Can hydroponic/aeroponic nutrients be home made (without relying on industrial chemistry)?

A simple compost tea will provide most of what you need. Mix in some manure into your compost. Don't use dog or cat manure or from any predator. I have two five gallon buckets I put tomato plants in every year. Compost tea is the only thing I add. My tomatoes do great and it's been nine years now.