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Conventional research on large language models (LLMs) has primarily focused on refining output distributions, while paying less attention to the decoding process that transforms these distributions into final responses. Recent advances,…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov…

Grounding is a critical step in classical planning, yet it often becomes a computational bottleneck due to the exponential growth in grounded actions and atoms as task size increases. Recent advances in partial grounding have addressed this…

Producing accurate software models is crucial in model-driven software engineering (MDE). However, modeling complex systems is an error-prone task that requires deep application domain knowledge. In the past decade, several automated…

With the increasing popularity of large language models (LLMs), reasoning on basic graph algorithm problems is an essential intermediate step in assessing their abilities to process and infer complex graph reasoning tasks. Existing methods…

The use of large language models (LLMs) for automated code generation has emerged as a significant focus within AI research. As these pretrained models continue to evolve, their ability to understand and generate complex code structures has…

Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose…

Neural network-based methods have emerged as powerful tools for solving partial differential equations (PDEs) in scientific and engineering applications, particularly when handling complex domains or incorporating empirical data. These…

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…

The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, a…

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent neural network-based approaches improve flexibility but often…

Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…

Large Language Models (LLMs), such as ChatGPT, are increasingly leveraged for generating both traditional software code and spreadsheet logic. Despite their impressive generative capabilities, these models frequently exhibit critical issues…

Task automation has been greatly empowered by the recent advances in Large Language Models (LLMs) via Python code, where the tasks ranging from software engineering development to general-purpose reasoning. While current benchmarks have…

Large language models (LLMs) often struggle with complex mathematical tasks, prone to "hallucinating" incorrect answers due to their reliance on statistical patterns. This limitation is further amplified in average Small LangSLMs with…

Large language models (LLMs) have recently shown impressive results on diverse code-related tasks, benefiting from large-scale training and instruction tuning. However, studies reveal that their grasp of fundamental programming concepts,…