The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

Boundary value problems (BVPs) play a central role in the mathematical analysis of
constrained physical systems subjected to external forces. Consequently, BVPs frequently …

Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and
prediction of these systems remains a challenge. Koopman operator theory circumvents …

Modern generative machine learning models are able to create realistic outputs far beyond
their training data, such as photorealistic artwork, accurate protein structures or …

Data-driven modeling continues to be enabled by modern machine learning algorithms and
deep learning architectures. The goals of such efforts revolve around the generation of …

Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and multi …

Koopman operator, acting on an infinite-dimensional Hilbert space of the observables,
provides a global systematic linear representation of nonlinear systems, which is a leading …

Despite recent achievements in the design and manufacture of advanced materials, the
contributions from first-principles modeling and simulation have remained limited, especially …

We develop a deep autoencoder architecture that can be used to find a coordinate
transformation which turns a non-linear partial differential equation (PDE) into a linear PDE …