Author: Pedro Pessoa

  • Bayesian PI

     Welcome file Introduction While I usually prefer the Day/Month/Year calendar format, I have to admit that the Month/Day/Year format offers something unique: it gives us 3/14, officially recognized as π\piπ day by the United States and Belize. A common example in sampling/Monte Carlo methods is the estimation of π\piπ. These examples typically involve running…

  • Solving differential equations using neural networks

    PINN_tutorial.md The damped harmonic oscillator and its differential equation Solving the ‘underdamped’ case Exact solution Solving with neural network Solving the ‘critically damped’ case Solving the ‘overdamped’ case Some comments on the results When the neural network does not work Further reading Neural networks have gathered enormous attention in the last decade. Our whole human…

  • A primer on the normal distribution

    normal.md A primer on the normal distribution Introduction Why is the normal distribution so important? Where does the (68.3,95.4,99.7)(68.3, 95.4, 99.7)(68.3,95.4,99.7) rule comes from? Integrating the normal distribution The standard normal Error function Conclusion Introduction New students in science and mathematics may have seen a figure such as the one below. This figure illustrates the…