differential equations

Blob Pitt's next big blockbuster We consider generative models among the most exciting applications of machine learning. This tech has reached a remarkable capacity to synthesize original multimedia content after learning a data distribution. In this arena, the state-of-the-art has been dominated by a family of models called generative adversarial networks or GANs. However, GANs are challenged by training instabilities. The latest StyleGAN2-ada mitigates mode collapse arising from overfit discriminators using test time data augmentation....

Recently, I’ve found a fascinating line of work directed at advancing computational fluid dynamics using machine-learned preconditioners to speed up convergence in linear iterative solvers. In fact, the number of steps until convergence influences the performance bound of many classical optimization algorithms. Machine learning helps us to trade a cheap, data-driven approximation for fewer, costly optimization steps in the endgame of convergence. Given this context, I’ve been revisiting my studies on numerical PDE like the Nonlinear Schrodinger Equation (NLS) and here I’ll share some of the background work I took part in during the Summer of 2012....

In a matter of months, the COVID-19 pandemic has besieged humanity and now the world wrestles to manage the population health challenges of a novel coronavirus with remarkable infectivity. Organizing an effective response to blunt the impact of such a large, complex challenge demands a principled and scientific approach. Better Planning by Forecasting Infections Reliable forecasting is crucial for planning and allocating limited resources efficiently and minimizing casualties....