Understanding inhomogeneous and anisotropic fluid flows requires mathematical and
computational tools that are tailored to such flows and distinct from methods used to …

The series aims to: present current and emerging innovations in GIScience; describe new
and robust GIScience methods for use in transdisciplinary problem solving and decision …

The generation of a magnetic field in an electrically conducting fluid generally involves the
complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process …

We present a new rank-adaptive tensor method to compute the numerical solution of high-
dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series …

Statistical (machine learning) tools for equation discovery require large amounts of data that
are typically computer generated rather than experimentally observed. Multiscale modeling …

Functional differential equations (FDEs) play a fundamental role in many areas of
mathematical physics, including fluid dynamics (Hopf characteristic functional equation) …

We develop new dynamically orthogonal tensor methods to approximate multivariate
functions and the solution of high-dimensional time-dependent nonlinear partial differential …

We introduce new methods for integrating nonlinear differential equations on low-rank
manifolds. These methods rely on interpolatory projections onto the tangent space, enabling …

We develop new adaptive algorithms for temporal integration of nonlinear evolution
equations on tensor manifolds. These algorithms, which we call step-truncation methods …

We develop a new data-driven closure approximation method to compute the statistical
properties of quantities of interest in high-dimensional stochastic dynamical systems. The …