Combining Physics and Deep Learning Models to Simulate the Flight of a Golf Ball

We introduce a new golf ball flight model powered by deep learning. Our method combines a physics model with a deep learning model by inserting a neural network directly into the differential equations governing the projectile motion of the golf ball. The role of the neural network is to estimate the aerodynamic coefficients based on the state of the golf ball at each time step. The entire model was made end-to-end differentiable, permitting us to train the neural network using only measured launch conditions and landing positions. However, in experiments we find that using additional loss terms, such as the max height error, improves the accuracy of the predicted landing position. The key to our approach is that we automatically learn the relationship between the aerodynamic coefficients and the state of the golf ball directly from the data as opposed to manually defining a model that imposes a bias. As a result, we are able to reduce the mean landing position error by 28% compared to a published model that learns the coefficients by fitting polynomials to the spin ratio. Our method is also computationally efficient, with a processing time of 35 ms for a single shot using a CPU.