Of course, predicting volcanoes in hindsight is easy. That’s going to bias any questions about what warning signs were there in any historical eruption.
Does Putin have a chief butler and a personal baker? He should get on this, if he does.
I think Putin probably has quite enough folks in his dungeons already. No need to encourage him further. Especially since (AFAIK) there’s not a current super-volcano threat within Russia.
All right, how about a giant reservoir of liquid nitrogen?
Well, prediction schediction. If the geologic event is long term we don’t care. The San Andreas Fault and the inundation of coastal Florida come to mind. We, as I see it, won’t do anything really about long term planning before imminent disaster renders it too late.
I recall a nice scifi story about scientists who spot a looming geological disaster on a planet they are studying. They mobilize a huge effort with much sacrifice to save these people and get someone across space to warn them. Well, ‘them’ is us and it’s the San Andreas, we respond, “yeah, we knew that. Nice of you to visit.”
I think you might have thought of something that would cost more than an actual supervolcano explosion. That’s impressive.
The question is, would it work? 
Why would it? What’s your rationale for suggesting it?
It’s really cold and non-reactive, and relatively common. Even when it gets very hot, it’s unlikely to contribute to ash clouds the way water apparently does.
Or what about a reservoir of some gooey non-reactive material that would coat the ash and keep it from traveling very high or far?
This issue WILL come up sooner or later, that’s why I’m curious. It would suck to reach the Singularity only to die by volcano ash shortly after.
To stop an eruption, you presumably have to provide something that has an equal amount of force.
Krakatoa, the largest volcano on record, is estimated to have had four times the force of Tsar Bomba, the largest nuclear device ever exploded, with a yield of 50 megatons. Four times that is 200 Mt.
How would liquid nitrogen have the counter-effect of 200 Mt?
It would be like…totally cold? But the ejecta is coming up so fast that it wouldn’t have much chance to lose heat to the nitrogen, and of course there’d be little loss of momentum, since liquid nitrogen is not especially dense or viscous.
You’re being misled by analogy with the puny sources of fire and heat we’re familiar with. You cannot “put out” a volcano. Nope, nuh-uh, no way. As Northern Piper pointed out, it would be like trying to “put out” a thermonuclear explosion.
Or how about this analogy… pretend you have a giant blob of magma. Suspend it in a vacuum at nearly absolute zero. Cover two thirds of it with a mixture of water and ice. Let it cool down for 5 billion years.
What? It still has volcanoes? 
Well actually they think the Earth’s internal heat is due to the continuous decay of radioactive elements; but I take your point. John Ringo wrote a series of military SF novels, the first of which features the building of a giant space fortress by melting a nickel-iron asteroid, inflating it and letting it cool into a metal bubble with (iirc) a four-kilometer thick shell. It occurred to me to wonder just how long it would really take to cool and I think “years” would be optimistic.
Maybe attach a bunch of long metal filaments as heat sinks, and hide the whole thing behind a planet or moon (out of direct sun) while it cools.
wouldn’t the internal gravity of something like that collapse it anyway, though? Four klicks of metal shell is a LOT of mass.
How do you hide it? It has to be in orbit around the planet or moon so it will be in the sun some times.
If it orbited a moon, you could put the base in reverse orbit around that moon, such that the moon blocked it from the sun as the moon transitted the sunny side of its planet.
Or just hide the whole thing behind Ceres ( or a giant piece of aluminum foil ). Whatever.
The magma under Yellowstone probably has some of those, too.
You’re going to need a lot of gooey non-reactive material. Previous Yellowstone eruptions have ejected at least 1000 cubic kilometers of stuff. You’re probably going to need at least a comparable quantity of whatever gooey stuff you’re planning to use. That’s a lot.
The ash doesn’t just come from the material that is on the surface when the volcano erupts. It comes from the magma and gases under the ground as well. You can’t prevent the ash from forming by just doing something to the ground, you’d have to do something to the magma as well. Lava is notoriously difficult to work with, and it, being above the ground, is going to be much easier to work with than magma.
Liquid nitrogen in the kind of quantities you’d need to make any difference to a supervolcano would probably be dangerous, too. Something that cold is inherently dangerous. Nitrogen in that kind of quantity is also dangerous. You can asphyxiate from breathing pure nitrogen, and it has happened from a spill of liquid nitrogen in an enclosed area. With that much liquid nitrogen, you might not need an enclosed area for it to be dangerous.
If we’re totally ignoring expense and practicality, why not buy homes elsewhere for all the people living in potentially affected areas? Any time the volcano looks threatening, send them all on a paid vacation elsewhere. Buying all of them condos in nice vacation spots is probably going to be cheaper and more feasible than the quantities of inert gooey stuff or liquid nitrogen that you’d be talking about. We can deal with the farming issue by building greenhouses in safe areas, if we’ve got this kind of money.
There’s also the problem that, if you’re spreading around cubic kilometers of gooey stuff or liquid nitrogen, you’re destroying a beautiful and unique area that literally millions of people like to visit every year. You’re wiping out a habitat for threatened and endangered species. You’re destroying a place where geologists can study supervolcanoes. Yellowstone isn’t the only one of these in the world that could explode. It’s not even the only one in the US, just the most famous.
The orbit of the moon around its planet is going to have a different time period than something orbiting around the moon. That’s a very complex bit of orbital mechanics, to make the orbit of the asteroid synch with the orbit of the moon.
Ceres is in motion, not static, and would be larger than the artificial asteroid. Ceres would have gravitational attraction to the asteroid. You would have to place the artificial asteroid close enough to Ceres to stay blocked by it, but that would likely be close enough that Ceres’ gravity would start pulling the artificial asteroid towards it, so that it would not be stable behind Ceres.
ETA: Sheesh. What’s a lawyer doing trying to figure out orbital mechanics? Where’s Chronos when you need him?
If you can create a giant space base by melting an asteroid, you probably also have the tech know-how to put it into any orbit you want.
And Ceres’s shadow extends farther away from it than any significant amount of its gravity.
This is actually a fairly simple piece of orbital mechanics, where by “simple” I mean “already solved by somebody else who had more free time than me”. Putting something in orbit around a moon with the same period as the moon’s orbit around its planet means putting it in the L2 Lagrange point between the moon and the planet. Unfortunately, this point is unstable, which means you’d need thrusters on your object to keep it there for any significant period of time, and it’ll also leave your object exposed to the Sun for a significant portion of its orbit, when both the moon and planet are “off to the side”.
The second solution is more practical: That’s the Sun-Earth (or Sun-Ceres, or whatever) L3 Lagrange point. It’s still unstable, but now at least you’re going to stay behind your planet all of the time. And in fact, some spacecraft are in fact launched to the L3 point, or its vicinity, for that reason.