Heat Demo

Million-cell adaptive heat diffusion.

A synthetic sparse-grid benchmark where a moving heat source changes only local regions. The page compares full recompute, CSC exact delta, and HST scheduled delta on the same measured trace.

Adaptive heat diffusion

1,000,000-cell adaptive heat field

A moving heat source perturbs a local region of a sparse diffusion grid. Most of the mesh is unchanged, so the measured question is how much stale work each method avoids.

Timestep 01 / 32

Measured on MacBook M1, 64GB RAM

A moving heat front makes the tile story visible.

Tiles are 32 x 32 grid blocks. When a heat source moves, only nearby blocks become dirty. Generic CSC exact delta is the strong baseline; HST wins when that local schedule is reused.

Dirty state -

HST vs CSC steady -

HST vs full context -

Build breakeven -

What this proves

When a local heat front moves through a sparse grid, HST's hot loop can beat a generic exact CSC delta path while matching full recompute numerically.

What this does not prove

One-shot HST is not the claim. If the dirty tile set changes every frame, schedule build cost can erase the hot-loop win.

Best fit

Repeated mesh fronts, heat plumes, shockwaves, localized source terms, or sensor sectors where the same local tile set stays active across many calls.

Primary example

Adaptive heat diffusion

The orange tiles are mesh blocks whose cell values changed this timestep. HST schedules the operator rows touched by those blocks and skips the cold mesh.

Radar translation

Use the same idea carefully

A radar sector can be modeled as a grid or tracking graph. A dirty tile is not a radar beam; it is a block of state variables affected by a local update.

Full recompute Context baseline: sparse operator sweep over all cells.

CSC exact delta Strong baseline: generic compressed sparse column traversal over dirty state.

HST scheduled delta Hot-loop path: precompiled tile-local schedule reused across timesteps.

Touched NNZ -

Dirty tiles -

Memory traffic -

One-shot route -

Capacity translation

Same CPU supports a larger adaptive field or a faster timestep rate when the dirty region stays local.

What changed

A local source moves; most state stays cold.

The visible field is a 1000 x 1000 mesh. Each timestep moves a localized heat source, which marks nearby 32 x 32 tiles dirty while the rest of the sparse operator remains structurally unchanged.

The benchmark is intentionally narrow: it demonstrates the workload shape where schedule reuse matters. If the dirty frontier changes unpredictably every frame, the page says so and shows the one-shot cost.