title: PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs
summary: 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 large language models (LLMs) to control systems governed by
  partial differential equations (PDEs). Our approach enables LLMs to transform
  informal natural language instructions into formal specifications, and then
  execute reasoning and planning steps to improve the utility of PDE control. We
  build a holistic solution comprising datasets (both human-written cases and 2
  million synthetic samples), math-reasoning models, and novel evaluation
  metrics, all of which require significant effort. Our PDE-Controller
  significantly outperforms prompting the latest open-source and GPT models in
  reasoning, autoformalization, and program synthesis, achieving up to a 62%
  improvement in utility gain for PDE control. By bridging the gap between
  language generation and PDE systems, we demonstrate the potential of LLMs in
  addressing complex scientific and engineering challenges. We will release all
  data, model checkpoints, and code at https://pde-controller.github.io/.
paper_authors._id: 67ad85a2e0aed508231406b6
paper_authors.name: Mauricio Soroco
paper_authors.status: claimed_verified
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paper_authors.fullname: Mauricio Soroco
paper_authors.type: user
paper_authors.user: maurice1671
paper_authors._id: 67ad85a2e0aed508231406b7
paper_authors.name: Jialin Song
paper_authors.status: claimed_verified
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paper_authors.fullname: Jialin Song
paper_authors.type: user
paper_authors.user: jsong2333333
paper_authors._id: 67ad85a2e0aed508231406b8
paper_authors.name: Mengzhou Xia
paper_authors._id: 67ad85a2e0aed508231406b9
paper_authors.name: Kye Emond
paper_authors._id: 67ad85a2e0aed508231406ba
paper_authors.name: Weiran Sun
paper_authors._id: 67ad85a2e0aed508231406bb
paper_authors.name: Wuyang Chen
paper_authors.status: extracted_confirmed
paper_authors.statusLastChangedAt: 2025-02-13T05:40:20.546Z
paper_authors._id: 64df97c628d5d234ce0bf83c
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/64df97c628d5d234ce0bf83c/BIEH7Ep4ffytiAcUIPFe-.jpeg
paper_authors.fullname: Wuyang Chen
paper_authors.type: user
paper_authors.user: wuyangchen
paper_title: PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs
paper_summary: 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 large language models (LLMs) to control systems governed by
  partial differential equations (PDEs). Our approach enables LLMs to transform
  informal natural language instructions into formal specifications, and then
  execute reasoning and planning steps to improve the utility of PDE control. We
  build a holistic solution comprising datasets (both human-written cases and 2
  million synthetic samples), math-reasoning models, and novel evaluation
  metrics, all of which require significant effort. Our PDE-Controller
  significantly outperforms prompting the latest open-source and GPT models in
  reasoning, autoformalization, and program synthesis, achieving up to a 62%
  improvement in utility gain for PDE control. By bridging the gap between
  language generation and PDE systems, we demonstrate the potential of LLMs in
  addressing complex scientific and engineering challenges. We will release all
  data, model checkpoints, and code at https://pde-controller.github.io/.
paper_ai_summary: PDE-Controller is a framework that leverages large language models to control systems governed by partial differential equations, transforming natural language instructions into formal specifications for better reasoning, autoformalization, and program synthesis.
paper_ai_keywords: large language models LLMs partial differential equations PDEs PDE-Controller autoformalization program synthesis