title: DiffusionPDE: Generative PDE-Solving Under Partial Observation
summary: We introduce a general framework for solving partial differential equations
  (PDEs) using generative diffusion models. In particular, we focus on the
  scenarios where we do not have the full knowledge of the scene necessary to
  apply classical solvers. Most existing forward or inverse PDE approaches
  perform poorly when the observations on the data or the underlying coefficients
  are incomplete, which is a common assumption for real-world measurements. In
  this work, we propose DiffusionPDE that can simultaneously fill in the missing
  information and solve a PDE by modeling the joint distribution of the solution
  and coefficient spaces. We show that the learned generative priors lead to a
  versatile framework for accurately solving a wide range of PDEs under partial
  observation, significantly outperforming the state-of-the-art methods for both
  forward and inverse directions.
paper_authors._id: 667b82ced0f52ca58a1c71eb
paper_authors.name: Jiahe Huang
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paper_authors.fullname: Jiahe Huang
paper_authors.type: user
paper_authors.user: jhhuangchloe
paper_authors._id: 667b82ced0f52ca58a1c71ec
paper_authors.name: Guandao Yang
paper_authors.status: claimed_verified
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paper_authors.fullname: Guandao Yang
paper_authors.type: user
paper_authors.user: guandao
paper_authors._id: 667b82ced0f52ca58a1c71ed
paper_authors.name: Zichen Wang
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-06-26T09:59:09.389Z
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paper_authors.fullname: zichen wang
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paper_authors.user: chn02
paper_authors._id: 667b82ced0f52ca58a1c71ee
paper_authors.name: Jeong Joon Park
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-07-11T17:34:38.907Z
paper_authors._id: 6517d7f84fadbeb643c68269
paper_authors.avatarUrl: /avatars/ad21288123abcd4488ae1bdcb10b54e7.svg
paper_authors.fullname: JJ Park
paper_authors.type: user
paper_authors.user: jjparkcv
paper_title: DiffusionPDE: Generative PDE-Solving Under Partial Observation
paper_summary: We introduce a general framework for solving partial differential equations
  (PDEs) using generative diffusion models. In particular, we focus on the
  scenarios where we do not have the full knowledge of the scene necessary to
  apply classical solvers. Most existing forward or inverse PDE approaches
  perform poorly when the observations on the data or the underlying coefficients
  are incomplete, which is a common assumption for real-world measurements. In
  this work, we propose DiffusionPDE that can simultaneously fill in the missing
  information and solve a PDE by modeling the joint distribution of the solution
  and coefficient spaces. We show that the learned generative priors lead to a
  versatile framework for accurately solving a wide range of PDEs under partial
  observation, significantly outperforming the state-of-the-art methods for both
  forward and inverse directions.
paper_ai_keywords: gener generative diffusion models partial text diffusion models paired PDE approaches PDEs partial differential equations forward solvers classical solvers missing information diffusion priors diffusion-based approach partial observation state-of-the-art performance forward and inverse generative diffusion models partial differential equations (PDEs) diffusion pri HEL text state-of-the-art methods diffusion priors diffusion-based approach