Day 2 · 9:00–9:45 · Prof. Qi Wang & SDSU students

Physics Simulation

How computers model the real world — the science behind games, movies, engineering… and AI.

The question

How does a computer "know" physics?

It doesn't. It only knows numbers and rules.

A simulation = the world's state (positions, speeds) + the rules (forces) + a clock.

Tick the clock in tiny steps, apply the rules each tick — reality emerges.

The whole engine · live

Two lines of code run every game you've played

speed = speed + gravity × dt height = height + speed × dt

Step size (dt) small & smooth · press P to pause

Cannon Challenge 🎯

LIVE GAME

Angle + power in, gravity does the rest — the same two lines of code flying the cannonball. Let students call out angles.

Same rule, new world: Orbit Lab 🪐

LIVE GAME

Identical gravity code — pointed at the sun instead of down — gives you the solar system. Flick too slow: crash. Too fast: escape. Just right: orbit.

A humbling truth · live

Chaos: tiny differences explode

Two double-pendulums, started 0.001° apart. Same rules, same computer — watch them disagree. This is why weather forecasts stop at ~10 days.

New idea · when the "thing" is everywhere

Smoke, heat, weather: chop the world into cells

🎈 A ball has ONE position. But smoke? Heat? Weather? They're everywhere at once
🔲 The trick: chop space into cells — each holds one number ("how much smoke here?")
🌬️ Advection: the wind carries it — chimney smoke drifting downstream
♨️ Diffusion: it spreads all by itself — perfume filling a room, milk swirling into tea

Every cell plays the same tiny game: look at your neighbors, update your number. That's ALL a weather supercomputer does — a billion times per second.

[23:00–25:00] — the setup for Computor. Two new words, both wrapped in pictures they know: ADVECTION = "carried along." Chimney smoke drifting downwind, a leaf riding a river, the smell of BBQ arriving from the neighbor's yard on a breezy day. The wind does the moving. DIFFUSION = "spreads by itself." Open a perfume bottle in a still room — no wind, yet it reaches every corner. Milk in tea before you stir. Heat creeping along a metal spoon. Ask the room: "Someone microwaves popcorn at the office — you smell it two rooms away with no fan. Advection or diffusion?" (Mostly diffusion — then a door opens and WHOOSH, advection.) The cells idea: we can't track every molecule, so we chop the world into boxes and store one number per box. A weather model is exactly this — cells the size of San Diego, one number each for temperature, wind, moisture. Land the punch: each cell only ever talks to its NEIGHBORS. Tease: "so who does the talking? YOU do. Next slide, someone becomes a cell."

Computor 🧑‍💻 — YOU are one cell

LIVE GAME — YOU DRIVE

One volunteer drives; the room predicts. Every ▶ Step = one tick of the future — and cell #8's arithmetic appears in plain left / me / right words with the answer. Predict, step, check… then crank ⏱️ Δt past the red line and meet the famous 💥.

[25:00–32:00] — LIVE DEMO, the heart of the new material. One volunteer drives; everyone in the room IS a cell in spirit. The ritual, every step: the room SHOUTS a prediction for cell #8's next number → volunteer hits ▶ Step → the work panel reveals the arithmetic in left/me/right words and the true value. Cheer near-misses. ROUND 1 — Advection (~2.5 min): three steps in, they'll spot the pattern in the formula: you take from UPWIND — the wind hands you what's behind you. Step until the puff marches through cell #8 and wraps around the ring. Point at the CFL number sitting inside the formula — "remember that number; it explodes in round 3." ROUND 2 — Diffusion (~1.5 min): switch tabs. The formula changes shape: move toward your neighbors' average. The puff melts flat. Ask: "will it ever un-spread?" (Never — like perfume. Diffusion is a one-way street.) ROUND 3 — the 💥 (~2 min): slowly crank ⏱️ Δt until the chip turns red, then ⏩ ×10. The grid explodes — let them gasp before you explain, with ZERO math: "in one tick the smoke had to jump PAST a whole cell, but a cell can only see its neighbors. The handoff was missed; the numbers panicked." That's the CFL speed limit: information may travel at most ONE cell per step. Real weather centers fight this exact limit daily — finer grids force smaller steps force bigger computers. ∑ Show the math generalizes the panel to every cell at once (one line per cell!) — open it only if someone asks; the game carries the idea without it. It's on the hub as "Computor" — every student can be their own cell at the break.

Draw it, then watch it flow: Wind Tunnel 🌬️

LIVE GAME

Doodle any shape and the wind peels off it into a Kármán vortex street — the same swirls behind cars, wings & flags. Real turbulence, simulated live.

Why it matters

Test it in the computer before you build it

✈️ Planes & rockets — thousands of crashes that never hurt anyone (my job!)
🌪️ Weather & climate — the whole planet in a supercomputer
🏥 Medicine — blood flow, drug design, surgery practice
🎬 Games & movies — every splash and explosion you've ever seen

Simulation meets AI: Train the Cannon 🎯🧠

LIVE GAME

Don't aim it yourself — collect practice shots in the simulator, train a model by gradient descent, and watch it learn to hit new targets.

The honest part

Simulation ≠ reality

Every simulation simplifies — perfect spheres, no wind, smooth tables
Small modeling errors + chaos = drift from the real world
Robots trained only in simulation stumble in reality (the "sim-to-real gap")
Rule of the pros: simulate, then TEST in the real world, then fix the simulator.

Recap

What you now know

🕰️ Simulation = state + rules + tiny time steps
⚖️ Step size is a trade-off: accuracy vs speed (too big → broken physics)
🌬️ Smoke & heat live on a grid of cells: advection carries, diffusion spreads — and steps past the CFL speed limit → 💥
🪐 One rule, many worlds: cannonballs and planets share an equation
🦋 Chaos limits prediction — even for perfect simulators
🤖 AI practices inside simulators — millions of free tries

Questions? 🙋

Up next at 9:45: AI World Models — what if the machine learns the rules itself?

Cannon, Orbit, Computor & Train-the-Cannon are all in the mini-games hub.