Is it possible to weakly solve Atomic Chess as a win for White? I've analysed a few lines good for White, but I am not sure about a general solution.
As a decently strong atomic player fairly connected with the atomic community including the strongest players, I feel I can answer this one. The short answer is: white probably wins, but there is no weak solution nor does it currently seem achievable to find one.
The current consensus among the strongest players and opening theoreticians is that White wins, but as of yet there is no public and/or convincing and exhaustive proof. Opinions differ on whether many different openings and lines are winning or drawn; however there tends to be agreement that the lines after
1. Nf3 f6 2. Nc3 Nh6 3. g4 (the first tabiyas in this rabbit hole would be after
3...c6 4. d4 e6 5. e4 f5 6. Nh4 or exf5 with many sideline branches on black's 2nd, 4th and 5th moves) give no hope for black if white plays perfectly (and by "perfectly", that tends to be 20+ move deep, widely branching theory in complicated middlegames, leading to nontrivial endgames). That said, from a practical point of view, these are also not easy to meet as black at high levels.
This, however, does not constitute a weak solution. We do not have an exhaustive (or even very aggressively pruned) game tree that leads to white wins everywhere. All we have is a lot of opening theory where both sides play sensible moves and where with precise play by white, just about everything leads to what seem to be winning white endgames. The branching factor for plausible moves appears to be too high for a weak solution to be within reach, though -- in addition, the endpoint endgames themselves may not be easy to evaluate for humans, and not for engines either.
A word on engines
The modern engine for atomic analysis is Stockfish 9, but using the 2018 or earlier builds, as more recent builds seem to give pruning issues leading to outright blunders and misevaluations in certain cases. Other engines exist like Atomkraft (an older engine), and offer different but also strong opinions.
A major shortfall of atomic engines in general, though, is their endgame knowledge is poor. One commonly-occurring situation is a pawn endgame where one side is up a whole bishop, yet cannot win because the bishop cannot take an enemy pawn, nor can passed pawns be created. This is known as "pawnitisation" (common enough to have a name since more than a decade ago!) and engines cannot detect this reliably, often giving a +3 to +4 evaluation to draws. They also, due to the horizon effect, tend to misevaluate simple endgames where one side is up two pawns for minor (yes, up) with rooks on the board, which is winning in general but can take many moves.
While 6-man tablebases exist for atomic, these do not solve the problem; many of these endgames have more than six units on the board.
This leads to the issue that engines, despite being stronger than humans (still not completely invincible though!), may not be fully relied on to accurately evaluate a position.
An engine-only "solution" of atomic would be met by skepticism due to their inability to accurately judge a fair number of endgames. In fact, even an engine-assisted weak solution would seem unattainable, also because of the high branching factor of plausible moves, and high depths (think at least 40+, probably more than 60+) needed for reliability.
I know there is at least some degree of theory in Atomic Chess, which indicates it hasn't been solved. Also from this Wikipedia article:
Under the "Strategy" section, it says "no attempts to prove a win for White have been successful". Although the article notes that White's advantage is much larger in Atomic Chess than regular chess, which obviously makes sense.
There's a version of Stockfish out there that can play Atomic Chess. I doubt it's as strong in the game as regular Stockfish is in chess, but it shows that even with strong tools available the game seems to have not been solved.
I don't know whether it's possible to solve it in the future though. It's highly unlikely regular chess will ever be fully solved, due to the sheer complexity of the game tree. For Atomic Chess though, maybe it's possible that there's some forced win (or forced draw?) relatively early on. This could be due to a few reasons:
As noted already, White has a larger advantage in Atomic Chess.
Pieces tend to come off the board faster, due to the explosions when a piece captures. This reduces the branching factor (i.e., number of possible moves), which reduces the complexity of how many paths need to be considered in the game tree. It also simplifies the game, potentially bringing it closer to some theoretically drawn endgame (in atomic chess).
While strong, I'm not sure how good this version of Stockfish actually is in Atomic Chess, since it was developed for standard chess. Our current engines could have to get stronger in the variant before finding a hidden solution.