We have a variety of highly interesting research papers in the works. Obviously, these are work in progress, but nonetheless warrant a quick preview at this time of the year. Here are two examples which can be found on arXiv by now. The first one targets the connection of classical optimization schemes and deep learning methods for physical systems (via what we’ve dubbed “physical gradients”).

*Physical Gradients for Deep Learning:* **https://arxiv.org/abs/2109.15048**

The second paper targets “incomplete” PDE solvers, i.e., solvers where only a part of the full PDE is known and available at training time, and the remainder is only specified via the training data. If you’ve worked with differentiable solvers, you can probably imagine that a neural network is able to learn the missing part of the PDE. However, it is nonetheless nice to have concrete results demonstrating this concept for several interesting and non-trivial reacting flow cases.

*Hybrid Neural Network PDE Solvers for Reacting Flows:* **https://arxiv.org/abs/2111.11185**