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

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…

We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a…

Software development has entered a new era where large language models (LLMs) now serve as general-purpose reasoning engines, enabling natural language interaction and transformative applications across diverse domains. This paradigm is now…

The rise of large language models (LLMs) has introduced transformative potential in automated code generation, addressing a wide range of software engineering challenges. However, empirical evaluation of LLM-based code generation lacks…

Operations research (OR) is widely deployed to solve critical decision-making problems with complex objectives and constraints, impacting manufacturing, logistics, finance, and healthcare outcomes. While Large Language Models (LLMs) have…

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…

Causal inference has been a pivotal challenge across diverse domains such as medicine and economics, demanding a complicated integration of human knowledge, mathematical reasoning, and data mining capabilities. Recent advancements in…

Large Language Models (LLMs) are increasingly deployed across diverse domains, raising the need for rigorous reliability assessment methods. Existing benchmark-based evaluations primarily offer descriptive statistics of model accuracy over…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

Active learning (AL) accelerates scientific discovery by prioritizing the most informative experiments, but traditional machine learning (ML) models used in AL suffer from cold-start limitations and domain-specific feature engineering,…

Operations Research (OR) serves as a core decision-support methodology for complex systems, with significant applications across mathematics, management science, and computer science. Traditional approaches heavily rely on expert knowledge…

Recent large language models (LLMs) have demonstrated the ability to perform explicit multi-step reasoning such as chain-of-thought prompting. However, their intermediate steps often contain errors that can propagate leading to inaccurate…

We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element discretization and aims at representing the solution…

Neuro-symbolic NLP methods aim to leverage the complementary strengths of large language models and formal logical solvers. However, current approaches are mostly static in nature, i.e., the integration of a target solver is predetermined…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation…

Large Language Models (LLMs) acquire extensive knowledge and remarkable abilities from extensive text corpora, making them powerful tools for various applications. To make LLMs more usable, aligning them with human preferences is essential.…

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…

Large language models (LLMs) achieve impressive results over various tasks, and ever-expanding public repositories contain an abundance of pre-trained models. Therefore, identifying the best-performing LLM for a given task is a significant…