TIS

Syllabus

What you will study

The in-person course runs for 18 hours of class. The time shown for each module is what it takes to work through its online page on your own, and is only a guideline.

  1. 1

    Mathematical models

    35–45 min

    What a model is, its parts, and the steps from observation to a model you can use.

    Essential definitions

    • The model as a shipping service
    • Variables, parameters, inputs, outputs
    • Relationships (governing equations)
    • Linear vs nonlinear models

    Interactive examples

    • HRmax = 220 − age (linear model)
    • Muscle force-length relationship (quadratic model)
    • Hill muscle model and power-velocity relationship
    • VO₂max estimation from professional cycling climbs

    The modeling process

    • Observation → conceptualization → formulation
    • Identification (calibration, fitting)
    • Verification and validation
    • Accreditation: can I use it in practice?
    Open Module 1
  2. 2

    Model calibration

    45–60 min

    Fitting parameters to data, the limits of a famous formula, and why extrapolation and overfitting mislead.

    Parameter estimation

    • The model as a machine with knobs
    • Root mean squared error (RMSE)
    • What an optimizer does
    • Excel and Google Sheets Solver (code in the optional Toolbox)

    The HRmax = 220 − age model

    • Historical origins and limitations
    • Alternative models (Tanaka, Gulati)
    • Population-specific calibration

    Interpolation vs extrapolation

    • Olympic records and linear projections
    • Physical limits and model boundaries

    Overfitting

    • Chicken growth polynomial example
    • Bias-variance tradeoff
    • Choosing between models
    Open Module 2
  3. 3

    Static models

    30–40 min

    Fixed-formula models of sport: the power-duration curve, the VO₂ response to a step, and the lactate curve after exercise.

    Intensity-duration relationships

    • Critical power (CP) and W′
    • The 3-min all-out test
    • Anaerobic Power Reserve (APR) model
    • 3-parameter CP and OmniPD models

    VO₂ kinetics (static version)

    • One-exponential model
    • Baseline, amplitude and time constant
    • Limitations and extensions

    Lactate kinetics (static version)

    • Two-pool lactate model
    • Rise and clearance after exercise
    Open Module 3
  4. 4

    Dynamic systems

    65–80 min

    From static to dynamic: VO₂ dynamics, the Banister model, one equation for many systems, a bike suspension and the motion of a cyclist.

    From static to dynamic

    • Static vs dynamic models on a real incremental test
    • Differential equations and time derivatives

    First-order systems

    • VO₂ kinetics (dynamic version)
    • Finite-difference solution
    • Supercompensation: the Banister model (CTL, ATL, TSB)
    • One equation, many systems

    Second-order systems

    • Newton's second law
    • Mass-spring-damper systems
    • Mountain bike suspension
    • Natural frequency and resonance

    Locomotor sports

    • Equation of motion of a cyclist
    • Aerodynamic drag, rolling resistance, gravity
    • Step-by-step solution with finite differences
    Open Module 4
  5. 5

    AI models

    40–50 min

    Neural networks from a single neuron, the curse of dimensionality, and how a language model predicts text.

    Neural network basics

    • The perceptron: weights and biases
    • Activation functions (ReLU)
    • A small network you train by hand

    Training vs validation

    • Minimizing the loss (MSE)
    • Why one data point is not enough

    The curse of dimensionality

    • How parameters grow with network size
    • Model size: from 175 billion parameters (GPT-3) to estimates above a trillion
    • Data needs, overfitting and interpretability

    How a large language model works

    • Text prediction as a modeling service
    • Input → parameters → output, applied to language
    Open Module 5
  6. 6

    The power of models

    30–40 min

    Models behind real decisions, association vs causation, and what a model must show before you use it.

    Models behind decisions

    • Car crash data and insurance premiums
    • Vehicle weight vs safety trade-offs
    • Responsibilities of modelers

    Association vs causation

    • Ice cream sales vs shark attacks
    • Spurious correlations and confounding
    • Training load and injury

    Wrapping up the course

    • Looking back: one equation, many systems
    • What a model must show before you use it
    Open Module 6