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Mathematical Geosciences
Hybrid Symbolic-Numeric Methods
Solution equations with uncertainty
This section proposes two novel methods for solving nonlinear geodetic equations as stochastic variables when the parameters of these equations have uncertainty characterized by probability distribution. The first method, an algebraic technique, partly employs symbolic computations and is applicable to polynomial systems having different uncertainty distributions of the parameters. The second method, a numerical technique, uses stochastic differential equations in Ito form.
Nature Inspired Global Optimization
This approach is based on natural phenomena such as Particle Swarm Optimization. It simulates, e.g., schools of fish or flocks of birds, and is extended through discussion of geodetic applications.
Black Hole Algorithm
This algorithm is based on the black hole phenomena. A new variant of the algorithm code is introduced and illustrated based on examples.
Gröbner Basis for Integer Programming
The application of the Gröbner Basis to integer programming based on numeric symbolic computation is introduced and illustrated by solving some standard problems.
Integer Programming in GNSS
An extension of the applications of integer programming solving phase ambiguity in Global Navigation Satellite Systems (GNSSs) is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. Three alternative algorithms are suggested, two of which are based on local and global linearization via McCormic Envelopes.
Machine Learning Techniques (MLT)
These techniques offer effective tools for stochastic process modelling. The Stochastic Modelling section is extended by the stochastic modelling via MLT, and their effectiveness is compared with that of the modelling via stochastic differential equations (SDE). Mixing MLT with SDE, also known as Neural Differential Equations, is introduced and illustrated by an image classification via a regression problem.
