19 citations · 53 across the 16 of their papers we have counts for
17 papers
Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions
Liangchen Liu, Juncai He, Richard Tsai
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objecti…
Corrected Trapezoidal Rule-IBIM for linearized Poisson-Boltzmann equation
Federico Izzo, Yimin Zhong, Olof Runborg +1
In this paper, we solve the linearized Poisson-Boltzmann equation, used to model the electric potential of macromolecules in a solvent. We derive a corrected trapezoidal rule with…
Convergence of a class of high order corrected trapezoidal rules
Federico Izzo, Olof Runborg, Richard Tsai
We present convergence theory for corrected quadrature rules on uniform Cartesian grids for functions with a point singularity. We begin by deriving an error estimate for the punct…
High order corrected trapezoidal rules for a class of singular integrals
Federico Izzo, Olof Runborg, Richard Tsai
We present a family of high order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integr…
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space
Juncai He, Richard Tsai, Rachel Ward
The low-dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low-dimensional manifolds em…
Numerical wave propagation aided by deep learning
Hieu Nguyen, Richard Tsai
We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the…
Corrected trapezoidal rules for singular implicit boundary integrals
Federico Izzo, Olof Runborg, Richard Tsai
We present new higher-order quadratures for a family of boundary integral operators re-derived using the approach introduced in [Kublik, Tanushev, and Tsai - J. Comp. Phys. 247: 27…
Strategy Synthesis for Surveillance-Evasion Games with Learning-Enabled Visibility Optimization
Suda Bharadwaj, Louis Ly, Bo Wu +2
This paper studies a two-player game with a quantitative surveillance requirement on an adversarial target moving in a discrete state space and a secondary objective to maximize sh…
Nearest Neighbor Sampling of Point Sets using Rays
Liangchen Liu, Louis Ly, Colin Macdonald +1
We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces. Our approach involve…
A stable parareal-like method for the second order wave equation
Hieu Nguyen, Richard Tsai
A new parallel-in-time iterative method is proposed for solving the homogeneous second-order wave equation. The new method involves a coarse scale propagator, allowing for larger t…
An implicit boundary integral method for computing electric potential of macromolecules in solvent
Yimin Zhong, Kui Ren, Richard Tsai
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics o…
Volumetric variational principles for a class of partial differential equations defined on surfaces and curves
Jay Chu, Richard Tsai
In this paper, we propose simple numerical algorithms for partial differential equations (PDEs) defined on closed, smooth surfaces (or curves). In particular, we consider PDEs that…
θ-parareal schemes
Gil Ariel, Hieu Nguyen, Richard Tsai
A weighted version of the parareal method for parallel-in-time computation of time dependent problems is presented. Linear stability analysis for a scalar weighing strategy shows t…
An extrapolative approach to integration over hypersurfaces in the level set framework
Catherine Kublik, Richard Tsai
We provide a new approach for computing integrals over hypersurfaces in the level set framework. The method is based on the discretization (via simple Riemann sums) of the classica…
An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics
Chieh Chen, Catherine Kublik, Richard Tsai
We present an algorithm for computing the nonlinear interface dynamics of the Mullins-Sekerka model for interfaces that are defined implicitly (e.g. by a level set function) using…
Integration over curves and surfaces defined by the closest point mapping
Catherine Kublik, Richard Tsai
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that…
Parareal methods for highly oscillatory dynamical systems
Gil Ariel, Seong Jun Kim, Richard Tsai
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes…