Few-shot regression with differentiable reference model

Abstract

Precise control models of industrial manufacturing are essential for high-quality products. In specific industrial fields, there usually exist certain theoretical results and analytical reference models. Due to the diversity of the control input and complex coupling effect on results, the analytical reference model often has strong assumptions and simplified conditions, so that the error can be large. However, it can characterize the overall trend of the real control curve. Deep learning is a promising solution for precise control model, but the huge data demand hinders its application. To this end, we propose a novel few-shot regression framework based on a differentiable reference model, where the gradient of reference model is used as the prior of the function fitter. We implement the framework on a neural network, named Gradient Guided Network, GGN, achieving accurate regression with few samples. Experimental results of sinusoidal regression and roll bend forming problem demonstrate the effectiveness and superior performance compared with meta learning methods. In addition, by combining the trend of the theoretical reference model with real data, our method also achieves better results than the reference model.