提出TRNN模型，用张量结构建模高维工业数据的非线性关系。
Tensor-on-tensor Regression Neural Networks for Process Modeling with High-dimensional Data
- 直接在张量上做回归，保持多维数据几何结构
- 结合张量运算与神经网络，捕捉复杂非线性交互
- 适合处理图像、点云等高维工业传感数据
现代传感与测量系统产生海量异构的高维数据，如数据剖面、图像和密集点云，其自然表达形式为多维张量。理解此类数据需要能保留张量几何结构且足够灵活以捕捉工业与机械过程中显著非线性交互的回归模型。现有张量回归方法虽满足结构保持要求，但本质上仍是线性的；传统神经网络虽具非线性能力，却需先展开为向量，导致空间结构丢失并带来巨大的参数量。本文提出张量-张量回归神经网络（TRNN），统一上述两种范式，实现高维数据的高效非线性建模。
原文摘要 · Abstract (English)
Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression models that preserve tensor geometry, yet remain expressive enough to capture the pronounced nonlinear interactions that dominate many industrial and mechanical processes. Existing tensor-based regressors meet the first requirement but remain essentially linear. Conversely, conventional neural networks offer nonlinearity only after flattening, thereby discarding spatial structure and incurring prohibitive parameter counts. This paper introduces a Tensor-on-Tensor Regression Neural Network (TRNN) that unifies these two paradigms.
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