Don't ask your model to learn what a formula already knows!
The formula encodes what we know. The model encodes what we cannot derive analytically.
The Problem
In a delivery-time prediction project (ETA), I had a choice: use the simple formula, or train the model from scratch.
The formula was obvious — estimated duration from distance and rider speed. Most competitors either used that formula directly, or ignored it and let XGBoost recover the relationship from raw features.
I did neither.
The Approach
I gave the formula's output to the model as a structured prior, then let the model learn the deviation.
The formula captures
The stable physical relationship (distance → time)
The model captures
What the formula systematically misses: traffic, geography, rider variability, time-of-day effects
The model's job is no longer "predict delivery time." It becomes "predict how wrong this estimate will be, and in which direction." That's a much easier learning problem.
Key Takeaway
Design insight: If you can write a formula that gets you 70% of the way there, don't throw it away. Feed it in. This applies anywhere you have a reasonable first-principles estimate: pricing, demand-forecasting, energy-consumption, manufacturing-yield.