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This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…

机器学习 · 统计学 2023-04-03 Da Long , Nicole Mrvaljevic , Shandian Zhe , Bamdad Hosseini

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…

软件工程 · 计算机科学 2025-09-29 Sathvik Joel , Jie JW Wu , Fatemeh H. Fard

Optimizing scientific software is a difficult task because codebases are often large and complex, and performance can depend upon several factors including the algorithm, its implementation, and hardware among others. Causes of poor…

分布式、并行与集群计算 · 计算机科学 2024-04-30 Daniel Nichols , Pranav Polasam , Harshitha Menon , Aniruddha Marathe , Todd Gamblin , Abhinav Bhatele

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

数值分析 · 数学 2025-01-28 Qi Wang , Yuan Mi , Haoyun Wang , Yi Zhang , Ruizhi Chengze , Hongsheng Liu , Ji-Rong Wen , Hao Sun

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

机器学习 · 计算机科学 2025-02-11 Elisa Negrini , Yuxuan Liu , Liu Yang , Stanley J. Osher , Hayden Schaeffer

Large Language Models (LLMs) have shown outstanding breakthroughs in code generation. Recent work improves code LLMs by training on synthetic data generated by some powerful LLMs, which can be challenging to scale due to the dependence on a…

Large Language Models (LLMs) have become extremely potent instruments with exceptional capacities for comprehending and producing human-like text in a wide range of applications. However, the increasing size and complexity of LLMs present…

机器学习 · 计算机科学 2024-06-18 Yingbing Huang , Lily Jiaxin Wan , Hanchen Ye , Manvi Jha , Jinghua Wang , Yuhong Li , Xiaofan Zhang , Deming Chen

Recent advances in Code Large Language Models (CodeLLMs) have primarily focused on open-ended code generation, often overlooking the crucial aspect of code understanding and reasoning. To bridge this gap, we introduce CodeMMLU, a…

软件工程 · 计算机科学 2025-04-10 Dung Nguyen Manh , Thang Phan Chau , Nam Le Hai , Thong T. Doan , Nam V. Nguyen , Quang Pham , Nghi D. Q. Bui

Large Language Models (LLMs) have recently advanced many applications on software engineering tasks, particularly the potential for code generation. Among contemporary challenges, code generated by LLMs often suffers from inaccuracies and…

软件工程 · 计算机科学 2024-08-29 Thai Tang Quoc , Duc Ha Minh , Tho Quan Thanh , Anh Nguyen-Duc

Effective code generation with language models hinges on two critical factors: accurately understanding the intent of the prompt and generating code that applies algorithmic reasoning to produce correct solutions capable of passing diverse…

人工智能 · 计算机科学 2025-10-21 Amir Jalilifard , Anderson de Rezende Rocha , Marcos Medeiros Raimundo

Code cloning, the duplication of code fragments, is common in software development. While some reuse aids productivity, excessive cloning hurts maintainability and introduces bugs. Hence, automatic code clone detection is vital. Meanwhile,…

软件工程 · 计算机科学 2023-08-08 Shihan Dou , Junjie Shan , Haoxiang Jia , Wenhao Deng , Zhiheng Xi , Wei He , Yueming Wu , Tao Gui , Yang Liu , Xuanjing Huang

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

数值分析 · 数学 2023-09-14 Yiran Wang , Suchuan Dong

Large language models (LLMs) have achieved remarkable progress in code generation, yet their true programming competence remains underexplored. We introduce the Code Triangle framework, which systematically evaluates LLMs across three…

计算与语言 · 计算机科学 2025-07-09 Taolin Zhang , Zihan Ma , Maosong Cao , Junnan Liu , Songyang Zhang , Kai Chen

Tool learning has emerged as a crucial capability for large language models (LLMs) to solve complex real-world tasks through interaction with external tools. Existing approaches face significant challenges, including reliance on…

计算与语言 · 计算机科学 2025-06-02 Hanxing Ding , Shuchang Tao , Liang Pang , Zihao Wei , Jinyang Gao , Bolin Ding , Huawei Shen , Xueqi Cheng

Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…

机器学习 · 计算机科学 2026-04-10 Yilong Dai , Shengyu Chen , Xiaowei Jia , Runlong Yu

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

机器学习 · 计算机科学 2022-08-08 Lorenz Richter , Julius Berner

Large Language Models (LLMs) have helped programmers increase efficiency through code generation, comprehension, and repair. However, their application to large-scale projects remains challenging due to complex interdependencies and the…

软件工程 · 计算机科学 2025-02-26 Wuyang Zhang , Yansong Li , Zeyu Dong , Yu Wu , Yingyao Zhou , Duolei Wang , Songsirou Xing , Chichun Zhou , Da Shen

This study presents a comprehensive empirical evaluation of six state-of-the-art large language models (LLMs) for code generation, including both general-purpose and code-specialized models. Using a dataset of 944 real-world LeetCode…

软件工程 · 计算机科学 2025-12-23 Le Zhang , Suresh Kothari

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during…

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…