In a way or to an extent that cannot be explained(adverb)
Wiktionary.org : Text is available under the Creative Commons Attribution-ShareAlike License
Use "unexplainably" in a sentence
"Following the Iraq war, they were unexplainably protected by the U.S. forces -- presumably because the Bush administration, with its less than profound understanding of Iranian political dynamics, wanted to keep the MKO as a potential weapon against the Islamic Republic."
"Never has a door unexplainably swinging a few inches in either direction caused me to freak out as much."
"She replied that she had been feeling unexplainably sad."