An idea about AI in medicine:
Fecal microbiota transplants have been gaining prominence as we discover that many diseases seem to have a relation with the gut microbiome. There seems to be therapeutic potential for certain gut infections, inflammatory bowel disease, obesity, metabolic syndrome, and functional gastrointestinal disorders.
What if you could use new high-throughput sequencing techniques like Nanopore to figure out what kinds of bacteria constitute the microbiome of tens of thousands of people?
Combine this with tons of computational power and the latest machine learning algorithms to find relationships between certain illnesses and symptoms and those people's microbiome. Maybe this would allow finding the perfect fecal transplant donor to reverse the relevant symptoms.

Do you know of any research institutes that provide no-strings-attached, multi-year funding and are committed to open science? I’m looking for examples of metascience, where they experiment with new ways of doing and funding science.
Institutions like Bell Labs or the Princeton Institute for Advanced Study are the historical reference class.
Based on this article in the Atlantic, I am aware of these 3 and am looking for similar examples:
I'm not sure whether, for example, Arcadia fits that bill of no-strings-attached funding given their research agenda on non-model organisms. But it's definitely a new science org. Something like Hypothesis Fund (https://www.hypothesisfund.org/) maybe.
I'd recommend having a look at the Overedge Catalogue (https://arbesman.net/overedge/)
The Overedge catalog looks extremely interesting. Thanks!