I have recently applied for a grant which offers a sizeable amount of GPU time. Here is an explanation of what would be pursued with that, since in the grant proposal itself I haven't mentioned it. (I don't have to tell you that the applications for this technology are infinite). Here is just what comes off the top of the mind.
We have obtained the GPUPlan algorithm and are attempting to compile it against modern libs. It is a hybrid SSD / GPGPU planning system which can optimally solve extremely demanding planning problems and games, like checkers. This is going to be applied to contingency and other types of planning for the Free Life Planner (https://dev.freelifeplanner.org (under construction)) (https://d-nb.info/1098312694/34) (https://www.aaai.org/ocs/index.php/ICAPS/ICAPS11/paper/viewFile/2699/3159) (https://github.com/aindilis/gpgpu-planning)
There are indeed GPGPU based implementations of Datalog (http://www-ps.informatik.uni-kiel.de/kdpd2013/talks/martinez-angeles.pdf), which is very similar to GDL the Game Description Language, used in the General Game Playing competition. This affords the possibility of Monte Carlo search and also theorem proving search.
Also, GPGPU based model checkers are in existence and would entirely solve many optimization and planning problems. For instance, subsets of program synthesis.
There is AlphaZero type training on games like Chess and Go. As the author of the Free Life Planner (https://frdcsa.org/~andrewdo/WebWiki/FreeLifePlanningCoachSoftware.html) (https://frdcsa.org/~andrewdo/writings/homeless-story.html), which has a considerably larger branching factor than does say Go, I am very interested in this training procedure.
There are numerous opportunities here. First is to package the various common NLP tasks such as parsing for which FLOSS code has been offered. An example would be puck (https://github.com/dlwh/puck)
Secondly there are opportunities to apply semantic text enrichment (including lexical, background/world knowledge, etc) to text and then using GPGPU-based machine learning algorithms to optimize a number of text processing algos, such as classification, information extraction, textual entailment recognition. In fact the opportunity is so great here that it really relegates existing approaches into obsolescence.
There is also textual prediction and authoring. This has application for Natural Language Generation, textual prediction for context sensitive help systems, grammatical inference and induction, etc.
im2markup based translation of mathematical images into LaTeX and finally into Mathematical Knowledge Management systems with formal verification through automated theorem proving. http://www.cs.chalmers.se/Cs/Research/Logic/TypesSS05/Extra/wiedijk_2.pdf
Human Activity Detection
3D Scene Reconstruction