I have an Nvidia GT 1030 video card with the Nvidia 450 driver installed. My PC is connected to the TV via HDMI cable through a HDMI 2.0 Switch.

On a fresh install of Ubuntu 20.04.1 I have after reboot 2 audio devices in the Setting -> Sound -> Output:
1. Digital Output (S/PIDIF) - Built-in Audio
2. HDMI/DisplayPort - GP108 High definition Audio Controller

With the 2nd audio output device selected (HDMI) my PC plays audio just fine. But if I switch the HDMI switch to another computer and later switch back, the audio is back on device 1, the default, and I have no choice for device #2, HDMI.

My HDMI display comes back when I switch, but not my audio.

Any idea how to fix this?

I have an idea for testing purposes. It's really a shot in the dark.

Try running dmesg and piping the results to a file before making the switch, doing the same thing after switching back, and using diff or meld or a similar tool to compare the two files. I'm wondering whether the devices appear in both files.

If there are no differences, I'm not sure what it would tell us, but, if they are differences, it might provide a clue.

thanks for the suggestion. I didn't see any differences with dmesg. I used journalctl looking around the time of the switching and could see the event related to Nvidia GPU, but nothing specific to audio.

However, I did get it working. This was my development system and I frequently rebuild it for whatever I need and when I installed from the latest Ubuntu 20.04.1 ISO, it failed to install because of a known bug caused by installing with the include 3rd party drivers on install. So I started over with the "3rd party drivers during install" button unchecked and the install worked.

After installation, I updated all software packages and then enabled Proprietary drivers which in my case is only Nvidia drivers. At this point I still had the audio switching problem. However, when I checked for updated packages I found a few more and they were mostly Nvidia driver updates to version 450.80.02.

After that the audio has been available after switching HDMI signals, i.e. disconnecting the cable electronically.