🧪 Scientific Research

This repository will store some stuff about my scientific research to UFABC.

Some codes and notes will not have a previous context.

⚗️ Thematic

This research is related to applied math about Optimization of Molecular Geometry.

The main thematic is Geometric Optimization.

Some previous research and general notes could be found in my Notion.

🎯 Objetive

The main objetive of this research is found a way to receive a generic function with n parameters, an initial point and return a point where the function converge, this point could be a local maximum, local minimum or a saddle.

To define a convergence, we check if norm of actual point (by default is Euclidian Norm) is equal os smaller than tolerance value (by default is 10e-5).

This method was called CBPD (Convergence Based in Partial Derivatives) and is bases in Newton's Method and Secant Method.

📝 Notes

Notes are formal research documents that explain the project step by step.

They are written using LaTeX and delve into the project's context, explain the algorithm logic, and present a performance comparison between CPBD and Newton's method to converge the SEP function of the F + H2O reaction.

The PDF file could be read here

🔬 CNMAC

CNMAC is a congress about applied math and computation.

The content in this directory is an abstract to submit to 2024 congress.

The abstract PDF could be read here

📊 Optimization

This module contains the code related to optmization:

• base.py: base code common to every optimization method
• cbpd.py: contains the logic of CBPD method
• scipy.py: contains some optimization methods from SciPy and my implementation of Newton's method
• result.py: contains result data of convergence, which is used by all methods

Example

The following code is an example of a convergence process of SEP used in this project

from fh2o_module import li_dawes_guo as ldg
from optimization import cbpd

ldg.init() # Required to SEP function works

point = [0.9901, 1.8261, 1.0003, 112.1962, 170.6405, -8.7494] # Initial Point
func = cbpd.FunctionCBPD(ldg.pes, point) # Create an object of optimization

result = func.converge_numerically(tolerance=0.00001,
                                max_iterations=100,
                                norm="euclidian")

print(result)

Output

Converge: True
Iterations: 24
Init Point: [0.9901, 1.8261, 1.0003, 112.1962, 170.6405, -8.7494]
Final Point: [0.9728234257540236, 1.7700969608929964, 0.9354300701098185, 108.64886591218642, 173.61687633352184, 0.10001533816143876]
Init Value: -19.63909180874393
Final Value: -22.337468737466477