Machine learning models are vulnerable to adversarial attacks. One approach to addressing this vulnerability is certification, which focuses on models that are guaranteed to be robust for a given perturbation size. A drawback of recent certified models is that they are stochastic: they require multiple computationally expensive model evaluations with random noise added to a given input. In our work, we present a deterministic certification approach which results in a certifiably robust model. This approach is based on an equivalence between training with a particular regularized loss, and the expected values of Gaussian averages. The derivation of our proposed loss function requires some work in numerical partial differential equations (PDEs). To this end, we show that we can achieve certifiably robust machine learning models by approximating the solution of a particular PDE in high dimensions using a deep neural network