Tensor-on-tensor Regression Neural Networks for Process Modeling with High-dimensional Data

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.