Mathematical modeling is used in research to predict phenomena like climate change. There are static and dynamic models. Static modeling creates diagrams of reservoir characteristics while dynamic modeling simulates airflows over time. Integrated static and dynamic modeling was used to study CO2 storage. Optimization techniques like genetic algorithms, simulated annealing, and particle swarm optimization are used to find optimal solutions to problems. Genetic algorithms evolve populations toward optimal solutions, simulated annealing finds global optima like metals cooling, and particle swarm optimization mimics flock behavior.

1. Mathematical modelling in Research

2. Mathematical modelling

4. https://ibmathsresources.com/2017/01/29/maths-of-global-warming-
modeling-climate-change/
Mathematical modelling for prediction

6. Mathematical modelling - example

7. Static model and dynamic model

8. Static modelling diagrams

9. Dyanamic modelling diagrams
Refer - https://www.slideshare.net/100arab/dynamic-and-static-modeling

10. Static modelling
3D static modelling of Reservoir characteristics
Static modelling diagrams

11. Computational fluid dynamic (CFD) modelling of airflows and velocities
during cone sampling with head placement within the cone.
Dynamic modelling

12. Integrated static modeling and dynamic simulation framework for CO2
storage capacity in Upper Qishn Clastics, S1A reservoir, Yemen
Integrated static and Dynamic modelling

13. System simulation

14. System simulation &research lab in IIT kanpur

15. Optimization techniques

16. Genetic algorithm
Refer - https://www.generativedesign.org/02-deeper-dive/02-04_genetic-algorithms/02-04-01_what-is-a-genetic-
algorithm
The genetic algorithm is a method for solving both constrained and
unconstrained optimization problems that is based on natural
selection, the process that drives biological evolution. The genetic
algorithm repeatedly modifies a population of individual solutions.
At each step, the genetic algorithm selects individuals from the
current population to be parents and uses them to produce the
children for the next generation. Over successive generations, the
population "evolves" toward an optimal solution.

17. Genetic algorithm

18. Simulated annealing
Simulated Annealing (SA) is an effective and general form of optimization. It is useful in
finding global optima in the presence of large numbers of local optima. “Annealing” refers
to an analogy with thermodynamics, specifically with the way that metals cool and
anneal. Simulated annealing uses the objective function of an optimization problem instead
of the energy of a material.
Simulated annealing searching for a
maximum. The objective here is to get to
the highest point. In this example, it is
not enough to use a simple hill climb
algorithm, as there are many local
maxima. By cooling the temperature
slowly the global maximum is found.

19. GA – Genetic algorithm

20. Particle swarm optimization (PSO) is a population-based optimization technique
inspired by the motion of bird flocks and schooling fish. PSO shares many
similarities with evolutionary computation techniques. The system is initialized with a
population of random solutions, and the search for the optimal solution is performed
by updating generations.
Particle swarm optimization