Related papers: A re-formulization of the transfer matrix method f…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…
This paper proposes a novel learning-based approach for achieving exponential stabilization of nonlinear control-affine systems. We leverage the Control Contraction Metrics (CCMs) framework to co-synthesize Neural Contraction Metrics (NCMs)…
This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…
A high order wavelet integral collocation method (WICM) is developed for general nonlinear boundary value problems in physics. This method is established based on Coiflet approximation of multiple integrals of interval bounded functions…
Deep Learning (DL) based methods for magnetic resonance (MR) image reconstruction have been shown to produce superior performance in recent years. However, these methods either only leverage under-sampled data or require a paired…
In this paper we propose an algorithm to classify tensor data. Our methodology is built on recent studies about matrix classification with the trace norm constrained weight matrix and the tensor trace norm. Similar to matrix classification,…
Tensor-based modulation (TBM) provides a multi-linear spreading framework for blind multi-user separation in unsourced random access. In this paper, we show that TBM is a coded modulation built on a non-binary linear block code over…
We introduce a new type of generalized Turing machines (GTMs), which are intended as a tool for the mathematician who studies computability in Analysis. In a single tape cell a GTM can store a symbol, a real number, a continuous real…
In this paper, we design constant modulus probing waveforms with good correlation properties for collocated multi-input multi-output (MIMO) radar systems. The main content is as follows: first, we formulate the design problem as a fourth…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…
We present high-order, finite element-based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to…
We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a…
We have proposed a novel numerical method to calculate accurately the physical quantities of the ground state with the tensor-network wave function in two dimensions. We determine the tensor network wavefunction by a projection approach…
The high-frequency Helmholtz equation on the entire space is truncated into a bounded domain using the perfectly matched layer (PML) technique and subsequently, discretized by the higher-order finite element method (FEM) and the continuous…
An original multiplex scheme is introduced, which is based on Mallat's multiresolution formulation of wavelet systems. This system is adaptable and its implementation is well matched to digital signal processors and computers. The approach…
We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted…