WyNDA — A Zero-Optimization Online Streaming Observer for real-time identification of nonlinear dynamical systems with time-varying parameters.

[scarwizz]

Hello SciML community !

I am an undergraduate researcher working at the intersection of Scientific ML and data-driven dynamics, and I wanted to share a framework I recently implemented that tackles a specific edge-case in system identification: sudden parameter drift.

I recently built a pure Python/NumPy implementation of the WyNDA (Wide-Array of Nonlinear Dynamics Approximation) framework, based on the recent paper MethodsX 12 (2024) 102625.

While ecosystems like SciML (and tools like SINDy) are the absolute gold standard for finding global governing equations from historical batches, I noticed that global optimization matrices can sometimes suffer from historical data contamination when a physical system experiences an abrupt structural change mid-run (e.g., component degradation or sudden stiffness loss).

To explore this, I built pywynda as a strict sample-by-sample streaming observer. It uses zero optimization libraries (no scikit-learn, no scipy.optimize) and relies entirely on recursive matrix algebra with exponential forgetting factors to track sudden parameter drifts in real time.

The Benchmark (WyNDA vs. Batch Regression)
I ran a comparative benchmark on a Mass-Spring-Damper system experiencing a sudden stiffness drop ($84 \to 40 \text{ N/m}$) at $t = 2.5\text{ s}$.

• The Batch Approach: Contaminated by 2,500 pre-drift data points, it converges to a weighted mean and fails to identify the new regime.
• The Streaming Approach (WyNDA): Discounting old data via a forgetting factor ($\lambda_\theta = 0.998$), it achieves a 1.8× RMSE improvement and settles into the new parameter regime with a detection latency of just 1040 ms.

I wanted to share this here because I believe online, adaptive streaming could be a really interesting complementary concept within the broader SciML and SINDy ecosystems. I would love to hear your thoughts on this architecture or if you see potential for real-time observer modules in future toolsets!

Repository & Code: https://github.com/scarwizz/pywynda

Thanks for all the incredible work you do for the scientific computing community!

Best regards,
Arpit Singh