I have a material. Some property of a material depends only on its structure. I want to find a structure that maximizes this material property. The structure of the material can be represented as a two-dimensional array with real elements ranging from 0 to 1. Calculating a property is a very long and hard process, so I want to find the best material using the fastest method.
I tried the genetic algorithm (thank you ahmedfgad and a very similar problem is image restoration), but I need several thousand iterations to find material with property that suit me. Is it possible to do that differently and faster? It seems to me that reinforcement learning can help me (for example shape optimization), вut I can't think of a problem statement. What is an agent and what is the actions of the agent for my case?
About physics of the problem:
I study the transmission of shock waves in various materials with a complex structure. My material is a composite of several substances, and the real number is the normalized density of the substance. The structure of the material is unambiguously described by a two-dimensional array 2D array is the input of ANSYS (engineering simulation sofware), which numerically calculates the attenuation coefficient of shock waves. In this regard, both the density values and the geometric positions of the subtances are important. For example
([[0.59, 0.08, 0.26],
[0.85, 0.45, 0.42],
[0.28, 0.66, 0.43]])
and
([[0.85, 0.45, 0.42],
[0.28, 0.66, 0.43],
[0.59, 0.08, 0.26]])
is a different materials that have different attenuation coefficients.
Аt the moment the array is not very large. There is 15x30 cells. When I studied materials consisting of only 2 substances (elements of array can be only 0 or 1), ANSYS needed to do more than 10,000 calculations to find the structure that gives the maximum attenuation coefficient. ANSYS can be viewed as a black box. If you show it the structure, ANSYS calculates a certain number - the attenuation coefficient.
As a result, it turned out that the denser material should be located on the diagonal of my structure and in the corners of the structure. Also the problem has no symmetry. I expect that in a more complex case (namely, when the substances in the composition of the material have random density), the material also have geometric patterns in its structure.