Earthquakes are one of the most catastrophic natural disasters, making accurate, fine-grained, and real-time earthquake forecasting extremely important for the safety and security of human lives. In this work, we propose DeepQuake, a hybrid physics and deep learning model for fine-grained earthquake forecasting using time-series data of the horizontal displacement of earth’s surface measured from continuously operating Global Positioning System (cGPS) data. Recent studies using cGPS data have established a link between transient deformation within earth's crust to climate variables. DeepQuake’s physics-based pre-processing algorithm extracts relevant features including the x, y, and xy components of strain in earth’s crust, capturing earth’s elastic response to these climate variables, and feeds it into a deep learning neural network to predict key earthquake variables such as the time, location, magnitude, and depth of a future earthquake. Results across California show promising correlations between cGPS derived strain patterns and the earthquake catalog ground truth for a given location and time.