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.

Bio: Nils is an Associate-Professor at the Technical University of Munich (TUM). He and his group focus on deep learning methods for physical simulations, with a particular focus on fluid phenomena. He acquired a Ph.D. for his work on liquid simulations in 2006 from the University of Erlangen-Nuremberg. Until 2010 he held a position as a post-doctoral researcher at ETH Zurich. He received a tech-Oscar from the AMPAS in 2013 for his research on controllable smoke effects. Subsequently, he worked for three years as R&D lead at ScanlineVFX, before starting at TUM in October 2013.