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The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…

This paper presents an advancement to an approach for model-independent surrogate-based optimization with adaptive batch sampling, known as Adaptive Model Refinement (AMR). While the original AMR method provides unique decisions with…

Pre-trained generalist policies are rapidly gaining relevance in robot learning due to their promise of fast adaptation to novel, in-domain tasks. This adaptation often relies on collecting new demonstrations for a specific task of interest…

Fine-tuning large language models (LLM) can be costly. Parameter-efficient fine-tuning (PEFT) addresses the problems by training a fraction of the parameters, whose success reveals the expressiveness and flexibility of pretrained models.…

Building on existing $hp$-adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propose a novel $h$-adaptive algorithm for a fixed polynomial…

The realization of a standard Adaptive Finite Element Method (AFEM) preserves the mesh conformity by performing a completion step in the refinement loop: in addition to elements marked for refinement due to their contribution to the global…

Item recommendation is a personalized ranking task. To this end, many recommender systems optimize models with pairwise ranking objectives, such as the Bayesian Personalized Ranking (BPR). Using matrix Factorization (MF) --- the most widely…

In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically…

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…

Adversarial training (AT) is widely considered the state-of-the-art technique for improving the robustness of deep neural networks (DNNs) against adversarial examples (AE). Nevertheless, recent studies have revealed that adversarially…

An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical…

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…

This paper presents novel refinement sensors for the application to adaptive mesh and algorithm refinement (AMAR) with kinetic models, such as discrete velocity and lattice Boltzmann methods. While refinement criteria for AMAR based on…

We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable parameters independent of the desired accuracy and the input…

Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the…

We have developed a simulation code with the techniques which enhance both spatial and time resolution of the PM method for which the spatial resolution is restricted by the spacing of structured mesh. The adaptive mesh refinement (AMR)…

Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…

With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and…