Article July 3, 2026 Turbulence Realm SINDy · Tracking · Fluid Dynamics

Turbulence Realm v2: Six SINDy Methods & Research-Grade Tracking

From raw video to a discovered equation. From scattered bubbles to a full physics report. Two desktop apps have grown into a complete fluid-dynamics workbench that runs on ordinary Windows and Linux machines — no Python, no dependencies, no setup.

SINDy v2.2.1 Tracker v3.2.0 PyTorch bundled OpenCV contrib bundled Windows · Linux

This release marks a step forward for Turbulence Realm SINDy and Tracker. SINDy now offers six distinct methods for discovering governing equations from video, while Tracker has grown from a simple region-clicking tool into a full analysis console for bubble-laden and multiphase flows. Both run as ordinary installers on Windows and Linux, with every major dependency included.

Why six methods, not one?

SINDy is a powerful idea: watch a video, extract motion, and let the software discover the simplest equation that explains what it sees. The catch is that fluid motion comes in many forms. A purely polynomial model can miss the physics when the data is noisy, when the equation has a denominator, or when the experiment is actively driven by a pump or actuator.

Instead of forcing a single algorithm to handle every situation, the new SINDy Model card gives you a dropdown with six sparse-regression methods. Choose the one that matches your data, and the interface adapts automatically.

MethodWhat it doesWhen to use it
Classical SINDyDiscovers clean, explicit equations from smooth dataYour default starting point
SINDy-PIHandles rational and implicit equationsThe equation has fractions or unknown denominators
PDE-FINDDiscovers partial differential equationsYou have spatial grid data, not just time series
WSINDyUses weak forms to resist noiseYour data is rough, sparse, or low quality
E-SINDyRuns an ensemble and keeps only the consistent termsYou need robust results from limited data
SINDYcIncludes external forcing or control inputsYour flow is driven by pumps, valves, or actuators

What this means in practice

If you have a clean video of a vortex street, Classical SINDy may give you the equation in seconds. If your video has pump-driven forcing, switch to SINDYc. If the data is grainy, try WSINDy or E-SINDy. The right method is now one click away.

Turbulence Realm SINDy v2.2.1 workflow overview
Figure 1. The SINDy v2.2.1 workflow: load a video, extract motion, choose a sparse-regression method, and discover the governing equation.

Cross-validation that keeps going

Validating a discovered equation used to be fragile. If one of the cross-validation folds hit a numerical edge case, the whole run stopped and you lost the rest of the results. The same was true when comparing different model settings.

Now each fold and each comparison run is isolated. A single failure is reported but does not stop the rest. You can compare libraries and settings confidently, knowing the results you see are real rather than the artifact of one bad fold.

Turbulence Realm SINDy spatial-error analysis
Figure 2. Spatial-error analysis gives a direct view of where the discovered equation fits the data and where it diverges.

A self-contained Windows installer

Earlier versions asked users to install PyTorch separately before machine-learning features would work. That broke the promise of a one-click installer. The new Windows installer now includes CPU-only PyTorch, the computer-vision library with all its extra modules, and the ONNX runtime, so everything works immediately after installation.

The installer is now 231 MB, but the trade-off is simple: open the file, accept the disclaimer, and start analyzing.

TR-SINDy velocity magnitude
Figure 3. Velocity magnitude field from TR-SINDy: the input video is processed, motion is extracted, and the resulting velocity magnitude is visualized.

Tracker: from clicks to full physics reports

While SINDy was expanding its methods, Tracker was becoming a research instrument. Drop in a video of bubbles, droplets, or particles, and it will:

  • Track every object automatically with multi-object tracking, so you do not have to click each bubble by hand.
  • Segment bubbles even when they touch, and report size distributions, aspect ratios, and circularity.
  • Compute fluid physics such as Reynolds, Weber, and Eötvös numbers, drag coefficients, and terminal-velocity comparisons with built-in presets for common fluids.
  • Build Eulerian flow fields with dense optical-flow maps, speed contours, vorticity, and divergence.
  • Detect events like coalescence, breakup, and detachment, and measure flux through a cross-section.
  • Propagate uncertainty from calibration and localization into the reported speeds and error bars.
  • Export a one-click PDF report with plots, tables, and statistics, plus a tidy table for notebooks.
Turbulence Realm Tracker live demo
Figure 4. Tracker in action: multi-object tracking, segmentation, and physics measurements running on a single video.

Download and try

Both apps are available as signed installers for Windows and Linux. No Python installation is needed. Each installer displays a no-liability disclaimer that must be accepted before installation.

Download from turbulencerealm.com/download and follow the tutorials at turbulencerealm.com/tutorials.