Related papers: Generating Finite Element Codes combining Adaptive…
Designing programming environments for physical simulation is challenging because simulations rely on diverse algorithms and geometric domains. These challenges are compounded when we try to run efficiently on heterogeneous parallel…
There is a significant potential for coding skills to transition fully to natural language in the future. In this context, large language models (LLMs) have shown impressive natural language processing abilities to generate sophisticated…
Data curation tasks that prepare data for analytics are critical for turning data into actionable insights. However, due to the diverse requirements of applications in different domains, generic off-the-shelf tools are typically…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
Large Language Models (LLMs) exhibit a unique phenomenon known as emergent abilities, demonstrating adeptness across numerous tasks, from text summarization to code generation. While these abilities open up novel avenues in software design…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…
The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…
Proteins adopt multiple structural conformations to perform their diverse biological functions, and understanding these conformations is crucial for advancing drug discovery. Traditional physics-based simulation methods often struggle with…
The escalating data scale in High-Energy Physics (HEP) fuels a growing aspiration for higher analytical efficiency. While Large Language Models (LLMs) offer a path toward automation via agentic AI, they struggle with complex scientific…
In this paper, a topology optimization framework utilizing automatic differentiation is presented as an efficient way for solving 2D density-based topology optimization problem by calculating gradients through the fully differentiable…
Large Language Models (LLMs) demonstrate impressive ability in handling reasoning tasks. However, unlike humans who can instinctively adapt their problem-solving strategies to the complexity of task, most LLM-based methods adopt a…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
Large Language Models (LLMs) have shown impressive capabilities in code generation for popular programming languages. However, their performance on Low-Resource Programming Languages (LRPLs) and Domain-Specific Languages (DSLs) remains a…
Large Language Models (LLMs) have demonstrated remarkable performance in code completion. However, due to the lack of domain-specific knowledge, they may not be optimal in completing code that requires intensive domain knowledge for example…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…
The growth of data to be processed in the Oil & Gas industry matches the requirements imposed by evolving algorithms based on stencil computations, such as Full Waveform Inversion and Reverse Time Migration. Graphical processing units…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…