相关论文: From Equations to Insights: Unraveling Symbolic St…
While recent AI-for-math has made strides in pure mathematics, areas of applied mathematics, particularly PDEs, remain underexplored despite their significant real-world applications. We present PDE-Controller, a framework that enables…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem…
Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of…
Exploring the capabilities of Large Language Models (LLMs) in puzzle solving unveils critical insights into their potential and challenges in AI, marking a significant step towards understanding their applicability in complex reasoning…
Solving Partial Differential Equations (PDEs) is ubiquitous in science and engineering. Computational complexity and difficulty in writing numerical solvers has motivated the development of data-driven machine learning techniques to…
Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the…
Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving…
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…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
There is a significant potential for coding skills to transition fully to natural language in the future. In this context, large language models (LLMs) have shown impressive natural language processing abilities to generate sophisticated…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical…
The trade-off between expressiveness and interpretability remains a core challenge when building human-centric predictive models for classification and decision-making. While symbolic rules offer interpretability, they often lack…
With recent Nobel Prizes recognising AI contributions to science, Large Language Models (LLMs) are transforming scientific research by enhancing productivity and reshaping the scientific method. LLMs are now involved in experimental design,…
Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence (AI), exhibiting remarkable capabilities across diverse tasks such as text generation, reasoning, and decision-making. While their success has…
The application of Artificial Intelligence (AI) in healthcare has been revolutionary, especially with the recent advancements in transformer-based Large Language Models (LLMs). However, the task of understanding unstructured electronic…
Large language models (LLMs) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
Partial differential equations (PDEs) encode fundamental physical laws, yet closed-form analytical solutions for many important equations remain unknown and typically require substantial human insight to derive. Existing numerical,…