Deriving Equations from Sensor Data Using Dimensional Function Synthesis

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 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 multi-modal sensor data for two physical systems using 90 laboratory experiments and 10 000 synthetic idealized measurements. We evaluate the performance of the compile-time phase of dimensional function synthesis as well as the calibration phase overhead, inference latency, and accuracy of the models our method generates. The results show that our technique can generate models in less than 300 ms on average across all the physical systems we evaluated. 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 (over 8660× improvement) and required arithmetic operations in inference (over 34× improvement). These significant gains are largely the result of exploiting information on the physics of signals that has hitherto been ignored.