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：物理学家在参数推断或场的新实现生成等任务中通常需要概率模型。为高度非高斯场建立此类模型颇具挑战，尤其在样本数量有限的情况下。本文针对稳态场引入散射谱模型，并证明这些模型能为物理学中广泛存在的各类场提供精确且稳健的统计描述。该模型基于散射系数的协方差，即由场的小波分解与逐点模运算构成的联合结构。在引入利用场在旋转与缩放变换下正则性的有效降维方法后，我们在多种多尺度物理场上验证了该模型，并证明其能复现包括四阶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征，捕捉了广泛物理场中的关键性质。此类通用模型可用于数据探索、分类、参数推断、对称性检测及成分分离。