Nils Thuerey’s talk at MIT’s “Distinguished Seminar Series in Computational Science and Engineering” is online now at:

And here’s the offical/original talk info: https://cse.mit.edu/events/thuerey22oct20seminar/

**Title:** Differentiable Physics Simulations for Deep Learning Algorithms

**Abstract:** Differentiable physics solvers (from the broader field of differentiable programming) show particular promise for including prior knowledge into machine learning algorithms. Differentiable operators were shown to be powerful tools to guide deep learning processes, and PDEs provide a wide range of components to build such operators. They also represent a natural way for traditional solvers and deep learning methods to coexist: Using PDE solvers as differentiable operators in neural networks allows us to leverage existing numerical methods for efficient solvers, e.g., to provide reliable and flexible gradients to update the weights during a learning run.

Interestingly, it turns out to be beneficial to combine “traditional” supervised and physics-based approaches. The former poses a much more straightforward and more stable learning task by providing explicit reference data, while physics-based learning can provide gradients for a larger space of states that are only encountered at training time. Here, differentiable solvers are particularly powerful, e.g., to provide neural networks with feedback about how inferred solutions influence a physical model’s long-term behavior. I will show and discuss examples with various advection-diffusion type PDEs, among others the Navier-Stokes equations for fluids, for different learning applications. These demonstrations will highlight the properties and capabilities of PDE-powered deep neural networks and serve as a starting point for discussing future developments.