Related papers: Automating the Design of Multigrid Methods with Ev…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
Large Language Models have seen increasing use in various software development tasks, especially in code generation. The most advanced recent methods attempt to incorporate feedback from code execution into prompts to help guide LLMs in…
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
As the discretization error for the solution of a partial differential equation (PDE) decreases, the precision required to store the corresponding coefficients naturally increases. Storing the solution's finite element coefficients…
Programming-by-example (PBE) is a synthesis paradigm that allows users to generate functions by simply providing input-output examples. While a promising interaction paradigm, synthesis is still too slow for realtime interaction and more…
This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the property of smoothing iterations in multigrid methods where…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
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…
Syntax-guided synthesis is a paradigm in program synthesis in which the search space of candidate solutions is constrained by a syntactic template in the form of a grammar. These syntactic constraints serve two purposes: constraining the…
Designing effective control policies for autonomous systems remains a fundamental challenge, traditionally addressed through reinforcement learning or manual engineering. While reinforcement learning has achieved remarkable success, it…
Working with complex, high-level MOEA meta-models such as Multiobjec-tive Optimization Hierarchic Genetic Strategy (MO-mHGS) with multi-deme support usually requires dedicated implementation and configuration for each internal (single-deme)…
Recently there have been many advances in research on language modeling of source code. Applications range from code suggestion and completion to code summarization. However, complete program synthesis of industry-grade programming…
A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a…
Many of the core disciplines of artificial intelligence have sets of standard benchmark problems well known and widely used by the community when developing new algorithms. Constraint programming and automated planning are examples of these…
Large Language Models (LLMs) excel in various tasks, but they rely on carefully crafted prompts that often demand substantial human effort. To automate this process, in this paper, we propose a novel framework for discrete prompt…
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…
The reasoning frontier of Large Language Models (LLMs) has advanced significantly through modern post-training paradigms (e.g., Reinforcement Learning from Verifiable Rewards (RLVR)). However, the efficacy of these methods remains…