• ES Español
• EN English

3.11. Computational and Data-Driven Physics (CDP)

This area covers numerical simulation methods, Monte Carlo techniques, machine learning for physical discovery, and physics-informed neural networks. It bridges physics and computing, equipping students to build simulations, analyze scientific data, and construct hybrid physics-ML models.

Knowledge Area (KA)	CS Core	KA Core
3.11.1 Numerical Methods for Differential Equations in Physics	Elective
3.11.2 Monte Carlo Methods and Simulations	Elective
3.11.3 Machine Learning for Physical Discovery	Elective

3.11.1. CDP/Numerical Methods for Differential Equations in Physics ↑ Back to top

Discrete approximations for solving fundamental equations of motion and field theories, essential for building physics simulators in computing.
Topics:
Core

• Runge-Kutta methods (RK2, RK4) for initial value problems
• Finite Difference Time Domain (FDTD) for Maxwell's equations
• Boundary value problems: shooting methods and relaxation techniques
• Symplectic integrators: Verlet and leapfrog algorithms for Hamiltonian systems
• Stability analysis and the Courant-Friedrichs-Lewy (CFL) condition

Learning Outcomes:
Core:

1. Explain the stability requirements of numerical ODE integrators and identify the CFL condition [Familiarity]
2. Implement a velocity Verlet algorithm to simulate a physical system with conserved energy [Usage]
3. Evaluate the scaling of discretization errors for different numerical integration orders [Assessment]

3.11.2. CDP/Monte Carlo Methods and Simulations ↑ Back to top

Stochastic sampling techniques for multi-dimensional integration and statistical physics, relevant to probabilistic inference and simulation in computing.
Topics:
Core

• Pseudo-random and quasi-random number generation algorithms
• The Metropolis-Hastings algorithm for Markov Chain Monte Carlo (MCMC)
• Monte Carlo simulation of the Ising model and phase transitions
• Importance sampling and variance reduction techniques
• Statistical error estimation and autocorrelation time in MCMC chains

Learning Outcomes:
Core:

1. Describe the Metropolis-Hastings acceptance criterion and explain its connection to detailed balance [Familiarity]
2. Develop an importance sampling scheme to integrate a peaked multidimensional function [Usage]
3. Analyze the statistical quality of a Monte Carlo estimate and quantify autocorrelation-induced bias [Assessment]

3.11.3. CDP/Machine Learning for Physical Discovery ↑ Back to top

Applying statistical learning to identify patterns and surrogate models in data, including physics-informed neural networks and neural operators for solving PDEs.
Topics:
Core

• Supervised learning: linear regression, LASSO, and Ridge for physics models
• Unsupervised learning: clustering and PCA for detecting phase transitions
• Gaussian Process Regression for uncertainty-aware surrogate modeling
• Symbolic regression for discovering analytical physical laws from data
• Physics-Informed Neural Networks (PINNs): incorporating PDE constraints into neural network loss functions

Learning Outcomes:
Core:

1. Explain how physics constraints can be encoded in the loss function of a neural network [Familiarity]
2. Train a regression or Gaussian Process model to predict a physical quantity and quantify uncertainty [Usage]
3. Evaluate and compare data-driven surrogate models with traditional numerical solvers on accuracy and computational cost [Assessment]