Related papers: OpInf-LLM: Parametric PDE Solving with LLMs via Op…

Partial differential equations (PDEs) are fundamental to modeling physical systems, yet solving them remains a complex challenge. Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive, while…

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…

Motivated by the remarkable success of artificial intelligence (AI) across diverse fields, the application of AI to solve scientific problems, often formulated as partial differential equations (PDEs), has garnered increasing attention.…

Growing renewable penetration introduces substantial uncertainty into power system operations, necessitating frequent adaptation of dispatch objectives and constraints and challenging expertise-intensive, near-real-time modeling workflows.…

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…

Foundation models -- large language models (LLMs) in particular -- have become ubiquitous, shaping daily life and driving breakthroughs across science, engineering, and technology. Harnessing their broad cross-domain knowledge,…

While scaling laws have been continuously validated in large language models (LLMs) with increasing model parameters, the inherent tension between the inference demands of LLMs and the limited resources of edge devices poses a critical…

Physics-informed neural networks (PINNs) provide a powerful approach for solving partial differential equations (PDEs), but constructing a usable PINN remains labor-intensive and error-prone. Scientists must interpret problems as PDE…

In this work, we propose an Operator Learning (OpL) method for solving boundary value inverse problems in partial differential equations (PDEs), focusing on recovering diffusion coefficients from boundary data. Inspired by the classical…

Optimization problems seek to find the best solution to an objective under a set of constraints, and have been widely investigated in real-world applications. Modeling and solving optimization problems in a specific domain typically require…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

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…

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…

Parameter-shared pre-trained language models (PLMs) have emerged as a successful approach in resource-constrained environments, enabling substantial reductions in model storage and memory costs without significant performance compromise.…

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…

Existing works on large language model (LLM) decomposition mainly focus on improving performance on downstream tasks, but they ignore the poor parallel inference performance when trying to scale up the model size. To mitigate this important…

In the field of software operations, Large Language Models (LLMs) have attracted increasing attention. However, existing research has not yet achieved efficient and effective end-to-end intelligent operations due to low-quality data,…

Optimization modeling plays a critical role in the application of Operations Research (OR) tools to address real-world problems, yet they pose challenges and require extensive expertise from OR experts. With the advent of large language…

Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise…

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…