Identifying physical properties of deformable objects by using particle filters

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We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subdomains ...

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...

The paper presents a method for the co-optimization of energy storage systems allocation and line reinforcement in active distribution networks. The objective is to guarantee the capability of an active distribution network to follow a dispatch plan by app ...

Isogeometric analysis (IGA) was introduced to integrate methods for analysis and computer-aided design (CAD) into a unified process. High-quality parameterization of a physical domain plays a crucial role in IGA. However, obtaining high-quality parameteriz ...

Soft Magnetic Composites (SMCs) demonstrate excellent potentials for electromagnetic applications. The isotropy is one critical feature in designing the composite. This work presents a shape optimization algorithm for SMCs subject to isotropy and volume co ...

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others. Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineer ...

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) hierarchical B-splines. We show that the locality of hier ...

Identifying physical properties of deformable objects by using particle filters

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A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

Conservation of Forces and Total Work at the Interface Using the Internodes Method

Optimal Co-Planning of ESSs and Line Reinforcement Considering the Dispatchability of Active Distribution Networks

TCB-spline-based isogeometric analysis method with high-quality parameterizations

Level-set-based Shape Optimization on Soft Magnetic Composites with Isotropy Constraint

Adaptive analysis-aware defeaturing

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Efficient algorithms for wave problems

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines