Related papers: An AI-aided algorithm for multivariate polynomial …
We present a graph-theoretic framework for constructing floor plans that support non-rectangular modules, with particular emphasis on L-shaped and T-shaped geometries. Unlike traditional approaches that primarily focus on rectangular…
We propose a modified form of a tensor renormalization group algorithm for evaluating partition functions of classical statistical mechanical models on 2D lattices. This algorithm coarse-grains only the rows and columns of the lattice…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
We give a combinatorial condition for the existence of efficient, LP-based FPT algorithms for a broad class of graph-theoretical optimisation problems. Our condition is based on the notion of biased graphs known from matroid theory.…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…
We present a data-assisted iterative regularization method for solving ill-posed inverse problems. The proposed approach, termed \texttt{IRMGL+\(\Psi\)}, integrates classical iterative techniques with a data-driven regularization term…
This paper presents an efficient high-order sharp-interface method for solving the three-dimensional (3D) Poisson equation with Dirichlet boundary conditions on a nonuniform Cartesian grid with irregular domain boundaries. The new approach…
For the arbitrary-Lagrangian-Eulerian (ALE) calculations, the geometric information needs to be calculated at each time step due to the movement of mesh. To achieve the high-order spatial accuracy, a large number of matrix inversions are…
We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence…
We present a method for generating large numbers of isomorphic physics problems using generative AI services such as ChatGPT, through prompt chaining and tool use. This approach enables precise control over structural variations-such as…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR)…
Traditional discrete learning methods involve discretizing continuous equations using difference schemes, necessitating considerations of stability and convergence. Integrable nonlinear lattice equations possess a profound mathematical…
We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a…