I am currently performing number-crunching using CUDA on my GPU, an NVIDIA GeForce GTX 1050 Ti. These operations often take months to complete, and during that time I leave my PC on 24/7.
Is doing so safe? Am I risking a potential overheating of my graphics card that might result in (worst case scenario) a house fire?
Note that the PC is correctly ventilated and there is no obstruction to its air flow.
Short answer: This should be safe on well-designed hardware.
Long answer: The GPU (and its software environment: drivers, OS, daemons) are designed to protect from overheating - the GPU should first turn the fans to a higher RPM, if that can't keep a safe temperature then the GPU throttles the workload (usually by reducing the clock frequency). This will assure a heat profile that will not damage the GPU and thus not the PC (or the room).
Caveat: There exist cheap knock-off graphic cards, where the firmware is specifically designed to sacrifice safety for performance. While I don't think those exist for a 1050, I am not 100% sure. You should also prefer the Nvidia drivers downloaded from their website over "optimized" vendor drivers, which might do the same thing.
A house fire is extremely unlikely, but the lifespan of the card may be reduced.
Long-term overheating of the GPU chip probably won't start a fire. The chip may deteriorate and start misbehaving or die completely, but silicon chips aren't too flammable. Bad things usually happen when electrolytic capacitors fail and blow up, but these won't be subject to overheating just because the card is doing a lot of crunching and you also hopefully have a metal PC case to contain the hot shrapnel that results from such failures.
However, consumer-grade parts aren't in general designed for long-term 24/7 loads. It is thus fairly likely that the card will die sooner than if it wasn't subject to such loads. It is hard to say how much sooner without having some more statistics on a given model. Some people in the HPC community advocate using high-end gaming GPUs instead of special HPC compute parts, and there seems to be some economical sense in that. Although the commodity parts die in a year or so, it's cheaper to keep replacing them because they're many times cheaper than the alternative
Yes, the card is likely to wear out sooner if it is under constant load. At small geometries, Electromigration is a significant source of device failures, and devices will typically be designed with a specific target lifetime in mind. This might be generous for typical operation (e.g. 5 years continuous operation), but might not assume 100% maximum operating point for all of that time. As soon as you start over-clocking, you can expect that target to reduce significantly. (Equally, running at only 80% load would maybe double the lifetime due to this failure mechanism).
There are of course other failures which relate to running components hot, or thermal cycling, this is just to point out that modern electronics (and even 1980's electronics when badly designed) can be suceptible to 'wearing out'.
If your cooling system works OK, and your hardware is of any kind of even vaguely modern design that includes on-chip temperature monitoring and thermal throttling/suspend/shutdown, then it's entirely safe. It can't overheat so long as the cooler keeps running, and if that fails, the chips will throttle back until they're no longer producing more heat than can be passively dissipated (which may mean having to suspend completely, appearing like a hang/crash).
Worst case, if the throttling doesn't kick in fast and hard enough to compensate for accumulated thermal load, some part of the chip may end up melting or burning out, and you'll end up with a dead board, but by that point the throttling circuitry should have slammed into complete emergency shutdown, maybe even tripping a (temporary or permanent) fuse on the power rail, preventing any kind of runaway dumping of the entire input voltage randomly across the die and an actual fire.
Thankfully, the PC platform worked out most of the kinks in that kind of thermal protection system 10-15 years ago, after the minor scandal of some mid generation PIIIs and Athlons proving entirely capable of completely smoking themselves (and thus being a fire risk) if the cooler failed or fell off whilst the CPU was running at full tilt. One generation of chips later and it could be easily demonstrated that an overclocked high-end processor barely exceeded the maximum rated temperature at the heat spreader surface if you tore the heatsink and fan off right in the middle of a heavy benchmark... the computer slowed to a crawl or even suffered a "fatal" (to the software; the hardware just needed the HSF replaced and rebooting) crash, but the chips survived and no risk arose. Hopefully any GPU maker worth their salt isn't going to be a decade and a half behind the curve, especially when their products can already run pretty close to their rated limits temperature-wise.
