509698 - PROBLEM SOLVING IN PHYSICS

The course is divided into various modules held by the four teachers. First part: General introduction to problem solving in physics. Fermi problems: choose assumtions and approximations, develop scientific reasoning and the ability to ask the right questions (and find the answers). Application to problems on climate change and renewable energies. Introduction to the Python language through the use of colab notebooks. In particular, we shall present the basics of the most used modules for data management, analysis and representation: numpy, pandas and matplotlib. These tools will then be used to analyze covid data (data driven analysis) and to numerically study the behavior of a physical system (the double pendulum). Introduction to the Mathematica language in the Wolfram Cloud environment. Multipole expansion in electrostatics: dipole, quadrupole ... and example of topological singularity. Finite potential well, bound and continuum states, transmission resonances, resonant tunneling, quasi-normal modes (Mathematica and Python). Applications to some problems in biomedical physics. Creation of a Spread Out Bragg Peak in hadrontherapy with fit of experimental data and numerical resolution of differential equations. Introduction to the Monte-Carlo Method, applications to the calculation of the geometric efficiency of a detector and of the radiation dose in space missions. Second part: We shall address a series of problems (physical and otherwise), whose resolution will require the simulation of trajectories, artificial intelligence / machine learning methods, data science and network theory. The first lecture will be dedicated to introducing the Matlab environment, which will be used subsequently for the numerical resolution of the various problems. Simulation and numerical solution of the differential equations of the SIS model. Simulation of random walks and Lévy flight. Comparison between random walks and financial returns. Introduction to networks and Erdos-Renyi model. Watt-Strogatz "small world" model. Barabási-Albert model of heterogeneous networks. Global air transport network analysis. Application of the disparity filter to air transport networks. Introduction to machine learning. Linear regression, determination of the coupling constant of a 1D Ising model via linear regression. Simulation of the 2D Ising model with Metropolis-Hastings algorithm. Introduction to classification and logistic regression problems, classification of the states of the 2D Ising model with logistic regression. Introduction to neural networks. Prediction of the position of a planet in the solar system using a neural network. Introduction to unsupervised machine learning. Clustering with k-means algorithm, application of k-means to clustering of the volatility of a financial security. Dimensionality reduction, introduction to principal component analysis (PCA), application of PCA to the analysis of financial markets.