The pictures you show appear to be the Library of Ephesus, a ROMAN building.Greek:
The library of Celsus is an ancient Roman building in Ephesus, Anatolia, now part of Selçuk, Turkey. It was built in honour of the Roman Senator Tiberius Julius Celsus Polemaeanus (completed in 135 AD) by Celsus' son, Gaius Julius Aquila (consul, 110 AD). The library was built to store 12,000 scrolls and to serve as a mausoleum for Celsus, who is buried in a crypt beneath the library. https://en.wikipedia.org/wiki/Library_of_Celsus
Next to it is the Temple 17, a 4th century Gupta period construction considered to be one of the earliest Gupta temple. According to John Marshall, this elegant temple conveys the genius of the people of that time and helps us understand the evolution of Indian temple architecture. The flat roofed temple with sanctum (garbhgriha) and portico (mandap) is known for its symmetry and proportions. This temple heralds the arrival of engineering and artistry that will go into the building of temples from here on. Sanchi ? of Serene and Secluded Stups | Ghumakkar ? Inspiring travel experiences.
the thing is, indian architecture from pre islamic periods has been never properly researched, an amateur like me can spend some time and find out the truth. These facts have been known for decades if not centuries, but no indian or western scholar has the guts to accept the facts. The whole idea of indian architecture of what's native and what's foreign has been completely based on colonial assumptions of indian architectureThe use of arches for roof construction is one thing, which is certainly not local to the Indian subcontinent. And even then, most of what one studies are regional and local not representative of a 'national' trend, as we see in Byzantium, the Omayyads in the Levant and in Spain, and even in the Persians and later the Moguls in Northern India.
To speak of the 'roof of a hut' as a precursor to Gothic arches in Europe is incredible and could be a breakthrough in the history of architecture if it was plausible, but other origins, nearer home, dismiss that notion, and so many others that bear no relationship to the History of Architecture.
it is said they are persipolis influenceThe Yavana (Ionian) influence on the Buddhist architecture (columns)
The Greek Influence in the western Deccan region of Maharashtra is usually implied in the term yavana from Ionia or Saka from the Scythians. Gopalachari's 1941 thesis on "An Early History of Andhra Country" provides a rich internet source for yavana history in the Western Deccan. There is evidence for a large element of yavanas in the western Deccan about from about 250 BC which is about the same time as the time of the Bhaja and Bedsa Caves. These yavanas were thoroughly "Indianised" , (if that is the word for that time), adopted Buddhism and Hindu family names. There was a Yavana settlement in a place called Dhenukakata in the vicinity of Karla which is close to that of Bhaja and Bedsa Caves.
There is believable evidence for a strong Greek/Ionian influence around the time the caves in Bhaja/Bedsa were being built. Similar crafting expertise from the builders of Persepolis/Xerxes complex seems to be evident in these caves at least as far as the outer pillars of Bedsa caves are concerned. The petal-like structure, of the capital, many times described as an inverted lotus flower, is found sometimes at the base of pillars at Persepolis (see Fig 4 of Plate XLIX of the Persepolis figure above, or the oneby its side). Vidya Dehejia would call the enclosed fluted torus-like sphere on top of the 'bell' as an enclosed amalaka, which is an ellipitial and fluted crown that is supposed to resemble the fruit amlaka or aamla the Indian gooseberry. The aamlaka feature on Hindu temples is uually on the top of the highest tower and the main or presiding deity is housed under the aamlaka. The petalled capital of Bedsa has an enclosed aamlaka which is unusual and probably has no religious significance. Such influences were short-lived and by the time the rock-cut caves in Nashik were made after the first century A.D., the 'bell'-shaped inverted Lotus flower with petals form of the Bedsa caves (with Sanchi influence) had become just an inverted 'pot'.
It has been noted that the influence of the Sakas and Yavanas in the western Deccan had completely diminished after the second century A.D. when it was replaced by the Satvahana dynasty. It seems that a Satvaahana Andhra king Gotamiputa SirinSatakani, of the second century AD, to whom the epithet Saka-Yavana-Palhava-nisudanasa applied, drove out these casteless foreigners from his newly rebuilt empire. He also preserved the purity of the four castes by stopping mixed marriages between them. In the context of this blog it would mean that the skill of the immigrant labourer was lost. The petalled 'bell' of the capital at Bedsa became an inverted pot.
Caprarius Aquacorn: Bedsa Caves : Speculations on Bedsa symbols and pillars