In machining, specific cutting forces and temperature fields in the shear zones are of primary interest. These quantities depend on many machining parameters, such as the cutting speed, rake angle, tool-tip radius, uncut chip thickness, etc. The finite element method (FEM) is the tool of choice for understanding the effect, that these parameters have on the cutting forces and temperatures. However, the simulations, even in the context of a two-dimensional orthogonal machining model, are time-consuming and thus, it is difficult to generate sufficient data that covers the entire parametric space of practical interest. The purpose of this work is to present, as a proof-of-concept, a hybrid methodology that combines finite element method and machine learning to predict specific cutting forces and maximum tool temperatures for a given set of machining conditions. The finite element method (FE method) was used to generate the training and test data, which consisted of various machining parameters and the corresponding specific cutting forces and maximum tool temperatures. The data was then used to build a neural network model that can be used for predictive purposes. The FE models consist of an orthogonal plane-strain machining model with the workpiece being made of the aluminum alloy, Al2024-T351. The finite element package ABAQUS/EXPLICIT was used for the simulations. The chip formation was simulated by using a recent fracture-based methodology introduced by Patel and Cherukuri. Specific cutting forces and maximum tool temperatures were calculated for several different combinations of uncut chip thickness, cutting speed and the rake angle. For the machine learning-based predictive models, artificial neural networks were selected. The neural network modeling was performed using Python with Adam as the training algorithm. Both shallow neural networks (SNN) and deep neural networks (DNN) were built and tested with various activation functions (ReLU, ELU, Tanh, Sigmoid, Linear) to predict specific cutting forces and maximum tool temperatures. The optimal neural network architecture along with the activation function that produced the least error in prediction was identified. By comparing the neural network predictions with the experimental data available in the literature, the neural network model is shown to be capable of accurately predicting specific cutting forces and temperatures.