Deriving Equations from Sensor Data

 Heres an interesting thing,  a kind of algorithm synthesis to do AI with?  Reading, Warning: Technical.  Note, this is research, but I am intrigued.  

Deriving Equations from Sensor Data Using Dimensional Function Synthesis  By Vasileios Tsoutsouras, Sam Willis, Phillip Stanley-Marbell

Communications of the ACM, July 2021, Vol. 64 No. 7, Pages 91-99  10.1145/3465216

We present a new method for deriving functions that model the relationship between multiple signals in a physical system. The method, which we call dimensional function synthesis, applies to data streams where the dimensions of the signals (e.g., length, mass, etc.) are known. The method comprises two phases: a compile-time synthesis phase and a subsequent calibration using sensor data. We implement dimensional function synthesis and use the implementation to demonstrate efficiently summarizing multimodal sensor data for two physical systems using 90 laboratory experiments and 10,000 synthetic idealized measurements. The results show that our technique can generate models in less than 300 ms on average across all the physical systems we evaluated. This is a marked improvement when compared to an average of 16 s for training neural networks of comparable accuracy on the same computing platform. When calibrated with sensor data, our models outperform traditional regression and neural network models in inference accuracy in all the cases we evaluated. In addition, our models perform better in training latency (up to 1096X improvement) and required arithmetic operations in inference (up to 34X improvement). These significant gains are largely the result of exploiting information on the physics of signals that has hitherto been ignored.

1. Introduction

Physical systems instrumented with sensors can generate large volumes of data. These data are useful in understanding previous behaviors of the systems that generate them (e.g., monitoring properties of components in aircraft) as well as in predicting future behaviors of those systems (e.g., predicting failures of components in machinery). Unlike data sources such as speech or text, data from sensors of physical phenomena must obey the laws of physics. Existing methods for constructing predictive models from sensor data however do not fully exploit prior knowledge of the physical interpretation of sensor data. In this work, we use information about physical dimensions of sensor signals to synthesize compact predictive models from sensor data. In keeping with the convention in physics, we use the term dimensions to refer to quantities such as length or time and we use the term units to refer to a value in a standardized system for quantifying values of a given dimension, such as centimeters or miles for length and Pascals or mmHg for pressure. The state of the art in deriving models from such data streams is to apply some form of machine learning.11, 19 Blindly applying machine learning to data from physical systems however ignores important prior knowledge about the physical implications of the signals.  ... '