用Transformer模型预测电磁波在不同材料间的反射透射，精度高且可泛化。
Predicting Wave Reflection and Transmission in Heterogeneous Media via Fourier Operator-Based Transformer Modeling
- 基于视觉变换器框架，融合傅里叶变换学习波的频率与物理特征嵌入。
- 在75个时间步内相对误差低于10%，界面处误差虽突增但整体可控。
- 适用于含未知材料属性和间断界面的复杂电磁波传播场景。
我们构建了一种机器学习代理模型，用于近似求解一维麦克斯韦方程组，聚焦于材料界面引起的电磁波反射与透射问题。训练数据源自高保真有限体积（FV）模拟，涵盖初始条件及单一材料光速的变化，使模型能学习多种波-材料相互作用行为。该模型在基于视觉变换器的框架中，通过自回归方式学习物理与频率嵌入。在潜在空间中引入傅里叶变换，使解的波数谱与仿真数据高度吻合。预测误差随时间近似线性增长，在材料界面处出现显著跃升。测试结果显示，尽管存在不连续性和未知材料属性，模型在超过75个时间步的滚动预测中仍保持低于10%的相对误差。
原文摘要 · Abstract (English)
We develop a machine learning (ML) surrogate model to approximate solutions to Maxwell's equations in one dimension, focusing on scenarios involving a material interface that reflects and transmits electro-magnetic waves. Derived from high-fidelity Finite Volume (FV) simulations, our training data includes variations of the initial conditions, as well as variations in one material's speed of light, allowing for the model to learn a range of wave-material interaction behaviors. The ML model autoregressively learns both the physical and frequency embeddings in a vision transformer-based framework. By incorporating Fourier transforms in the latent space, the wave number spectra of the solutions aligns closely with the simulation data. Prediction errors exhibit an approximately linear growth over time with a sharp increase at the material interface. Test results show that the ML solution has adequate relative errors below $10\%$ in over $75$ time step rollouts, despite the presence of the discontinuity and unknown material properties.
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。