Latest Research
Multigrid methods for 3$D$ $H(\mathbf{curl})$ problems with nonoverlapping domain decomposition smoothers
We propose V--cycle multigrid methods for vector field problems arising from the lowest order hexahedral N\'{e}d\'{e}lec finite element.
Numerical Analysis Numerical Analysis
Numerical method for approximately optimal solutions of two-stage distributionally robust optimization with marginal constraints
The ambiguity set is constrained by fixed marginal distributions that are not necessarily discrete.
Optimization and Control Numerical Analysis Numerical Analysis Probability
Peel-and-Bound: Generating Stronger Relaxed Bounds with Multivalued Decision Diagrams
Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization.
Optimization and Control 90-08
Finite Elements with Switch Detection for Direct Optimal Control of Nonsmooth Systems
The efficacy of FESD in demonstrated on several simulation and optimal control examples.
Optimization and Control 34A36, 49M25, 49Q12, 65L99, 49M37
Optimizing a DIscrete Loss (ODIL) to solve forward and inverse problems for partial differential equations using machine learning tools
We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools.
Numerical Analysis Numerical Analysis Computational Physics
Consensus based optimization via jump-diffusion stochastic differential equations
We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations.
Probability Numerical Analysis Numerical Analysis Optimization and Control 60H10 90C26 65C30 65C35 60J76
Deep Learning-based Schemes for Singularly Perturbed Convection-Diffusion Problems
Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs).
Numerical Analysis Numerical Analysis
Arkhipov's theorem, graph minors, and linear system nonlocal games
We extend Arkhipov's theorem by showing that, for graph incidence games of connected two-coloured graphs, every quotient closed property of the solution group has a forbidden minor characterization.
Combinatorics Group Theory Quantum Physics
Data-driven Tensor Train Gradient Cross Approximation for Hamilton-Jacobi-Bellman Equations
A gradient-enhanced functional tensor train cross approximation method for the resolution of the Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control of nonlinear dynamics is presented.
Numerical Analysis Numerical Analysis Optimization and Control 15A69, 15A23, 65F10, 65N22, 49J20, 49LXX, 49MXX
Towards a Geometric Understanding of the 4-Dimensional Point Groups
We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes.
Metric Geometry
