A new machine-learning algorithm has been developed that can determine the governing equations and control parameters of a system from a few measurements. The algorithm, developed by a team at the University of Washington, Seattle, has been improved from its 2016 version to now be able to identify key behavior-controlling parameters of a system, as well as predict its behavior under conditions for which there are currently no data.
The algorithm works by taking data points from a system, such as the surface of a cup of coffee over time, and inferring which parameters are key to predicting its behavior. The researchers demonstrated their method by generating two libraries of parameters, one containing hundreds of terms that might appear in an equation describing a system’s behavior and the other listing all possible control parameters. The algorithm then uses a technique known as sparse matrix regression to filter the library terms until it has the minimal number of terms needed to correctly describe the data and its controlling factors.
The updated algorithm also includes a training step that helps it recognize when two datasets come from measurements of the same system. This allows the algorithm to infer critical values for control parameters, such as the fastest speed you can walk without spilling your coffee. However, the accuracy of the algorithm-determined governing equations can depend on the level of noise in the measurements. Despite this, the algorithm includes a noise-mitigation strategy, but if the noise exceeds a certain threshold, the algorithm may produce an ill-fitted model.
The team believes this approach could be useful in understanding any system for which there is a lot of data but no way of determining behavior from first principles. Possible applications include understanding turbulence and modeling the behavior of neurons in the brain, two areas where scientists are currently struggling to build reliable mathematical models.
Key Takeaways:
- A new machine-learning algorithm has been developed that can identify the governing equations and key behavior-controlling parameters of a system using a few measurements.
- The algorithm can be useful for gaining insights about real systems with unknown control parameters and predicting system behavior under conditions with no existing data.
- Despite improvements, the accuracy of the algorithm’s predictions can be affected by the level of noise in the measurements, potentially leading to ill-fitted models if the noise exceeds a certain threshold.
“Using a few measurements of a pattern-forming system, a new machine-learning algorithm can determine the system’s governing equations and their parameters in a form that is interpretable by scientists.”
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