Related papers: CodePDE: An Inference Framework for LLM-driven PDE…

While Large Language Models (LLMs) have demonstrated remarkable capabilities in code generation, they often produce solutions that lack guarantees of correctness, robustness, and efficiency. This limitation is particularly acute in domains…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Large language models (LLMs) can often generate functionally correct code, but their ability to produce efficient implementations for performance-critical systems tasks remains limited. Existing code benchmarks mainly emphasize correctness…

With the emergence of Large Language Models (LLMs), there has been a significant improvement in the programming capabilities of models, attracting growing attention from researchers. Evaluating the programming capabilities of LLMs is…

With the unprecedented advancements in Large Language Models (LLMs), their application domains have expanded to include code generation tasks across various programming languages. While significant progress has been made in enhancing LLMs…

Programmers increasingly rely on Large Language Models (LLMs) for code generation. However, misalignment between programmers' goals and generated code complicates the code evaluation process and demands frequent switching between prompt…

Large Language Models (LLMs) have exhibited remarkable capabilities across diverse domains, prompting investigations into their potential as generic reasoning engines. While recent studies have explored inference-time computation to enhance…

The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…

Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…

Large language models (LLMs) have shown remarkable capabilities in automated code generation. While effective for mainstream languages, they may underperform on less common or domain-specific languages, prompting companies to develop…

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…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

Solving complex planning problems requires Large Language Models (LLMs) to explicitly model the state transition to avoid rule violations, comply with constraints, and ensure optimality-a task hindered by the inherent ambiguity of natural…

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been…

Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains, including software development, education, and technical assistance. Among these, software development is one of the key areas where LLMs are…

Large language models (LLMs) have achieved impressive performance on code generation. Although prior studies enhanced LLMs with prompting techniques and code refinement, they still struggle with complex programming problems due to rigid…

This work presents an analytical framework for the design and analysis of LLM-based algorithms, i.e., algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Large Language Models (LLMs) have been widely used to automate programming tasks. Their capabilities have been evaluated by assessing the quality of generated code through tests or proofs. The extent to which they can reason about code is a…

One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE…