The financial risk early warning model is an effective means of risk prevention. This paper’s linear partial differential equation is innovatively applied to financial institutions’ financial risk early warning system. At the same time, we construct a partial differential equation, linear discriminant model, based on the extreme value principle. The system can effectively avoid the problem of fractional model failure. The simulation results show that the algorithm in this paper improves the accuracy and speed of financial risk early warning and significantly reduces the two-class classification error rate of the model.