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Distributed optimization and learning algorithms are designed to operate over large scale networks enabling processing of vast amounts of data effectively and efficiently. One of the main challenges for ensuring a smooth learning process in…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…
Currently the only techniques for sharing governance of a deep learning model are homomorphic encryption and secure multiparty computation. Unfortunately, neither of these techniques is applicable to the training of large neural networks…
A framework is introduced for actively and adaptively solving a sequence of machine learning problems, which are changing in bounded manner from one time step to the next. An algorithm is developed that actively queries the labels of the…
Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…
High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…
We consider online learning problems under a partial observability model capturing situations where the information conveyed to the learner is between full information and bandit feedback. In the simplest variant, we assume that in addition…
This paper introduces a novel methodology for solving distributed-order fractional differential equations using a physics-informed machine learning framework. The core of this approach involves extending the support vector regression (SVR)…
This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…
Datasets often incorporate various functional patterns related to different aspects or regimes, which are typically not equally present throughout the dataset. We propose a novel, general-purpose partitioning algorithm that utilizes…
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…