In all honesty how did the Romans become so good at innovating in this TL. Cause OTL they were not good at it. They adapted a lot of other people's stuff and particularly by the 2nd century, there was very little creativity. Empires have a habit of stifling creativity, Rome was no exception. While a few innovations are fine, I'd like to ask what are the conditions in TTL that allowed so much innovation to emerge? It might have been elaborated before, but it would help to have it restated. I know a little about Military Academies, and technical engineering training introduced, and officials competing to innovate and share their novel inventions, but it still doesn't explain so much innovation springing up in every corner of the empire seemingly unrelated to these developments.
Well quite a few of the projects or innovations mentionned in the story so far have been OTL discoveries made more widespread (The trevery reaper, most hydraulic inventions -see Barbegual mill to see a large roman hydraulic complex of industrial proportions which worked from the late 1st century to the 3rd century-, even the windmills if one follows books such as Cesare Rossi, Flavio Russo and Ferruccio Russo's "Ancient Engineers' Inventions", 2009, ISBN: 978-90-481-2252-3). Others have been pure luck for the cases where there was no reason it could not have happened earlier : the stirrups for instance, initially just to help a wounded soldier mount his horse and then spreading, or the cast iron born from a smithy accident.
Then comes the academy, and that helps to disperse knowledge and bring the main cities of the empire all to the same level of knowledge, which is something that did not happen at the time, but also helps develop a new attitude toward mechanics and experimental science, but mostly based on elder, hellenistic, inventions. Thus for instance the experiments with steam engine, which are simply re-using inventions from a century before and thinkering with them until something new happens. And while is seems short for you the readers, there have been 40 years of change now, and patronage of the elite that see a new way to compete through those discoveries, in some way similar to Italian Renaissance nobles.
The academy also bring a scale which is larger than anything otl in this timeframe: even with an output of a few dozen candidates a year (initially training some 30 candidates/year, expended to twice that about a decade later), it means that the academy has trained some 2000 people by now, about half of which are active at anytime either in public or private capacity.
Between the boost in productivity brought about by the increased mecanization (and once more they are mostly just building OTL inventions but more of them) and the prestige war of the elites, many people see a good reason why investing in technology is a good idea. Add philosophical justification through contestation of Aristotle and some intelligent men agreeing to admit they were wrong and who try to set things right (Claudius Ptolemy, 10 years ago in story time), and you help remove an important issue.
This does not mean we have a full industrial revolution in our hands. If you looked at the documentary on the water raising system, you've seen how many days were spent just forging the metallic links that held the buckets together. It is a non trivial investment in time and materials, but it is being done. But overall there has not yet been a real agricultural revolution, nor are issues related to transport of goods solved yet : it would require either more canals or trains...
That is my vision at least, but I'm open to discussion/challenge/other opinions !