Forward: set the flume angle and draw a sand mass on the slope — see where it comes to rest. Inverse: draw a deposit — find the slope and sand block that would leave it. Both run a neural-network surrogate of many LS-DYNA SPH simulations in your browser, using the calibrated μ(I) + power-law Perzyna rheology of the dry-sand flume study.
Searches the slope angle and a rectangular sand block (position, length, thickness) whose predicted deposit best matches the target.
The same quasi-2D flume as the experiments: a 1 cm slice of dry sand (1276.3 kg/m³) released at rest on a rigid slope that pivots about a fixed point above a horizontal floor. Each LS-DYNA run solves the release with SPH until the mass settles; the page predicts the final deposit surface, drawn as height above the slope or floor beneath it.
The inverse search runs the same forward network a few thousand times: a space-filling scan of slope angle and block front position, length and thickness, then a Nelder–Mead refinement from the best few starts. The misfit is the RMS height difference over the columns where either the target or the prediction has sand, inside the observation window (for the experiments, the part of the floor the camera saw). Different sources can leave nearly the same deposit — a steeper slope with less sand, a gentler one with more — so the page lists distinct candidates rather than a single answer. Fixing the angle when it is known removes most of that ambiguity.
Run on the seven digitised experiments, every one of which came from the same block (0.46 × 0.14 m, 644 particles = 1 V₀, front 1.94 m up the slope). Loading an experiment fixes what the experiment itself tells you — where the box sat and its proportions — and leaves the angle and the amount of sand to be found:
| Experiment | Angle free: angle found | Angle free: volume | Angle fixed: volume |
|---|---|---|---|
| 30° | 30.0° | 1.00 V₀ | 1.00 V₀ |
| 35° | 30.0° | 2.05 V₀ | 1.16 V₀ |
| 40° | 34.8° | 1.43 V₀ | 1.00 V₀ |
| 45° | 59.3° | 0.87 V₀ | 0.75 V₀ |
| 50° | 49.8° | 0.75 V₀ | 0.75 V₀ |
| 55° | 51.1° | 0.89 V₀ | 0.89 V₀ |
| 60° | 53.8° | 0.98 V₀ | 0.89 V₀ |
With the angle fixed as well, the volume comes back within about 13 % on average — exactly, block size included, at 30° and 40° — and on the low side (0.75–0.89 V₀) at 45–60°, because at steep slopes the photographed deposit is lower and shorter than the calibrated model predicts for the real block. Left free, the angle is found within about 5° on average but the steep-slope deposits look so alike in the camera window that 45° can come back as 59°. Without the release position and proportions fixed, the search finds sources that match the photographed deposit even better and are physically different — a 2 cm sheet lying at the toe, a tall column at the top of the slope — because the part of a deposit a camera sees on the floor does not pin down where the sand started or what shape it had. The options are there so that whatever you know can be fixed.
The network learned only what its training shapes look like: one connected mass, at most three humps, and outlines no more jagged than the random polylines it was trained on. The page checks every drawing against those three limits, measured on the 1 cm columns you draw. Sand in several separate pieces gets no prediction at all (several masses can catch up with and pile into each other, which no training run shows); a single piece with too many humps or too jagged an outline gets a grey dashed prediction marked unreliable. All 149 held-out test shapes pass the checks. A statistical test on the network’s 5 cm-averaged input was tried first and rejected: it let a drawing of five thin separate patches through, because averaging makes them look like one long thin layer.
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Scored on random shapes generated with a different seed and never used for training or model selection:
The light-blue band is the spread of the five ensemble members — their disagreement, not a calibrated probability. Sand size, thickness and position along the slope are covered by simulation over everything the page lets you draw (see the training data); drawing stops at the largest simulated thickness and particle count. The slope angle is the one input that is not: the rheology was calibrated on 30–60°, and outside that the page says the prediction is an extrapolation.
Only the final deposit is predicted, not the flow. The underlying model was calibrated against one block size at seven angles; other sizes and shapes are model predictions, not experimentally validated. Below about 35° the calibrated rheology keeps creeping slowly after the main flow stops, so the deposit shape there depends on when the simulation ends.