Crude oil pricing models are frequently studied in energy economics through classical linear regression models subject to various limitations (e.g., normality, stationarity) and diagnostic evidence (e.g., information criterion Occams razor principle). In contrast to conventional practices, sparse identification approach makes a breakthrough in economic analysis by eliminating the vast majority of fundamental assumptions of regression models and supporting noise bound control. This paper proposes a method for modeling the governing dynamics of crude oil and LNG prices by utilizing a bundle (set) of potential inputs. The modeling approach generates a sparse network that models the influences of various factors and also considers the structural breaks in multiple factors. The study is designed on two response variables: Crude oil prices (West Texas Intermediate-WTI, Cushing OK, Dollars per Barrel, monthly averages) and LNG prices (Mont Belvieu TX, Dollars per Gallon, monthly averages). Numerical results reflect the spillover between crude oil and LNG prices driven by substitution in various uses and products (e.g., power systems, generators, petrochemicals such as ethylene resins). In contrast to former studies, sparse network identification prefers SP500 stock market index to represent inflationary component rather than traditional price indices or interest rates. Also, the structural break parameter captures the change in the U.S. oil export regime which can be utilized for re-echoing the analogy of regime shift in future studies.