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Many active solutions across different fields are used to combine the modern ML/DL environment with conventional mathematical modelling techniques. For instance, you can combine state-space modelling techniques with ML in a thermodynamic parameter estimation problem to infer unobserved system parameters. Or, you can combine ML-based forecasting of consumer behaviour with a broader mathematical optimization in a marketing coupon optimization issue to optimise the coupons sent.

Manifold has extensive experience with signal processing interfaces and ML. Using signal processing for feature engineering and combining it with modern ML to identify temporal events based on these features is a common pattern we have deployed. Features inspired by multi-variate time series signal processing, such as short time short time Fourier Transform (STFT), exponential moving averages, and edge finders, allow domain experts to quickly encode information into the modelling problem. Using ML helps the device to learn from additional annotated data continuously and improve its output over time.

In the end, that’s what’s crucial to remember: all of these methods are complementary, and to build data products that solve real business challenges, you need to remember all of them. The forest for the trees is overlooked by an unnecessarily limited emphasis on ML.