Related papers: FIAT: improving performance and accuracy for high-…
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
Deep classifiers may encounter significant performance degradation when processing unseen testing data from varying centers, vendors, and protocols. Ensuring the robustness of deep models against these domain shifts is crucial for their…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
The current technology landscape lacks a foundational AI model for solving process engineering calculations. In this work, we introduce a novel autonomous agent framework leveraging Retrieval-Augmented Instruction-Tuning (RAIT) to enhance…
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
Data annotation is an essential component of the machine learning pipeline; it is also a costly and time-consuming process. With the introduction of transformer-based models, annotation at the document level is increasingly popular;…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
Familia is an open-source toolkit for pragmatic topic modeling in industry. Familia abstracts the utilities of topic modeling in industry as two paradigms: semantic representation and semantic matching. Efficient implementations of the two…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…
We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…
An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…
Large Language Models have demonstrated strong performance across a wide range of tasks, but adapting them efficiently to new domains remains a key challenge. Parameter-Efficient Fine-Tuning (PEFT) methods address this by introducing…
Foundation models excel across diverse tasks, but adapting them to specialized applications often requires fine-tuning, an approach that is memory and compute-intensive. Parameter-efficient fine-tuning (PEFT) methods mitigate this by…
The purpose of this paper is to discuss representations of high order $C^0$ finite element spaces on simplicial meshes in any dimension. When computing with high order piecewise polynomials the conditioning of the basis is likely to be…
In recent years, the multiple-stage strategy has become a popular trend for visual tracking. This strategy first utilizes a base tracker to coarsely locate the target and then exploits a refinement module to obtain more accurate results.…
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. It is based on…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
Robust Fine-Tuning (RFT) is a low-cost strategy to obtain adversarial robustness in downstream applications, without requiring a lot of computational resources and collecting significant amounts of data. This paper uncovers an issue with…
In this paper, we discuss how to efficiently evaluate and assemble general finite element variational forms on H(div) and H(curl). The proposed strategy relies on a decomposition of the element tensor into a precomputable reference tensor…