LifeSpanLogs

Enhancing LifeSpans Through Reproducible LifeStyles

Differential Equations from Data

Developing fast data processing technologies capable of extracting least squares models for real-time dynamics and control exclusively from noisy Multi-Input Multi-Output (MIMO) time-series data is the goal of this website.

Most existing methods rely on domain specific knowledge to develop the dynamics and control models from first principles.

The data processing appraoch here is to extract a least squares fit in real-time from data continuously as it is being sampled. The poles of the spectral components may be anywhere in the complex number space. Compare this to the linear or polynomial regression where the poles of the spectral components are restricted to be only at 0 in the complex number space.

The data processing proposed here is meant for data that display good correlations and good signal/noise ratios. This data processing may not be able to adequately address data that show poor correlations or show poor signal/noise ratios.

This least square fit from time-series data to differential equations may have broader application where time-series data may be exclusively used to capture system behavior. Author may be contacted at lifespanlogs@gmail.com.

Caution: While it is okay to refer to other users' lifestyle data for comparison, biomarker dynamics may not be reproducible.  Dynamics from one's own logged  input-lifestyle output-biomarker are likely to be more reproducible.

Limitations: Sampling interval, sampling window, non-existent input dynamics.

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