Learn ML / Stage 6
6 · Computational modelling
Modelling real systems in code: numerical methods, differential equations, dynamical systems, signals and physics-informed machine learning. Builds on stages 1 and 2.
By the end of this stage, you can…simulate a system of differential equations, analyse its stability and long-term behaviour, clean up a noisy signal, and choose a numerical method that is accurate enough for the question.
What you will learn
- Numerical methods Essential
- Differential equations Essential
- Dynamical systems and chaos Essential
- Signal processing If you need it
- Scientific ML and physics-informed networks If you need it
Resources per subject
proof-based you learn by proving results · practical you learn by computing and applying
Numerical methods Essential
- Justin Solomon, Numerical Algorithms, Stanford UniversityHow computers actually do linear algebra and calculus, and where precision goes wrong.★ recommended · practicalvideos
- Laurent Demanet, MIT 18.330: Introduction to Numerical Analysisproof-basednotes · exercises
- Todd Young & Martin Mohlenkamp, Introduction to Numerical Methods (MATLAB), Ohio Universitypracticalfree book · exercises
1 more option
- Wikiversity, Numerical Analysispracticalnotes · exercises
Differential equations Essential
- Arthur Mattuck & Haynes Miller, MIT 18.03: Differential EquationsOrdinary differential equations with videos, notes and exercises. The partial differential equation courses are listed below it.★ recommended · practicalvideos · notes · exercises
- Khan Academy, Differential equationspracticalvideos · exercises
- Gilbert Strang, Differential Equations and Linear Algebra (MathWorks)practicalvideos · exercises
10 more options
- Steven G. Johnson, MIT 18.303: Linear Partial Differential EquationspracticalPDEs · notes · exercises
- Matthew Hancock, MIT 18.303: Linear Partial Differential EquationspracticalPDEs · notes · exercises
- Jared Speck, MIT 18.152: Introduction to Partial Differential Equationsproof-basedPDEs · notes
- Lawrence Guth, MIT 18.156: Partial Differential Equations and Fourier Analysisproof-basedPDEs · notes · exercises
- Philippe Trinh, Vectors and PDEs, University of BathpracticalPDEs · videos
- Giovanni Bellettini, Partial Differential Equations (ICTP)proof-basedPDEs · videos
- Lamar University, Partial Differential EquationspracticalPDEs · videos · notes
- Christopher Lum, Partial Differential Equations (University of Washington)practicalPDEs · videos
- Commutant, Partial Differential EquationspracticalPDEs · videos
- Faculty of Khan, Partial Differential EquationspracticalPDEs · videos
Dynamical systems and chaos Essential
- Steven Strogatz, Nonlinear Dynamics and Chaos, Cornell UniversityThe classic lecture series; the basis for neural and physiological dynamics.★ recommended · practicalvideos
- Rodolfo Rosales, MIT 18.385J: Nonlinear Dynamics and Chaospracticalnotes · exercises
- David Feldman, Introduction to Dynamical Systems and Chaos (Santa Fe Institute)practicalvideos · exercises
2 more options
- Math Insight, Bifurcationspracticalnotes · videos
- George Datseris, Introduction to dynamical systems in Juliapracticalvideo · Julia
Signal processing If you need it
- Think DSP (Downey)Hands-on, in Python; useful for physiological and neural signals.★ recommended · free book · Python code
- SciPy signal processing tutorialdocs · code
Scientific ML and physics-informed networks If you need it
- Data-Driven Science and Engineering (Brunton & Kutz, University of Washington)Data-driven modelling of dynamical systems, then physics-informed networks.★ recommended · free book · videos
- Physics-based Deep Learning (Thuerey et al., TU Munich)free book · code
- Chris Rackauckas, MIT 18.337: Parallel Computing and Scientific Machine Learningfree book · videos