Numerical Simulation Methods
Численные методы моделирования
Course Overview
This eight-lecture course develops a practical scientific-computing workflow for thermophysics. It begins with Python, NumPy, Matplotlib, Linux, WSL, and HPC environments, then introduces deterministic numerical methods for algebraic and differential equations.
The second half covers Monte Carlo methods and transport, neural-network fundamentals, surrogate modeling, physics-informed neural networks, and machine-learned interatomic potentials. The goal is to equip students to choose, implement, and evaluate computational methods for modern physics and engineering problems.
Schedule
Python language fundamentals, NumPy, and data visualization with Matplotlib.
Scientific workflows from a local computer to Linux servers and HPC systems.
Numerical errors, root finding, linear systems, interpolation, differentiation, and integration.
Ordinary and partial differential equations, Euler and Runge–Kutta methods, and finite differences.
Random sampling, Monte Carlo integration, random walks, and diffusion.
From random walks to the Boltzmann equation and phonon transport.
Perceptrons, neural networks, multilayer architectures, and model training.
Surrogate models, physics-informed neural networks, and machine-learned interatomic potentials.