Machine learning has been widely used in the area of intelligent driving. Model training is the key point for the application of machine learning. Due to the insufficient training data for all driving situiaitons, serious traffic accidents would happen if the intelligent driving system fails under the extreme conditions. By applying the viability theory to the dynamic adaptive analysis of the vehicle, the maximum safety space in high-dimension can be objectively calculated, which reflects the special advantages of this theory in the field of vehicle's safety. However, due to the high complexity of computation and long analyzing time, the iterative algorithm of this theory cannot meet the real-time control requirements of high-speed vehicles. The surface of the viability kernel is also too complex to be used directly by the intelligent driving system, for which the viability kernel eads to be transformed into the optimal path of the road. Therefore, we design a training method for machine learning of local path planning by the viability theory. According to the character analysis of multiple machine learning, we finally select radial basis function(RBF) neural network to output the central line projection of the viaibity kernel. By comparing two training methods, analyzing the parameter sensitivity and generalization ability, the proposed training method is approved to be rational. Simulation experiments show that the data-driven model trained by our method can output the safety results quickly and precisely. Meanwhile, the control margin is large, so it can help to drive the unmanned vehicles in a high challenging environment by a simple control rule. Since the safety of the machine learning method can be guaranteed by the theory, and the computing speed is enhanced, the method has a wide application in the area of intelligent driving.