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We propose a novel quantum algorithm for solving linear autonomous ordinary differential equations (ODEs) using the Pad\'e approximation. For linear autonomous ODEs, the discretized solution can be represented by a product of matrix…
The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for seismic tomography with high-frequency data. FGA has been previously…
Averaging techniques such as Ruppert--Polyak averaging and exponential movering averaging (EMA) are powerful approaches to accelerate optimization procedures of stochastic gradient descent (SGD) optimization methods such as the popular ADAM…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…
We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…
Unmanned aerial vehicles (UAVs) integrated into cellular networks face significant challenges from air-to-ground interference. To address this, we propose a downlink UAV communication system that leverages a fluid antenna system (FAS)-…
Considering the high computation cost produced in conventional computation fluid dynamic simulations, machine learning methods have been introduced to flow dynamic simulations in recent years. However, most of studies focus mainly on…
We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the…
We propose a flexible scenario-based regularized Sample Average Approximation (SBR-SAA) framework for stochastic optimization. This work is motivated by challenges in standard Wasserstein Distributionally Robust Optimization (WDRO), where…
We study unconstrained smooth convex optimization under stochastic first- and zeroth-order oracles subject only to finite-moment bounds, naturally admitting persistent bias and heavy-tailed noise. In this hostile environment, integrating…
We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based…
This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…
Machine learning is a promising technique for angle-of-arrival (AOA) estimation of waves impinging a sensor array. However, the majority of the methods proposed so far only consider a known, fixed number of impinging waves, i.e., a fixed…
We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
Second-order optimization methods offer notable advantages in training deep neural networks by utilizing curvature information to achieve faster convergence. However, traditional second-order techniques are computationally prohibitive,…
Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. Recently, there are robust learning methods aiming at this…
The objective of this paper is to report some computational results for the theory of DAE stability boundary, with the aim of advancing applications in power system voltage stability studies. Firstly, a new regularization transformation for…
The aim of this paper is to analyze the robust convergence of a class of parareal algorithms for solving parabolic problems. The coarse propagator is fixed to the backward Euler method and the fine propagator is a high-order single step…
Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…