PYTHON · NUMPY

Predict the next state

Meet the world model in one line: a map from (state, action) to the next state, learned from experience.

01Challenge

Fit a one-line linear world model to a torqued pendulum and confirm it predicts the next state far better than assuming nothing moves.

Predict firstTo predict where a pendulum is a moment from now, how well does simply assuming it does not move at all do?

02Model

A world model is a learned simulator. Give it where a system is and what you do, and it tells you what happens next — no equations of motion written by hand, just a function fit to data. That is the whole idea behind Dreamer, DIAMOND, and Genie: replace the real world, or the real game engine, with a network you can run in your head. Here you build the smallest possible one. A pendulum is the real world; you collect what it does; you fit a single linear map to predict its next state. It won't be perfect, but it will already beat the naive baseline of assuming nothing changes, and that gap is where every world model lives.

03Guided practice

1. The real world. A pendulum's step() is the ground truth we want to imitate. 2. The data. Collect (state, action) → next state. 3. The model. One linear map, solved by least squares, predicts the next state — and beats the do-nothing baseline. That map, made bigger and nonlinear, is every world model.

04Feedback

PASS WHEN PASS when the learned model's one-step error is well under the do-nothing baseline.

If your run fails, check:

Read the bench’s printed result — it passes when the learned model's one-step error is well under the do-nothing baseline. Run the cells top to bottom; if one errors, the FAIL line names the step to fix.
The model should clearly beat the do-nothing baseline.

05Retrieve & space

What does a world model map from and to? (from a state and action, to the next state).
Why is 'assume nothing moves' the baseline to beat? (it's the trivial predictor that ignores dynamics).
What replaces the hand-written physics in a world model? (a function fit to observed transitions).

06Mastery & project

You can state what a world model is and fit the smallest one to real transitions.

The habit under the whole course: a world model is just next-state prediction, learned from data.

← World Models: Learn a Simulator You Can Imagine In Imagine a trajectory →

PYTHON · NUMPY

Predict the next state

Fit a linear next-state predictor and beat the do-nothing baseline.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you