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Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy.…

Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…

Large language models (LLMs) demonstrate remarkable emergent abilities to perform in-context learning across various tasks, including time series forecasting. This work investigates LLMs' ability to estimate probability density functions…

Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…

Large language models (LLMs) have achieved notable success in code generation. However, they still frequently produce uncompilable output because their next-token inference procedure does not model formal aspects of code. Although…

Large Language Models (LLMs) have become a popular choice for many Natural Language Processing (NLP) tasks due to their versatility and ability to produce high-quality results. Specifically, they are increasingly used for automatic code…

Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swath, there exist situations in which PDE models fail to…

Large language models (LLMs) have been a disruptive innovation in recent years, and they play a crucial role in our daily lives due to their ability to understand and generate human-like text. Their capabilities include natural language…

Although large language models (LLMs) have demonstrated impressive ability in code generation, they are still struggling to address the complicated intent provided by humans. It is widely acknowledged that humans typically employ planning…

Large Language Models (LLMs) often struggle with code generation tasks involving niche software libraries. Existing code generation techniques with only human-oriented documentation can fail -- even when the LLM has access to web search and…

Large language models (LLMs) are becoming increasingly better at a wide range of Natural Language Processing tasks (NLP), such as text generation and understanding. Recently, these models have extended their capabilities to coding tasks,…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across…

Recent studies have revealed that when LLMs are appropriately prompted and configured, they demonstrate mixed results. Such results often meet or exceed the baseline performance. However, these comparisons have two primary issues. First,…

To perform effective causal inference in high-dimensional datasets, initiating the process with causal discovery is imperative, wherein a causal graph is generated based on observational data. However, obtaining a complete and accurate…

The rise of large language models (LLMs) has led to dramatic improvements across a wide range of natural language tasks. Their performance on certain tasks can be further enhanced by incorporating test-time reasoning techniques. These…

Large Language Models for Code (or code LLMs) are increasingly gaining popularity and capabilities, offering a wide array of functionalities such as code completion, code generation, code summarization, test generation, code translation,…

Reasoning about code and explaining its purpose are fundamental skills for computer scientists. There has been extensive research in the field of computing education on the relationship between a student's ability to explain code and other…