Exploring Scaling Laws in Large Learning Models for Inverse Scattering With Spatial–Temporal Diffusion

Recently, deep learning schemes have shown successes in both electromagnetic forward and inverse problems, whereas the scaling laws, i.e., the relationships between performances of solving electromagnetic problems and model sizes and data, are seldom explored. In this work, we study empirical scaling laws in solving inverse scattering problems (ISPs), where, to improve the scalability of traditional learning models in electromagnetic society, a multiple-channel current diffusion model (MCDM) is firstly proposed to directly reconstruct induced currents from scattering fields and quantify the uncertainty simultaneously. The proposed MCDM demonstrates accurate reconstruction and robust generalization through tests on both in-range dataset and out-of-range dataset, where the process of gradual denoising along time steps provides low learning difficulty with 3-D convolution and spatial-temporal attention capturing local and non-local information, respectively. More importantly, by utilizing the scalability of the proposed MCDM, we further explore the scaling laws of ISPs for the first time, which provide guidance to set appropriate training hyperparameters under limited sources and explore the potential performances of large learning models in solving electromagnetic problems. For comparison, MCDM significantly outperforms the traditional convolution-based direct inversion scheme (DIS) under both numerical and experimental tests, where 24.6% improvement is observed for out-of-range tests. In addition, it is also found that by incorporating physics into learning data, the resource requirements are largely reduced.