ABSTRACT A classical theorem of A.D. Alexandrov asserts that a connected compact smooth hypersurface in Euclidean space with constant mean curvature must be a sphere....

ABSTRACT We study the application of well-known physics-informed neural networks (PINNs) for solving non-smooth PDE-constrained optimization problems....

ABSTRACT In this talk, we discuss some recent results for photonic and quantum interacting systems....

ABSTRACT We present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media....

ABSTRACT Solutions of nonlinear scalar hyperbolic conservation laws (HCLs) are often discontinuous due to shock formation; moreover, locations of shocks are a priori unknown....

ABSTRACT In this talk I will discuss the numerical approximation of PDE eigenvalue problems depending on a finite number of deterministic parameters....

ABSTRACT In the era of big data, the analysis of large scale text and network data has become a widely studied hot topic....

ABSTRACT We develop a systematic information-theoretic framework for quantification and mitigation of error in probabilistic Lagrangian (i.e., path-based) predictions which are obtained from dynami...

ABSTRACT The endoplasmic reticulum (ER) is an extensive organelle of eukaryotic cells, which reaches outward from the cell's nucleus all the way to the plasma membrane.  For 70 years, electron...

ABSTRACT We will consider a class of $n$th-order linear ordinary differential equations with a large parameter $u$....