Related papers: A unified framework for mesh refinement in random …
This paper presents a novel framework for simultaneously implementing localization and segmentation, which are two of the most important vision-based tasks for robotics. While the goals and techniques used for them were considered to be…
I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell…
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement…
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…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…
Feature transformation aims to extract a good representation (feature) space by mathematically transforming existing features. It is crucial to address the curse of dimensionality, enhance model generalization, overcome data sparsity, and…
Magnetic Resonance Imaging (MRI) has become an important technique in the clinic for the visualization, detection, and diagnosis of various diseases. However, one bottleneck limitation of MRI is the relatively slow data acquisition process.…
The ability to construct, use, and revise models is a crucial experimental physics skill. Many existing frameworks describe modeling in science education at introductory levels. However, most have limited applicability to the context of…
In this paper, we modify and apply the recently introduced Mixed Newton Method, which is originally designed for minimizing real-valued functions of complex variables, to the minimization of real-valued functions of real variables by…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
Unified multimodal models (UMMs) integrate visual understanding and generation within a single framework. For text-to-image (T2I) tasks, this unified capability allows UMMs to refine outputs after their initial generation, potentially…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
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…
Rendering is the process of generating 2D images from 3D assets, simulated in a virtual environment, typically with a graphics pipeline. By inverting such renderer, one can think of a learning approach to predict a 3D shape from an input…
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…
In the past few years, following the differentiable programming paradigm, there has been a growing interest in computing the gradient information of physical processes (e.g., physical simulation, image rendering). However, such processes…