New Advance of Statistical Analysis and Low Dimensional Topology

Dear Colleagues,

In a wide variety of subjects, it is believed that the large-scale manifold models of problems at hand can be precisely estimated by an appropriate selection and construction of a low-dimensional space. The projection to a reduced dimensional manifold is based on a proven fact in many fields that multivariate analysis in the original manifold topology relates to the appropriately selected low-dimensional space. A successful simulation and analysis in reduced-dimensional manifolds might depend on pre-processing of the original actual data, appropriate mapping, reconstruction techniques, and the feasibility of implementing a solution in the reduced space. The feasibility of simulation implementation in the reduced length can be greatly dependent on preserving the original space’s governing equations. To avoid additional term(s) which may result from mapping to low-dimensional topology, the original governing equations of a system should be approximated as closely as possible. Additionally, the resulting reduced system should preserve the stability of the original one. Reviews or new research studies on any techniques and latest algorithms in developing reduced models from the pre-processing of high-fidelity data through the implementation of analysis/simulation in the reduced manifold space to the reconstruction of the original variables’ solution are welcome in this particular issue.

Dr. Hessam Mirgolbabaei
Dr. Hamed Honari
Guest Editors

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• low-dimensional manifold
• numerical approach
• analytical solution
• data analysis
• reduced topology simulation
• computation time saving (computational efficiency)
• model reduction