Recently looked into state of earthquake predicting and was somewhat shocked / horrified.
One of the best experts we had, Jim Berkland (who was highly controversial), pioneered to this day one of the most empirically supported techniques for predicting earthquakes...missing cat (specially cat) notices in the newspaper. The guy only had a BA too. I was horrified when I read this, but significant enough results were achieved and the field is just about devoid of anything with predictive power currently sadly. Also the underling statistics were done in the early 1980's and forms of media change, so I'm not sure if the technique would even yield usable results today.
Other things that are interesting about earthquakes:
1. The moon plays some role. The gravitational pull of the moon is enough to influence the tension on the crust. Scientists have struggled to yield anything predictive from this, but the math suggests the forces must have some effect
2. Plate tectonics plays less of a role than previously thought. The classic example is China. No major plate boundaries where new crust is being formed (like off the coast of Japan) or of volcanic hotspots (Hawaii), yet an absolutely devastating history of earthquakes that are well recorded going back 3,000 years or so.
3. The influence of large weighted bodies on earthquakes. Again back to China, where it is thought, and the Chinese Academy of Sciences has done fascinating research, that big enough fans form pools of water that destabilize the underlying crust.
Note this (larger?) study from 2013 found no correlation and is not referenced in the article linked in the OP, which seems to cover very similar ground.
Interesting. Made me think of the discovery that solar activty changes the rate of radioactive decay on earth by unknown mechanism from about 10 years ago.
The University of Auckland has developed a CubeSat specifically for measuring ionospheric disturbances and researching whether there is any relation to earthquake activity. They aren't looking at solar proton activity specifically but nonetheless may find something interesting.
Scientific Reports is low quality online mega journal with increasingly bad reputation. Their peer review is a joke and they publish junk science.
Here is Derek Lowe's opinion: More on Scientific Reports, And on Faked Papers https://blogs.sciencemag.org/pipeline/archives/2016/06/15/mo...