between the length of the pendulum and its time of oscillation. A more sophisticated and general approach uses the derived dimensionless parameters as input features to train machine learning models… Click to show full abstract
between the length of the pendulum and its time of oscillation. A more sophisticated and general approach uses the derived dimensionless parameters as input features to train machine learning models on the observed data. This approach compares quite favorably to other off-the-shelf approaches. Thus, the authors present an elegant approach to inferring models from data that incorporate some of the known relationships between the quantities being modeled using dimensional analysis. Elsewhere, dimensional analysis has been shown to be quite effective in detecting defects in robotic software using dimensions as type annotations that can be derived using program analysis techniques.2 Furthermore, dimensions provide a type system for physical quantities. Such type systems are quite useful in machine learning models wherein we often seek to avoid overfitting by imposing constraints such as monotonicity on the models.3 I see the proposed dimensional consistency approach as a precursor to strongly typed machine learning models that can leverage the power of dependent type systems to specify more sophisticated properties including monotonicity.1
               
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