HPC Tier Module
SINDy - Governing Equation Discovery
Recover the symbolic equations behind a time series - deterministic, reproducible, no neural net.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
The problem
Discovering the governing equations behind measured dynamics is usually done with opaque trained models that are not reproducible and offer no built-in residual check.
The local-first solution
This plugin runs SINDy in the browser - finite-difference derivatives, a polynomial-plus-trig candidate library, and sequentially thresholded least squares - to read off the symbolic equations deterministically, with a residual-based trust verdict.
What it does
4th-order finite-difference state-derivative estimates from the samples
Polynomial (and optional trigonometric) candidate-term library
Sequentially thresholded least squares so only the few true terms survive
Built-in known systems (linear, cubic oscillator, Lorenz) or your own t,x1,x2 CSV
Time series, phase portrait, model overlay, 3D orbit, and a GeoNum residual trust verdict
Honest scope
The method is deterministic - least squares plus a fixed threshold, no neural net, no stochastic training, fully reproducible. Plain STLSQ-SINDy is sensitive to measurement noise through the derivative estimate; the noise-robust weak/integral form (Weak-SINDy) is cited but not implemented here, and the discovered model is a data fit, not guaranteed ground truth - confirm against domain knowledge.
Authorities cited
- Brunton, Proctor, Kutz, "Discovering governing equations from data by sparse identification of nonlinear dynamical systems", PNAS 113(15):3932-3937 (2016) - the SINDy method + STLSQ.
- Messenger & Bortz, "Weak SINDy for partial differential equations", J. Comput. Phys. 443:110525 (2021) - the noise-robust integral formulation (cited; not implemented here).
- Lorenz, "Deterministic Nonperiodic Flow", J. Atmos. Sci. 20:130-141 (1963) - the built-in Lorenz validation system.
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Discover the equations
Run discovery in the browser and save the structured result to Sandbox, attach it to a Worklog engagement, or route it into a Gate client portal. Nothing is uploaded to anyone's cloud.