Related papers: A Reduced Basis Method for the Stochastic Landau-L…
The Z2 gauge-Higgs model in three dimensions has two different types of phase transition, confinement-deconfinement and Higgs magnetization. Here they are explored through two order parameters, the Coulomb magnetization which is a local…
Micromagnetics simulations require accurate approximation of the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, which is nonlinear, nonlocal, and has a non-convex constraint, posing interesting challenges in…
Surrogate models are widely used in mechanical design and manufacturing process optimization, where high-fidelity computational models may be unavailable or prohibitively expensive. Their effectiveness, however, is often limited by data…
We consider a stochastic gradient descent (SGD) algorithm for solving linear inverse problems (e.g., CT image reconstruction) in the Banach space framework of variable exponent Lebesgue spaces $\ell^{(p_n)}(\mathbb{R})$. Such non-standard…
The Landau-Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which pose…
The Landau--Lifshitz--Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. We study LLB…
A radial basis function (RBF) based sequential surrogate reliability method (SSRM) is proposed, in which a special optimization problem is solved to update the surrogate model of the limit state function (LSF) iteratively. The objective of…
We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical…
This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its key characteristics such as being more efficient and having…
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
In the framework of the Landau-Lifshitz equations without any dissipation (an approximation which may also be helpful for finite but weak Gilbert damping), with all interactions included, for general ground states, geometries and domain…
This work presents a generalized, assumption-free, and stencil-independent theoretical analyses of the recently proposed Onsager-Regularized (OReg) lattice Boltzmann (LB) method [Jonnalagadda et al., Phys. Rev. E 104, 015313 (2021)] and…
Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…
We propose a generalized stochastic Landau-Lifshitz equation and its corresponding Fokker-Planck equation for the magnetization dynamics in the presence of spin transfer torques. Since the spin transfer torque can pump a magnetic energy…
Heat assisted magnetic recording (HAMR) technology represents the most promising candidate to replace the current perpendicular recording paradigm to achieve higher storage densities. To better understand HAMR dynamics in granular media we…
We present preconditioned stochastic gradient descent (SGD) algorithms for the $\ell_1$ minimization problem $\min_{x}\|A x - b\|_1$ in the overdetermined case, where there are far more constraints than variables. Specifically, we have $A…
Low-rank approximation using time-dependent bases (TDBs) has proven effective for reduced-order modeling of stochastic partial differential equations (SPDEs). In these techniques, the random field is decomposed to a set of deterministic…
This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…
This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with pure jump noise in Marcus canonical form, which describes the dynamics of magnetic spin field in a ferromagnet at elevated temperatures with the effective…