Data-Driven Modeling in Science & Engineering

ML for Science

Interactive lectures covering the foundations of scientific modeling, numerical methods, dynamical systems, and machine learning — from first principles to physics-informed neural networks.

Lectures

10 modules

Scientific Modeling Principles and Differential Equations

Conservation laws, dimensional analysis, ODEs, and the art of building models from first principles.

Numerical Computing and Differential Equations

Euler methods, predator-prey, pendulums, chaos, and the Lorenz attractor.

Complex Systems and Probabilistic Modeling

Emergence, self-organization, random variables, and probabilistic reasoning.

Time Series Analysis: Starting from Data

Fourier decomposition, autoregressive models, and ARIMA.

SVD & PCA: Dimensionality Reduction

Eigenvalues, singular value decomposition, principal component analysis, and low-rank approximation.

Linear Dynamical Systems & DMD

Linear dynamical systems, eigenvalue dynamics, and Dynamic Mode Decomposition.

SINDy: Learning Equations from Data

Sparse identification of nonlinear dynamics: from time-series to governing equations.

Introduction to Deep Learning

From McCulloch-Pitts neurons to deep networks: self-organization, universal approximation, and backpropagation.

Symbolic Regression

Discovering symbolic expressions from data using genetic programming and modern methods.

Physics-Informed Neural Networks

Embedding physical laws into neural network training: theory, practice, and limitations.