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Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…

Machine learning force fields (MLFFs) are gradually evolving towards enabling molecular dynamics simulations of molecules and materials with ab initio accuracy but at a small fraction of the computational cost. However, several challenges…

This paper studies the limitations of the generic approaches to solving cryptographic problems in classical and quantum settings in various models. - In the classical generic group model (GGM), we find simple alternative proofs for the…

In this paper, we study the problem of estimating smooth Generalized Linear Models (GLMs) in the Non-interactive Local Differential Privacy (NLDP) model. Different from its classical setting, our model allows the server to access some…

Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is…

A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.

In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the…

This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…

A novel sequential inferential method for Bayesian dynamic generalised linear models is presented, addressing both univariate and multivariate $k$-parametric exponential families. It efficiently handles diverse responses, including…

A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…

Vision-Language Models (VLMs) have recently shown promising advancements in sequential decision-making tasks through task-specific fine-tuning. However, common fine-tuning methods, such as Supervised Fine-Tuning (SFT) and Reinforcement…

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…

One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been proposed and successfully used for various applications. In…

This work is concerned with the rigorous analysis on the Generalized Multiscale Finite Element Methods (GMsFEMs) for elliptic problems with high-contrast heterogeneous coefficients. GMsFEMs are popular numerical methods for solving flow…

Generalized linear models (GLM) are link function based statistical models. Many supervised learning algorithms are extensions of GLMs and have link functions built into the algorithm to model different outcome distributions. There are two…

We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…

The scalability of Generalized Linear Models (GLMs) for large-scale, high-dimensional data often forces a trade-off between computational feasibility and statistical accuracy, particularly for inference on pre-specified parameters. While…

Data in many applications follows systems of Ordinary Differential Equations (ODEs). This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following…

To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing…