In this paper we want to investigate the contribution of different kinds of information to improve the accuracy of time-dependent O-D matrix estimation.
In this paper, inspired by micro-macro decomposition methods for kinetic equations, we present a class of schemes which are capable to preserve the steady state solution and achieve high order accuracy for a class of time dependent partial differential equations including nonlinear diffusion equations and kinetic equations.
Numerical examples of time dependent HJ equations in 2, 3 and 4 dimensions illustrate the accuracy of the new methods.
In particular, three technical components are proposed including: i) an accuracy metric for time dependent model responses under uncertainty, ii) effective approaches for time dependent model bias calibration and approximation, and iii) reliability analysis considering the time dependent model bias.
A simulation study showed that the WC model improved the accuracy of the regression parameters estimates of time-dependent exposure variables as compared with standard logistic regression with fixed-in-time covariates [ 4].
This post-processing technique was able to improve the order of accuracy of the approximation to the solution of time-dependent symmetric linear hyperbolic partial differential equations from order k+1 to order 2k+1 over a uniform mesh; this was extended to include one-sided post-processing as well as post-processing over non-uniform meshes.
Static and dynamic tests of one-dimensional flow over a perturbed wall confirm the accuracy of the time-dependent transformation.
Then the differential equations, given as a coupled pair of time-dependent and time-independent equations, are altered to a fully time-dependent form, without loss of accuracy, but with much greater amenability to an efficient numerical solution method.
Predictive accuracy of the 3-gene model was also high, though the uncertainty associated with the prediction was also high (AUC of time-dependent ROC at 5th year: 92.8%, 95%CI: 80.3 99.3).
In the experiment setup, a positional depth accuracy of about ±0.4 mm for relative object distances and an absolute depth accuracy of about ±1.4 mm for time dependent phenomena was reached.
"We do not question the accuracy of time," Dr. Droste says.
