Related papers: Optimizing the Diffusion System Based on Continuou…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known results in discrete time. We analyse…
In this work, we determine the full expression for the global truncation error of hyperbolic partial differential equations (PDEs). In particular, we use theoretical analysis and symbolic algebra to find exact expressions for the…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…
We study the compressive diffusion strategies over distributed networks based on the diffusion implementation and adaptive extraction of the information from the compressed diffusion data. We demonstrate that one can achieve a comparable…
Distributed stochastic optimization algorithms can simultaneously process large-scale datasets, significantly accelerating model training. However, their effectiveness is often hindered by the sparsity of distributed networks and data…
We consider diffusion-controlled release of particles from $d$-dimensional radially-symmetric geometries. A quantity commonly used to characterise such diffusive processes is the proportion of particles remaining within the geometry over…
This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Optimizing over the stationary distribution of stochastic differential equations (SDEs) is computationally challenging. A new forward propagation algorithm has been recently proposed for the online optimization of SDEs. The algorithm solves…
Distributed estimation and processing in networks modeled by graphs have received a great deal of interest recently, due to the benefits of decentralised processing in terms of performance and robustness to communications link failure…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…
We design the weights in consensus algorithms with spatially correlated random topologies. These arise with: 1) networks with spatially correlated random link failures and 2) networks with randomized averaging protocols. We show that the…
The design of sensor networks capable of reaching a consensus on a globally optimal decision test, without the need for a fusion center, is a problem that has received considerable attention in the last years. Many consensus algorithms have…
In this paper we are concerned with the global minimization of a possibly non-smooth and non-convex objective function constrained on the unit hypersphere by means of a multi-agent derivative-free method. The proposed algorithm falls into…