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We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations…

Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…

The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…

Particle swarm optimization (PSO) is a search algorithm based on stochastic and population-based adaptive optimization. In this paper, a pathfinding strategy is proposed to improve the efficiency of path planning for a broad range of…

In this paper, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to…

The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial,…

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

In this work, we present an adaptive adjoint-oriented neural network (adaptive AONN) for solving parametric optimal control problems governed by partial differential equations. The proposed method integrates deep adaptive sampling…

Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…

This paper aims to provide a machine learning framework to simulate two-phase flow in porous media. The proposed algorithm is based on Physics-informed neural networks (PINN). A novel residual-based adaptive PINN is developed and compared…

Deep neural networks (DNNs) play an important role in machine learning due to its outstanding performance compared to other alternatives. However, DNNs are not suitable for safety-critical applications since DNNs can be easily fooled by…

Division-of-focal-plane (DoFP) polarization imaging technical recently has been applied in many fields. However, the images captured by such sensors cannot be used directly because they suffer from instantaneous field-of-view errors and low…

This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…

In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…

Recent works on deep non-linear spatially selective filters demonstrate exceptional enhancement performance with computationally lightweight architectures for stationary speakers of known directions. However, to maintain this performance in…

Online parameter controllers for evolutionary algorithms adjust values of parameters during the run of an evolutionary algorithm. Recently a new efficient parameter controller based on reinforcement learning was proposed by Karafotias et…

Trajectory planning for mobile robots in cluttered environments remains a major challenge due to narrow passages, where conventional methods often fail or generate suboptimal paths. To address this issue, we propose the adaptive trajectory…

Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are…

The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using…

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size.…