OK, let's get one thing clear at the outset. Art is not science, and science is not art. That may seem like a pretty banal point but it's one that gets violated a lot in the liminal space between them. It's not enough to take a pretty function and put it on a graph for it to be artwork. (I'm talking about you, fractals).
It's not enough to take an interesting discovery and put it on stage for it to be art. That goes doubly when the plot is overwhelmed by a ham-handed attempt to demonstrate a (controversial) interpretation of the science through 'non-linear' plotlines. (I'm talking about you, Copenhagen). If I want a great, shimmering example of the fallibility of reconstructed memory, Rashomon is the touchstone; Kurosawa's film has nothing whatever to do with quantum mechanics per se.
Art is a commentary on life, and art that takes science seriously has to be a comment on science, full of metaphor and instability for it to be fruitful and interesting. A lot of art in this space is more commentary on technology than science; I include most all of SF. Nothing wrong with that, of course, I love SF. But commenting on the methods and techniques of science is rather different than commenting on hyperdrives, artificial intelligence or gene hacking.
So then what would it be to comment on science? What are the hallmarks of science? It's too much for me to get into a lengthy treatise here on that problem, but for a start we can point to carefully controlled, repeatable testing; analysis into smaller, simpler parts; and mathematization. These processes lead to theory formation that leads to enhanced powers of prediction. When prediction breaks down, science returns to the drawing board with further analysis, testing or revised mathematical theorization.
That's science in a nutshell.
Who are some artists that comment most incisively on this method? A few who come to mind are, in the visual arts, Chuck Close, Jennifer Bartlett, Agnes Martin and Jaq Chartier, and in opera, Phil Glass and Robert Wilson's Einstein on the Beach.
Close and Bartlett's work comes in a tradition of color and form analysis that goes back at least to the pointillist painters, most famously Georges Seurat. There are many ways to analyze form and color, but it's a comment on the science of optics and the physics of atoms to do so in terms of a more limited color palette and smaller dot-size. The large and complex is understood in terms of the small and simple.
Chuck Close is best known for his paintings of faces, done in very large, complex grids of dots. Note that Close often uses grids, not open canvas. A grid can be a comment on technology (e.g., the technology of the cathode ray tube or computer monitor), but it's also something that comes from mathematics, geometry, the gridded sheet of paper. A grid is a sectioning of the plane into a regular lattice. The sections can be counted and hence easily mathematized; an open canvas cannot so easily. A grid's analysis of space comments on the method of science.
Bartlett as well is known for her paintings on large, gridded panels. She analyzes painting into color, line, shape, and simple subjects. Simplifying subject matter is a hallmark of the scientific method of analysis; not in the sense that the scientist makes a subject more simple than it is, but rather that he or she tries to begin an analysis on the most tractable part of the problem.
Though she considered herself an expressionist, Agnes Martin's work is more directly minimalist: commentary on the grid itself and the color on which it lies. Personally, I find that the cold, Platonic purity of her canvases make them problematic as artwork; much of the most rigorous minimalism is that way, and it flirts with boredom. But there's more than a little of boredom in the obsessive accuracy in science.
Jaq Chartier (mentioned below) often uses the same grid, the same rigorously linear design, in her work. She adds another aspect of the scientific method: testing. Her pieces are in concept and execution test patterns of color bleed through a painted surface, and many of them, in particular her Sun Test series, include bleaching from solar exposure. In form I find her work reminiscent of the gridded surfaces of Close and Bartlett as much as they comment on scientific testing. It's the fruitful range of metaphor that makes her pieces particularly interesting.
To change gears, these artists bring to mind one work of artistic science commentary in the world of opera: Philip Glass and Robert Wilson's masterpiece, Einstein on the Beach. A work that premiered in the mid-70s, Einstein is an expressionist, dreamlike meditation on the great scientist's work and legacy. There's no attempt at a linear plot, and very little narrative of any sort. The work is supported by Wilson's highly demanding stagecraft and Glass's minimalist musical score. Glass's music is particularly relevant to the present essay. Along with nonsense poetry and short passages, Glass's lyrics are filled with numbers and solfège symbols: beat and note. In the same way that the grid analyzes physical space, beat and note analyze musical time.
Of course, such rigorous analysis, repetitive and obsessive, threatens to bore. I've never found it that way in Einstein, though I know many have; instead I've found it intensely meditative. But again, so too can science be boring in practice. It isn't always accompanied by brilliant stagecraft.
This is by no means intended to be an exhaustive treatment of the subject, rather a few short thoughts on what comes to mind. I'd be interested in other ideas!
(Click on images for larger reproductions).