We present a novel graph transformer framework, HAMLET, designed to address the
challenges in solving partial differential equations (PDEs) using neural networks. The …

Computational Fluid Dynamics (CFD) plays a crucial role in investigating new physical
phenomena and exploring the principles of fluid mechanics. However, CFD numerical …

In this work, we revisit the marking decisions made in the standard adaptive finite element
method (AFEM). Experience shows that a naïve marking policy leads to inefficient use of …

Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of
complex physical phenomenon, as it allocates limited computational budget based on the …

Mesh degeneration is a bottleneck for fluid–structure interaction (FSI) simulations and for
shape optimization via the method of mappings. In both cases, an appropriate mesh motion …

We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh
Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost …

We show how to construct a deep neural network (DNN) expert to predict quasi-optimal hp-
refinements for a given finite element problem in presence of singularities. The main idea is …

Adaptive meshes are pivotal in numerical modeling and simulation, offering a means to
efficiently, precisely, and flexibly represent intricate physical phenomena, particularly when …

In this study, we propose a new approach for automatically generating high-quality non-
uniform meshes based on supervised learning. The proposed framework, GMR-Net, is …

The rapid growth of data-driven applications is ubiquitous across virtually all scientific
domains, and has led to an increasing demand for effective methods to handle data …