Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Fusing Loop and GPS Probe Measurements to Estimate Freeway Density

In an age of ever-increasing penetration of GPS-enabled mobile devices, the potential of real-time "probe" location information for estimating the state of transportation networks is receiving increasing attention. Much work has been done on using probe data to estimate the current speed of vehicle traffic (or equivalently, trip travel time). While travel times are useful to individual drivers, the state variable for a large class of traffic models and control algorithms is vehicle density. Our goal is to use probe data to supplement traditional, fixed-location loop detector data for density estimation. To this end, we derive a method based on Rao-Blackwellized particle filters, a sequential Monte Carlo scheme. We present a simulation where we obtain a 30\% reduction in density mean absolute percentage error from fusing loop and probe data, vs. using loop data alone. We also present results using real data from a 19-mile freeway section in Los Angeles, California, where we obtain a 31\% reduction. In addition, our method's estimate when using only the real-world probe data, and no loop data, outperformed the estimate produced when only loop data were used (an 18\% reduction). These results demonstrate that probe data can be used for traffic density estimation

Limit Distribution of Evolving Strategies in Financial Markets

In this paper we model a financial market composed of agents with heterogeneous beliefs who change their strategy over time. We propose two different solution methods which lead to two different types of endogenous dynamics. The first makes use of the maximum entropy approach to obtain an exponential type probability function for strategies, analogous to the well known Brock and Hommes (1997) model, but with the endogenous specification for the intensity of choice parameter, which varies over time as a consequence of the relative performances of each strategy. The second type of dynamics is obtained by setting up a master equation and solving it using recently developed asymptotic solution techniques, which yield a system of differential equations describing the evolution of the share of each strategy in the market. The performance sof the two solutions are then compared and contrasted with the empirical evidence.