Learn Spanish (Latin America): Se sabe que este proceso predecible es tedioso. - It is known that this predictable process is tedious.

Both are grammatically correct, but the passive se construction (se sabe) is the standard, most natural way to say 'it is known' or 'people know' in everyday Spanish. Es sabido uses the true passive voice and sounds noticeably more formal or literary.

Why do we use 'es' instead of 'está' with 'tedioso'?

We use es (from the verb ser) because being tedious is presented here as a permanent, defining characteristic of this specific predictable process. If you used está (from estar), it would imply the process isn't normally tedious, but just happens to feel that way right now.

Could I place 'predecible' before the noun, like 'este predecible proceso'?

Yes, but placing the adjective after the noun (proceso predecible) is standard in Spanish to objectively distinguish what kind of process it is. Putting it before the noun (predecible proceso) makes it sound more poetic or subjective, emphasizing its predictability as its most defining, almost dramatic trait.

How would I change this sentence to say 'just any predictable process' using the structure from this lesson?

You would replace este proceso with un proceso cualquiera. The sentence would become Se sabe que un proceso predecible cualquiera es tedioso. Placing cualquiera after the noun phrase emphasizes that you mean 'any old' or 'just any' predictable process, perfectly capturing that sense of insignificance.