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Published at December 5

A Physics-Informed Scenario Approach with Data Mitigation for Safety Verification of Nonlinear Systems

eess.SY

cs.SY

Released Date: December 5, 2024

Authors: Ali Aminzadeh¹, MohammadHossein Ashoori¹, Amy Nejati¹, Abolfazl Lavaei¹

Aff.: ¹School of Computing, Newcastle University, United Kingdom

Arxiv: http://arxiv.org/pdf/2412.03932v1

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Case Study	Guarantee	Approach	Samples	$\delta$	$\epsilon^{\max}$	$\varphi$	$\mathscr{L}$	$\eta$	% Change ( $\eta$ )	Condition	% Change (Condition)
Supply-Demand	Deterministic	Traditional	220,000	-	$5\times 10^{-6}$	-	67.90	-0.0235	-	-0.0231	-
	Deterministic	Physics-informed	110,228	0.005	$9\times 10^{-5}$	-	103.72	-0.0527	-124%	-0.0434	-87%
	Probabilistic	Traditional	300,000	-	-	$3.1\times 10^{-5}$	11.51	-0.2078	-	-0.2070	-
	Probabilistic	Physics-informed	150,260	0.005	-	$6.18\times 10^{-5}$	11.51	-0.2094	-0.74 %	-0.2078	-0.36 %
Logistic Growth	Deterministic	Traditional	90,000	-	$5\times 10^{-6}$	-	25.25	-0.0065	-	-0.0064	-
	Deterministic	Physics-informed	45,175	0.005	$8\times 10^{-5}$	-	222.87	-0.0694	-967 %	-0.0515	-704 %
	Probabilistic	Traditional	260,000	-	-	$4.05\times 10^{-5}$	2.9479	$-6.4189\times 10^{-4}$	-	$-5.3444\times 10^{-4}$	-
	Probabilistic	Physics-informed	130,234	0.005	-	$8.08\times 10^{-5}$	5.0397	$-0.0021$	-221%	$-0.0017$	-217%