notesum.ai

Published at December 4

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

math.NA

cs.AI

cs.NA

65M32, 68T99

G.1.8; G.1.10

Released Date: December 4, 2024

Authors: Sung Woong Cho¹, Hwijae Son²

Aff.: ¹Korea Advanced Institute of Science and Technology; ²Konkuk University

Arxiv: http://arxiv.org/pdf/2412.03161v1

Model

# Train data

Reaction Diffusion

Darcy Flow

Helmholtz equation

DeepONet w/ MLP, CNN branch (Supervised)

33.60%

20.15%

64.17%

500

1.29%

9.06%

23.56%

1000

1.10%

8.77%

7.86%

DeepONet w/ FNO branch (Supervised)

42.78%

28.79%

74.45%

500

32.23%

12.78%

23.61%

1000

21.10%

9.12%

11.30%

FNO (Supervised)

N/A

10.11%

38.42%

500

N/A

5.59%

28.23%

1000

N/A

3.41%

25.85%

PI-DION(Ours)

(Supervised)

1000

1.04%

3.45%

5.64%

PI-DION(Ours)

(Unsupervised)

1000

1.03%

8.10%

8.05%