How machine learning and optimization work well together

A guest post exploring three recurring patterns for combining machine learning and mathematical optimization in real-world systems. Pattern 1 covers decision-making under uncertainty, emphasizing that passing full probabilistic distributions (not just averages) to optimizers enables better decisions in inventory management and similar domains. Pattern 2 describes replacing computationally difficult equations with surrogate ML models, illustrated by using neural networks to approximate thermodynamic relationships in industrial optimization. Pattern 3 addresses systems with no governing physical laws, where ML learns behavioral patterns from data and feeds them into constrained optimizers. The core thesis is that ML excels at describing reality from data while optimization excels at choosing actions under constraints, and the two are most powerful when each handles what it does best.