# Is there any known technique to determine a graph from a 1D signal pattern?

I'd like to evaluate the possibility of using a Machine/Deep Learning technique as a sort of pattern recognition and parameters estimation.

The problem I want to address can be stated as follows: Let's consider that I have a set of interacting "particles" that can be represented as a graph in which the vertices represent the particles and the edges the magnitude of the interaction amongst them. For instance, in the diagram below I'm showing a particle graph formed by 4 interacting particles.

So each particle/vertex has a value (e.g. $$A=3.1$$, $$B = 4.2$$, etc.) and each edge contains the magnitude of the interaction between two connected nodes/àrticles (e.g. $$AB = 5.3$$, $$AC = 1.1$$, $$DB = 0$$, etc).

With all this information, there exists a quantum mechanics algorithm that, after some complex calculations, results in a 1D signal (the pattern; essentially a vector of X-Y values). The overall process is illustrated in the figure below:

The appearance of the obtained signal will therefore depend upon the values of the graph. The goal is, in this case, the inverse problem: given one of these 1D signals (that is, a characteristic pattern), is it possible to determine the graph with its corresponding values?

I could create a training set formed by a very large number of simulated graphs with corresponding 1D patterns.

Since my experience with ML has so far focused only on simple classification problems, it is not clear to me which ML method would be more convenient or whether or not this problem can actually be addressed by an ML technique. Any general recommendation or advice would be highly appreciated.

• To put in other words what you ask: Given RMN signal is it possible to identify the molecule? – penkovsky Mar 11 at 11:26
• Not really, this is not about molecules. It is about a graph which actually represents a spin system. A spin system can be part of a molecule, but they are not the same thing. – Jaldropio Mar 17 at 17:04
• OK. However, conceptually both problems are not that different, are they? We have a 1D signal and we would like to recreate a spatial relationship? – penkovsky Mar 17 at 17:32