PHYS96010 - Computational Physics. Includes Problem Sheets, Assignments, and Project
- Topics covered include : LU Decomposition, Gradient Descent, Gaussian Elimination, Pseudo-random generators, numeric integrators, differentiatiors
Abstract—Negative Log-Likelihood (NLL) for the survival probability of neutrino oscillations was minimised to find model values that described the physical phenomenon. A 2D Univariate parabolic minimiser and N-dimensional Simulated Annealing minimiser was applied to obtain these parameters. Errors for Univariate were found by assessing the curvature and errors for Simulated Annealing assessing NLL shifted by 0.5. For Univariate, NLL = 605.1 and for Simulated Annealing, NLL= 113.2 where θ_23 = 0.7278 ± 0.0168rad, ∆m_23 = (2.8541 ± 0.0398) × 10 eV and α = 1.6162 ± 0.0803m eV
Additionally, the methods were verified and tested using the Ackley and sphere function, with colour maps plotted to assess the steps taken by each minimiser. Error using the second derivative of the negative log-likelihood was also explored to assess closeness of fit. A ‘Probabilistic Cooling Scheme’ in Simulated Annealing was implemented to reduce temperatures efficiently.
Full Report |