Events

Mean field games (MFGs) study strategic decision-making in large populations where individual players  interact via specific mean-field quantities. They have recently gained enormous popularity as powerful research tools with vast applications. For example, the Nash equilibrium of MFGs forms a pair of PDEs, which connects and extends variational optimal transport problems. This talk will present…

Realistic image generation has benefited from recent groundbreaking advances in the ML community. At the core of generative models lies the capability to sample high-dimensional distributions with relatively small support and a priori unknown shape. In many scientific applications, this capability is a limiting factor that has led to modeling choices that circumvent the sampling…

At the heart of modern deep learning is the deep neural nets accompanied by stochastic optimization and sampling algorithms. These architectures and algorithms have an explicit flavor. In particular, traditional deep nets compose affine and simple nonlinear transformations, defining an explicit function for representation learning. The explicit deep nets lack flexibility and adaptivity for modeling…

Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT, the measured data consist of time-dependent signals measured on an observation surface. In contrast, the measured data from the recently invented full-field detection technique…

A major challenge in the study of dynamical systems is that of model discovery: turning data into reduced order models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their…