，用于从稀疏速度数据重构立方瑞利-贝纳德对流的温度场，结果显示重构质量显著提升，且每个训练步骤的计算成本没有大幅增加。反之，改进的架构能够以更低的成本达到相似的重构质量。分析这些网络的数学结构表明，改进源于同时传递正弦和余弦函数的特性。这样，后续层能够调整所提供的潜在周期函数的相位，并对其每个神经元单独进行调整。
英文摘要
Architectures with periodic activation functions have already been shown to be beneficial in comparison to monotonic counterparts for a wide range of applications of physics-informed neural networks. Here, we investigate a network architecture which uses the complex exponential function, generating pairs of sine and cosine outputs as activation functions. Testing it against comparable, sine-activated multi-layer perceptrons for the task of temperature reconstruction from sparse velocity data for cubic Rayleigh-Bénard convection reveals significant improvements in the reconstruction quality without a substantial increase in computational cost per training step. Vice versa, the improved architecture enables reaching similar reconstruction qualities for a fraction of the expense. Analyzing the mathematical structure of these networks points to the improvements being rooted in the property of passing both a sine and cosine function forward. This way, the subsequent layer is able to adapt the phase of the provided latent periodic functions, and doing it individually for each of its neurons.
