Subfields Of Sciences As Inspiration For Machine Learning Algorithms/Paradigms

• Perceptrons and Neural Networks were inspired by Models of Neuron of the brain. So Neuroscience is obviously a major inspiration.
• Genetic Algorithms, Genetic Programming, Evolutionary Algorithms are inspired by Genetics and Evolutionary Theory.
• Simulated annealing [1] Algorithm was invented for solving problems in Statistical Physics and later used in Optimization problems in Artificial Intelligence and Machine Learning.
• Reinforcement Learning was first studied in Psychology, more specifically in Behavioral Psychology. Now Reinforcement Learning is a branch of Machine Learning. 
• Statistics is the field most closely tied with Machine Learning apart from Computer Science. Many Regression and Clustering techniques from Statistics act as inspiration to Machine Learning Algorithms. 
• Bayesian Models, (Hidden) Markov Models were first studied as part of Probability Theory. 
• The study of Logic acts as the basis for many Knowledge Based Machine Learning Paradigms:
• Explanation Based Learning
• Relevance Based Learning
• Inductive Logic Programming

References:

1. Simulated Annealing - Wikipedia