Differentiable simulation techniques are the core of scientific machine learning methods which are used in the automatic discovery of mechanistic models through infusing neural network training into the simulation process. In this talk we will start by showcasing some of the ways that differentiable simulation is being used, from discovery of extrapolatory epidemic models to nonlinear mixed effects models in pharmacology. From there, we will discuss the computational techniques behind the training process, focusing on the numerical issues involved in handling differentiation of highly stiff and chaotic systems. The viewers will leave with an understanding of how compiler techniques are being infused into the simulation stack to provide the future of differentiable simulation which merges machine learning with traditional biological and physical modeling. Bio: Chris is the Director of Scientific Research at Pumas-AI, the Director of Modeling and Simulation at Julia Computing, Co-PI of the Julia Lab at MIT, and the lead developer of the SciML Open Source Software Organization. He is the lead developer of the Pumas project and has received a top presentation award at every ACoP in the last 3 years for improving methods for uncertainty quantification, automated GPU acceleration of nonlinear mixed effects modeling (NLME), and machine learning assisted construction of NLME models with DeepNLME. For these achievements, Chris received the Emerging Scientist award from ISoP. For his work in mechanistic machine learning, his work is credited for the 15,000x acceleration of NASA Launch Services simulations and recently demonstrated a 60x-570x acceleration over Modelica tools in HVAC simulation, earning Chris the US Air Force Artificial Intelligence Accelerator Scientific Excellence Award.