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We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components…
Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and…
Identifying informative components in binary data is an essential task in many research areas, including life sciences, social sciences, and recommendation systems. Boolean matrix factorization (BMF) is a family of methods that performs…
This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
This article introduces a novel approach for broken-FEEC (Finite Element Exterior Calculus), extending its application to locally refined spline spaces with non-matching interfaces. Traditional broken-FEEC allows for discontinuous…
We propose a concise function representation based on deterministic finite state automata for exact most probable explanation and constrained optimization tasks in graphical models. We then exploit our concise representation within Bucket…
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…
In this paper we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
Parameter-Efficient Fine-Tuning (PEFT) methods like Low-Rank Adaptation (LoRA) optimize federated training by reducing computational and communication costs. We propose RoLoRA, a federated framework using alternating optimization to…
As an efficient alternative to conventional full finetuning, parameter-efficient finetuning (PEFT) is becoming the prevailing method to adapt pretrained language models. In PEFT, a lightweight module is learned on each dataset while the…
In this paper, we compute stiffness matrix of the nonlocal Laplacian discretized by the piecewise linear finite element on nonuniform meshes, and implement the FEM in the Fourier transformed domain. We derive useful integral expressions of…
The usage of numerical homogenization to obtain structure-property relations using the finite element method at both the micro and macroscale has gained much interest in the research community. However the computational cost of this so…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
Combinatorial optimization problems are ubiquitous in science and engineering. Still, learning-based approaches to accelerate combinatorial optimization often require solving a large number of difficult instances to collect training data,…
Finite element simulations are essential in biomechanics, enabling detailed modeling of tissues and organs. However, architectural inefficiencies in current hardware and software stacks limit performance and scalability, especially for…
We describe a set of lower-level abstractions to improve performance on modern large scale heterogeneous systems. These provide portable access to system- and hardware-dependent features, automatically apply dynamic optimizations at run…
This paper studies a new task of federated learning (FL) for semantic parsing, where multiple clients collaboratively train one global model without sharing their semantic parsing data. By leveraging data from multiple clients, the FL…