"进行严酷的训练" 可以用英文表示为 "undergo rigorous training"。
"Rigorous" 这个词的意思是 "严格的，严谨的"，所以 "rigorous training" 就是指 "严格的训练"。
"Undergo" 这个词的意思是 "经历，承受"，所以 "undergo rigorous training" 就是指 "经历严格的训练"。
下面是一些英文例句和中文翻译：
She underwent rigorous training to prepare for the marathon. (她经历了严格的训练来为马拉松做准备。)
The soldiers had to undergo rigorous training before they were sent to the battlefield. (士兵们必须经历严格的训练才能被派往战场。)