Abstract
A major challenge in network science is to determine parameters governing complex network dynamics from experimental observations and theoretical models. In complex chemical reaction networks, for example, such as those describing processes in internal combustion engines and power generators, rate constant estimates vary significantly across studies despite substantial experimental efforts. Here, we examine the possibility that variability in measured constants can be largely attributed to the impact of missing network information on parameter estimation. Through the numerical simulation of measurements in incomplete chemical reaction networks, we show that unaccountability of network links presumed unimportant (with local sensitivity amounting to less than two percent of that of a measured link) can create apparent rate constant variations as large as one order of magnitude even if no experimental errors are present in the data. Furthermore, the correlation coefficient between the logarithmic deviation of the rate constant estimate and the cumulative relative sensitivity of the neglected reactions was less than $0.5$ in all cases. Thus, for dynamical processes on complex networks, iteratively expanding a model by determining new parameters from data collected under specific conditions is unlikely to produce reliable results.
Highlights
In the study of real complex network systems, information about the system components is often incomplete, unreliable, or unknown
In the remainder of the paper, we show that for complex chemical reaction networks in particular, missing information about the underlying network can lead to significant variations in rate constants estimated under different conditions even when the local sensitivities for the neglected links are small compared to those for the links being measured
We focus on important chemical reaction networks involved in natural gas combustion in Sec
Summary
In the study of real complex network systems, information about the system components is often incomplete, unreliable, or unknown. “Weak” nodes and links may be systematically neglected to reduce the number of parameters and derive minimal models, but it is unclear how these missing elements may affect the estimated parameters, and the predicted dynamics, of the parts of the network that are retained. That is, it remains largely unknown what impact missing and deliberately omitted structural (a) –+ V1. V with a discussion of implications and directions for future research
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