I want Houdini to refresh(render) the viewport every frame while the animation is playing.

From my investigation, Houdini calls GR_Primitive::render and DM_SceneRenderHook::render in two cases:
1. When the geometry data changes and needs to be updated.
2. When keyframes are added to the geometry or camera.
However, in my case, the geometry data does not need to change, and adding keyframes is not an ideal solution.

Is there an HDK function or parameter that forces Houdini to call viewport to render every frame(to make it time-dependent)? Or is there any built-in Houdini setting that can achieve this?

Might not be the "correct" way but you could create an unnecessary attribute let it equal to $F.