Related papers: PDE-Agent: A toolchain-augmented multi-agent frame…

Flow physics and more broadly physical phenomena governed by partial differential equations (PDEs), are inherently continuous, high-dimensional and often chaotic in nature. Traditionally, researchers have explored these rich spatiotemporal…

This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

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,…

Agentic AI has significantly extended the capabilities of large language models (LLMs) by enabling complex reasoning and tool use. However, most existing frameworks are tailored to domains such as mathematics, coding, or web automation, and…

Task planning, the problem of sequencing actions to reach a goal from an initial state, is a core capability requirement for autonomous robotic systems. Whether large language models (LLMs) can serve as viable planners alongside classical…

The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as…

Large language models (LLMs) are catalyzing the development of autonomous AI research agents for scientific and engineering discovery. We present FM Agent, a novel and general-purpose multi-agent framework that leverages a synergistic…

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

Large Language Model (LLM)-based agents have recently shown impressive capabilities in complex reasoning and tool use via multi-step interactions with their environments. While these agents have the potential to tackle complicated tasks,…

The integration of Large Language Models (LLMs) into software engineering has driven a transition from traditional rule-based systems to autonomous agentic systems capable of solving complex problems. However, systematic progress is…

This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of…

We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly…

Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

Large language models (LLMs) serve as an active and promising field of generative artificial intelligence and have demonstrated abilities to perform complex tasks in multiple domains, including mathematical and scientific reasoning. In this…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Large language models (LLMs) exhibit strong performance on self-contained programming tasks. However, they still struggle with repository-level software engineering (SWE), which demands (1) deep codebase navigation with effective context…

Large reasoning models have demonstrated strong problem-solving abilities, yet real-world tasks often require external tools and long-horizon interactions. Existing agent frameworks typically follow predefined workflows, which limit…

Issue resolution has made remarkable progress thanks to the advanced reasoning capabilities of large language models (LLMs). Recently, agent-based frameworks such as SWE-agent have further advanced this progress by enabling autonomous,…