[100% Off] Data Science For Dynamical Systems - Masterclass

Dynamical Modeling, Model Identification & Selection, Optimization, Feature Engineering, Control, Koopman Operator

Added on November 21, 2025 Development 4 min read

What you’ll learn

Model and simulate complex dynamical systems using both analytical and numerical techniques.
Identify and build predictive models from data
including linear and nonlinear systems.
Apply optimization and machine learning methods to train models and solve control problems.
Design data-driven control strategies for real-world applications using advanced algorithms.
Understand the fundamentals of dynamical modeling
including ODEs
PDEs
and state-space representations.
Master linear model identification techniques
such as least squares
recursive estimation
and Dynamic Mode Decomposition (DMD).
Learn optimization methods for machine learning
including gradient descent
stochastic optimization
and constrained optimization.
Explore nonlinear model identification approaches
including Neural ODEs and Hammerstein-Wiener models.
Develop feature engineering skills for dimensionality reduction and improved model performance.
Apply model selection techniques
including cross-validation
LASSO
and sparse modeling (SINDy).
Implement optimal and predictive control strategies
including Model Predictive Control (MPC) and differential predictive control.
Analyze complex systems using Koopman operator theory and Extended Dynamic Mode Decomposition (EDMD).

Requirements

Basic knowledge of linear algebra (matrices
eigenvalues
eigenvectors).
Introductory concepts in probability and statistics (helpful for data-driven modeling).
Familiarity with optimization basics (gradient descent
constraints) is a plus.
Basic understanding of machine learning concepts.
Basic Python programming (loops
functions
arrays)
A computer capable of running Python and Jupyter notebooks.
Exposure to control systems or dynamical systems theory.

Description

Modern engineering, science, and technology increasingly rely on data-driven approaches to understand, predict, and control complex dynamical systems. From robotics and aerospace to energy systems and finance, dynamical models form the backbone of decision-making and automation. This course, Data Science for Dynamical Systems, bridges the gap between classical system theory and cutting-edge data science techniques, offering a comprehensive journey from fundamental principles to advanced applications.

Through a structured progression of topics, learners will explore how mathematical modeling, numerical simulation, and machine learning converge to create powerful tools for analyzing and controlling dynamic behavior. The course emphasizes practical implementation, equipping learners with the skills to apply these concepts using modern computational tools.

Why This Course?

Traditional approaches to dynamical systems often rely on first-principles modeling, which can be challenging when systems are highly nonlinear or data-rich. Conversely, data science offers tools for extracting insights directly from measurements, enabling data-driven modeling, system identification, and predictive control. This course combines these paradigms, providing a unified framework that is both theoretically rigorous and practically relevant.

By the end of this course, learners will understand:

How to model dynamical systems using ODEs, PDEs, and state-space representations.
Techniques for linear and nonlinear system identification using data.
Optimization strategies for training models and solving control problems.
Advanced methods like Dynamic Mode Decomposition (DMD) and Koopman operators for high-dimensional systems.
The role of feature engineering, model selection, and machine learning in modern dynamical analysis.

Section 1: Course Introduction

We begin with an overview of the course objectives and the interplay between data science and dynamical systems. Learners will gain a clear understanding of the scope, applications, and the transformative potential of data-driven approaches in engineering and science.

Section 2: Dynamical Modeling Fundamentals

This section lays the foundation by revisiting classical modeling techniques:

Scalar and vectorial ODEs: Learn how to solve autonomous systems analytically.
Matrix exponential and diagonalization: Understand solutions for linear systems.
State-space representation: Explore stability and system properties.
Nonlinear dynamics: Introduction to nonlinear ODEs and their implications.
Numerical methods: Practical algorithms for simulating complex systems.
Partial Differential Equations (PDEs): Learn spatial and temporal discretization for distributed systems.

By the end of this section, learners will be able to model and simulate a wide range of dynamical systems using both analytical and numerical techniques.

Section 3: Linear Model Identification

Here, we transition from theory to data-driven modeling:

Least Squares Estimation: Understand ordinary and weighted least squares.
Recursive methods: Efficient algorithms for real-time identification.
Multicollinearity and Ridge Regression: Address challenges in parameter estimation.
Dynamic Mode Decomposition (DMD): A powerful tool for extracting dynamic patterns from data.
Singular Value Decomposition (SVD) and Eigendecomposition: Learn how these techniques underpin modern system analysis.

This section equips learners with the ability to identify linear models from data, a critical step in predictive modeling and control.

Section 4: Optimization for Machine Learning

Optimization is the engine behind modern data science. This section covers:

Gradient-based methods: From basic gradient descent to advanced variants.
Stochastic optimization: Techniques for large-scale problems.
Newton’s method and second-order approaches: Improve convergence rates.
Constrained optimization: Learn penalty methods and active set strategies.
Differentiation techniques: Symbolic, algorithmic, and automatic differentiation for efficient computation.

Learners will master optimization strategies essential for training models and solving control problems.

Section 5: Nonlinear Model Identification

Building on previous sections, we tackle nonlinear systems:

Prediction error methods: Identify nonlinear dynamics from data.
Global vs. local optima: Understand optimization challenges.
Neural ODEs: Explore deep learning approaches for dynamic modeling.
Hammerstein-Wiener models: Hybrid structures for complex systems.
Extrapolation and robustness: Ensure reliability in real-world scenarios.

This section introduces cutting-edge techniques for modeling systems where linear assumptions fail.

Section 6: Feature Engineering

Features are the lifeblood of machine learning. Here, learners will:

Understand the role of features in dynamic models.
Learn manual and automated feature extraction techniques.
Explore autoencoders for dimensionality reduction.
Discover how feature engineering impacts deep learning performance.

Section 7: Model Selection

Choosing the right model is as important as building it. This section covers:

Bias-variance tradeoff and overfitting.
Cross-validation for robust evaluation.
Sparse modeling: LASSO and SINDy for interpretable models.
Subdifferentials and non-differentiable optimization: Advanced mathematical tools for model selection.

Section 8: Control and Koopman Operator Theory

Finally, we apply everything to control and advanced analysis:

Optimal control: Learn strategies for linear and nonlinear systems.
Model Predictive Control (MPC): Data-driven approaches for real-time decision-making.
Koopman operator theory: A revolutionary framework for analyzing nonlinear dynamics using linear techniques.
Extended Dynamic Mode Decomposition (EDMD): Practical algorithms for high-dimensional systems.

This section demonstrates how data science transforms classical control theory, enabling predictive and adaptive strategies for complex systems.

Key Highlights

Comprehensive coverage: From fundamentals to advanced topics like Koopman operators and Neural ODEs.
Hands-on approach: Practical examples and coding exercises using Python.
Real-world relevance: Applications in robotics, aerospace, energy, and beyond.
Cutting-edge methods: Learn techniques at the intersection of machine learning and dynamical systems.