DiffusionPDE: Generative PDE-Solving Under Partial Observation
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.
667b82ced0f52ca58a1c71eb
Jiahe Huang
claimed_verified
2024-06-26T08:03:48.529Z
666e723d2c1f3a8ddf450c71
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Jiahe (Chloe) Huang
user
jhhuangchloe
667b82ced0f52ca58a1c71ec
Guandao Yang
claimed_verified
2024-06-26T08:03:46.756Z
64547ca006728ff79a38e7a5
https://cdn-avatars.huggingface.co/v1/production/uploads/64547ca006728ff79a38e7a5/xfTVQXMSfRv-IbljFpswQ.jpeg
Guandao Yang
user
guandao
667b82ced0f52ca58a1c71ed
Zichen Wang
admin_assigned
2024-06-26T09:59:09.389Z
663cc440d3292216e9b8280f
/avatars/e6938c81a5b2b3dc19454d43ab1a6abc.svg
zichen wang
user
chn02
667b82ced0f52ca58a1c71ee
Jeong Joon Park
claimed_verified
2024-07-11T17:34:38.907Z
6517d7f84fadbeb643c68269
/avatars/ad21288123abcd4488ae1bdcb10b54e7.svg
JJ Park
user
jjparkcv
DiffusionPDE: Generative PDE-Solving Under Partial Observation
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.
DiffusionPDE, a generative diffusion model framework, solves PDEs effectively under partial observations by modeling the joint distribution of solutions and coefficients.
generative diffusion models partial differential equations (PDEs) classical solvers DiffusionPDE generative priors