I work with a series of input materials labelled M (M1, M2, M3, …) and additional materials labelled add (add1, add2, add3, …). These materials are combined to produce a product with certain chemical elements, such as ele1, ele2, ele3, etc.
For certain elements, there is a mass balance where the amount of the element in the input materials contributes directly to the final product. In such cases, we plan to use linear regression models with only the data set M as input to predict the quantity of these elements in each input material (M1, M2, M3, …). It is expected that the coefficients obtained from these models represent the quantity of these elements in the respective input materials.
For other elements, however, the situation is more complex. The additional materials may influence the amount of these elements in the final product, and we cannot rely only on linear regression models with the data set M.
For elements that are influenced by additional materials, I run into a problem. The additional materials (add1, add2, add3, …) do not inherently contain ele1, ele2 and other specific elements. I don’t know how to find out the quantity of element 2 for each material (M1, M2, …) in data set M. I need to solve this problem with a data-driven method. Does anyone have an idea?