The overall PhyE2E framework. Top: the training dataset was augmented with a large-scale synthetic dataset generated by an LLM. MLP, multilayer perceptron. Middle: a variable-interaction technique was integrated to decompose the original symbolic regression problem into simpler subproblems, referred to as D&C. An end-to-end model was trained to predict the target formula using observed data points and prior physical knowledge (referred to as 'physical prio