However, that doesn't make this kind of treatment entirely "safe" for the transistors on the chip. Heavyweight "number crunching" (Bitcoin? Protein folding?) using GPUs is by now a rather infamous way of literally wearing out the silicon. The combination of high voltage and current, continual switching billions of times per second, plus sustained high temperatures stress the components quite a bit, both the chips and the support parts like capacitors, so their operating lifetime can be reduced to barely two years in some cases, at least at full speed. They can then run on a bit longer if derated (maximum clock speed limited etc) and employed for less demanding purposes, like last year's games, but are on borrowed time once they start erroring out at maximum speed.
So it's not going to catch on fire, but I wouldn't bank on the card still being reliable past its third birthday in that employment...
As you have mentioned, ventilation is good, so no need to worry about this factor of risk.
Talking about the GPU, it will be worn stronger, than on usual office work for 8-16 hours a day, so when using on 100% 24/7/365 it is unlikely it will be able to work for 5-10 years and more. But you must also consider that the GPU can have a poor design of the cooling system of the GPU itself (not a PC overall), a bad overall design, software and firmware bugs, bad production quality or production defect(s) with different severity and defect rate - from single-instance defects to massive ones. These factors can make the heating worse, cause system failure, little lifetime, short-circuiting or even might cause a fire or make you electric struck. Some factors depend on the model and the revision, some are being gradually fixed with the software/firmware updates, some vary from one single item to another. Better choose models with proven reliability reputation with a proper revision (usually the latest possible). Also, it can have a bad influence and interfere badly with the other components, for example, by generating extra electric/electronic signal noise. Also, do not forget about the fact, that the thermal paste can gradually lose its qualities and make cooling worse.
I must mention, that the graphics card is not the only component to be considered, because a PC is a complex system and its successful work depends on the state of multiple components. Every single little, even if unnecessary and unused, bad component, even the floppy drive or some decorative lights may break the PC down or cause the problems close to the ones mentioned about the GPU. For example, a bad on/off button may cause shutdown or reboot. And now more deep about the key components:
Professional enterprise 24/7/365 systems and components are better designed for that and have a reserve on all the components, even CPUs and BIOSes, and feature hot-replacement of components or modules, but even they do not feature 100% uptime (close, but not equal), professional Nvidia cards are faster for CUDA (especially neural networks) but I do not think it is your use case.
Assembling the system is not less important, than the components themselves. Do not forget about any single action, do not make something wrong, do not make a PC like a stupid and everything must be fine.
Make sure no software will forcibly shut down, reboot the PC or kill the process. If you are a Win10 user, you may think there is no way of entirely disabling the updates, but there are workarounds and pieces of software on the Web for that (Warning: it can violate EULA).
Peripherals can also cause problems, like the PC`s components. For example, a bad or worn mouse can register a button press when there is no press.
About key external circumstances:
Summing up: There is no solid warranty that everything will be good (literally, only death is guaranteed) and anyway you must accept the risks (they never will be equal to zero), but having a good choice of components, proper assembling and not having bad luck in buying defected components allows you use the PC that way with lower risk, then the question author initially assumed, unless you are going to do it for years and years and expect reliability for 5, 10 and more years.
Is it safe to keep the GPU on 100% utilization for a very long time?
Yes. It's actually safer than using it for the intended purpose, that is playing a game once in a while.
The most wear (of the electronics) comes from mechanical stress from changing temperature. The components heat up at different rates, their thermal expansion coefficients are different, therefore every heat up, cool down cycle results in forces that try to tear the card apart, often resulting in micro-damages that accumulate and can eventually lead to failure. Don't be alarmed, it's supposed to take decades. (Unlike the infamous 2006 nVidia laptop GPUs that used wrong solder so the failures occurred soon enough to be noticeable within component's lifetime)
If you start your computation and keep them at constant rate, it's actually less stressful to the card, as it warms up and then stays there, without the thermal cycles.
The only parts that will see increased wear are the fans, which are usually easy to replace.
As to your plan on actual 100% utilization - 100% is inefficient. Learn from the lesson that cryptominers taught us: as you underclock and undervolt the card, the flops go down, but consumed power goes down even more. You'll get more performance per watt. And even better lifespan.
