PDE-Controller is a breakthrough framework enabling large language models to understand, formalize, and control systems governed by partial differential equations.

• Transforms natural language instructions into formal mathematical specifications
• Executes multi-step reasoning and planning for PDE systems
• Bridges the gap between AI advances in pure math and practical engineering applications
• Demonstrates potential for AI-assisted control of complex physical systems

This research extends AI capabilities into critical engineering domains like fluid dynamics, heat transfer, and structural mechanics, offering new approaches to solving complex real-world problems through automated mathematical reasoning.

PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs