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 (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.