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Published at October 31

GEPS: Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioning

cs.LG

cs.AI

Released Date: October 31, 2024

Authors: Armand Kassaï Koupaï¹, Jorge Misfut Benet, Yuan Yin², Jean-Noël Vittaut³, Patrick Gallinari⁴

Aff.: ¹Sorbonne Université, CNRS, ISIR, 75005 Paris, France; ²Valeo.ai, Paris, France; ³Sorbonne Université, CNRS, LIP6, 75005 Paris, France; ⁴Sorbonne Université, CNRS, ISIR, 75005 Paris, France; Criteo AI Lab, Paris, France

Arxiv: http://arxiv.org/abs/2410.23889v1

Method	Pendulum $(\times 10^{-2})$		Gray-Scott $(\times 10^{-2})$		Burgers $(\times 10^{-3})$		Kolmogorov $(\times 10^{-1})$
	In-d	Out-d	In-d	Out-d	In-d	Out-d	In-d	Out-d
Data-driven
LEADS	20.8 $\pm$ 1.01	51.1 $\pm$ 3.47	3.11 $\pm$ 0.25	3.81 $\pm$ 0.77	6.31 $\pm$ 0.52	64.1 $\pm$ 2.65	5.61 $\pm$ 0.37	9.18 $\pm$ 0.14
CAVIA	56.8 $\pm$ 9.73	91.8 $\pm$ 15.8	1.63 $\pm$ 3.82	23.1 $\pm$ 6.86	15.5 $\pm$ 1.06	225 $\pm$ 7.94	6.19 $\pm$ 0.02	8.48 $\pm$ 0.16
FOCA	41.0 $\pm$ 4.31	91.4 $\pm$ 9.70	1.71 $\pm$ 5.10	14.5 $\pm$ 3.34	92.2 $\pm$ 8.21	157 $\pm$ 23.6	6.30 $\pm$ 0.02	9.18 $\pm$ 0.14
CoDA	21.7 $\pm$ 1.08	66.2 $\pm$ 3.17	3.19 $\pm$ 0.07	2.89 $\pm$ 4.03	4.98 $\pm$ 0.19	74.5 $\pm$ 6.15	4.02 $\pm$ 0.57	6.34 $\pm$ 1.11
GEPS	20.8 $\pm$ 0.10	50.8 $\pm$ 3.90	2.22 $\pm$ 0.18	1.86 $\pm$ 2.11	2.59 $\pm$ 0.02	52.9 $\pm$ 5.87	2.94 $\pm$ 0.04	5.10 $\pm$ 0.11
Hybrid
APHYNITY	67.2 $\pm$ 9.68	69.0 $\pm$ 0.35	0.14 $\pm$ 0.04	0.20 $\pm$ 0.01	31.9 $\pm$ 0.08	307 $\pm$ 1.40	–	–
Phys-Ad	64.4 $\pm$ 1.10	58.4 $\pm$ 1.85	1.55 $\pm$ 1.41	1.82 $\pm$ 6.42	15.1 $\pm$ 0.10	89.9 $\pm$ 8.65	–	–
GEPS-Phy	8.04 $\pm$ 0.81	46.0 $\pm$ 3.64	0.67 $\pm$ 0.05	0.83 $\pm$ 0.05	5.43 $\pm$ 0.35	68.1 $\pm$ 3.75	2.78 $\pm$ 0.03	4.47 $\pm$ 0.17