PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs
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/.
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Mauricio Soroco
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2025-02-14T08:01:31.427Z
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Mauricio Soroco
user
maurice1671
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Jialin Song
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2025-02-18T09:34:16.573Z
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Jialin Song
user
jsong2333333
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Mengzhou Xia
67ad85a2e0aed508231406b9
Kye Emond
67ad85a2e0aed508231406ba
Weiran Sun
67ad85a2e0aed508231406bb
Wuyang Chen
extracted_confirmed
2025-02-13T05:40:20.546Z
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Wuyang Chen
user
wuyangchen
PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs
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/.
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.
large language models LLMs partial differential equations PDEs PDE-Controller autoformalization program synthesis