Related papers: Generating Finite Element Codes combining Adaptive…
When a domain specific language (DSL) shall be commonly used, it is important for the development team to have a comfortable editor well integrated in the project's development environment. As DSL are rather often subject to changes,…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
How can we build surrogate solvers that train on small domains but scale to larger ones without intrusive access to PDE operators? Inspired by the Data-Driven Finite Element Method (DD-FEM) framework for modular data-driven solvers, we…
Domain-specific languages (DSLs) are touted as both easy to embed in programs and easy to optimize. Yet these goals are often in tension. Embedded or internal DSLs fit naturally with a host language, while inheriting the host's performance…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
High-performance DSL developers work hard to take advantage of modern hardware. The DSL compilers have to build their own complex middle-ends before they can target a common back-end such as LLVM, which only handles single instruction…
Large language models (LLMs) have been enormously successful in solving a wide variety of structured and unstructured generative tasks, but they struggle to generate procedural geometry in Computer Aided Design (CAD). These difficulties…
We study the problem of synthesizing domain-specific languages (DSLs) for few-shot learning in symbolic domains. Given a base language and instances of few-shot learning problems, where each instance is split into training and testing…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
Finite element (FE) analysis guides the design and verification of nearly all manufactured objects. It is at the core of computational engineering, enabling simulation of complex physical systems, from fluids and solids to multiphysics…
Numerical simulations can help solve complex problems. Most of these algorithms are massively parallel and thus good candidates for FPGA acceleration thanks to spatial parallelism. Modern FPGA devices can leverage high-bandwidth memory…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
We propose Decision by Supervised Learning (DSL), a practical framework for robust portfolio optimization. DSL reframes portfolio construction as a supervised learning problem: models are trained to predict optimal portfolio weights, using…
The use of nonlinear PDEs has led to significant advancements in various fields, such as physics, biology, ecology, and quantum mechanics. However, finding multiple solutions for nonlinear PDEs can be a challenging task, especially when…
We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…
This paper contributes to speeding up the design and deployment of engineering dynamical systems by proposing a strategy for exploiting domain and expert knowledge for the automated generation of a dynamical system computational model…
Automated code generation can systematically exceed expert hand-optimization for recurrence relations-computational primitives ubiquitous in orthogonal polynomials, special functions, numerical integration, and molecular integral…
Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…