Roman science was an extension of the Greek scientific tradition - indeed, most of the scientific thinkers of the Roman period were Greeks (or Greek speakers) living in the Greek-speaking eastern part of the empire.
One exception was Pliny the Elder, a senior Roman official writing in Latin. He compiled a huge collection of facts (interspersed with many fictions!) about the natural world. In many cases he sought to explain natural phenomena - for example, he was the first to realize that amber is the fossilized resin of pine trees.
Ptolemy of Alexandria (one of the great cities of the Hellenistic world) systematized Greek knowledge of astronomy. His theories of the movements of the heavenly bodies would have a profound influence on later European thinkers.
The doctor Galen also systematized Hellenistic anatomical knowledge; but he also extended this knowledge considerably, based on his own careful dissections of animals. He was the first to assert that veins carried blood, not air; and his writings formed the primary foundation for Medieval medical theory and practice.