Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a point-wise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multi-scale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to 4th order. These scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.

翻译：物理学家在进行参数推断或生成新场实现等任务时，通常需要概率模型。对于高度非高斯场，建立此类模型是一项挑战，尤其是在样本数量有限的情况下。本文针对平稳场引入了散射谱模型，并证明其能为物理学中遇到的各种场提供准确且稳健的统计描述。这些模型基于散射系数的协方差——即场的波束分解与逐点模运算的耦合。通过利用场在旋转和缩放下的规律性进行有效的降维处理后，我们在多种多尺度物理场上验证了这些模型，证明其能够复现包括四阶以下空间矩在内的标准统计量。这些散射谱为我们提供了低维结构化表示，能够捕捉各类物理场中的关键特性。此类通用模型可用于数据探索、分类、参数推断、对称性检测及分量分离等任务。