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Two-stage stochastic unit commitment (2S-SUC) problems have been widely adopted to manage the uncertainties introduced by high penetrations of intermittent renewable energy resources. While decomposition-based algorithms such as…

It is a widely accepted fact that data representations intervene noticeably in machine learning tools. The more they are well defined the better the performance results are. Feature extraction-based methods such as autoencoders are…

This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver…

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…

Current Retrieval-Augmented Generation (RAG) systems predominantly rely on relevance-based dense retrieval, sequentially fetching documents to maximize semantic similarity with the query. However, in knowledge-intensive and real-world…

Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a…

We propose an adaptive mixed precision and dynamically scaled preconditioned conjugate gradient algorithm (AMP-PCG). It dynamically adjusts the precision for storing vectors and computing, exploiting low precision when appropriate, while…

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Recurrent stochastic configuration networks (RSCNs) have shown promise in modelling nonlinear dynamic systems with order uncertainty due to their advantages of easy implementation, less human intervention, and strong approximation…

Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular…

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…

Recent advances in Low-Power Wide-Area Networks have mitigated interference by using cloud assistance. Those methods transmit the RSSI samples and corrupted packets to the cloud to restore the correct message. However, the effectiveness of…

Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks…

Symbolic Regression aims to automatically identify compact and interpretable mathematical expressions that model the functional relationship between input and output variables. Most existing search-based symbolic regression methods…

This work is based on the seminar titled ``Resiliency in Numerical Algorithm Design for Extreme Scale Simulations'' held March 1-6, 2020 at Schloss Dagstuhl, that was attended by all the authors. Naive versions of conventional resilience…

We study risk-sensitive reinforcement learning (RL) based on an entropic risk measure in episodic non-stationary Markov decision processes (MDPs). Both the reward functions and the state transition kernels are unknown and allowed to vary…

Despite their success, large pretrained vision models remain vulnerable to catastrophic forgetting when adapted to new tasks in class-incremental settings. Parameter-efficient fine-tuning (PEFT) alleviates this by restricting trainable…

Robust subspace recovery (RSR) is a fundamental problem in robust representation learning. Here we focus on a recently proposed RSR method termed Dual Principal Component Pursuit (DPCP) approach, which aims to recover a basis of the…

We consider stopping criteria that balance algebraic and discretization errors for the conjugate gradient algorithm applied to high-order finite element discretizations of Poisson problems. Firstly, we introduce a new stopping criterion…