Hello everyone.
I’m new to Pytorch and machine learning methods, so I hope I’m not asking a question that is too obvious. As part of my research, I am trying to develop a surrogate model that accurately captures the results calculated by the finite element method, but in a much shorter time frame (evaluating my finite element model is computationally very expensive). In particular, I am trying to mimic the scalar field response of a 3D surface defined by a mesh (defined by nodes and connectivities), the inputs being a series of scalar floats. As a first idea, I thought I could do this with a series of linear layers of neural networks with certain activation functions, but I realised that I would need a very large number of results to get a sufficiently high accuracy. My hypothesis is that the underlying field shape is somehow C0 and perhaps C1 continuous, so if I can somehow incorporate the information in the form of correlations between neighbouring nodes, I should be able to get the same result with a smaller number of outputs. I have seen cases in the literature where convolutional neural networks are used to replicate the results of finite element models, but in these cases they also use images as input data. In my particular case, the inputs are a few scalar values. In principle, it would be preferable for the method to work for a structured and unstructured model, but if it were only for a structured model, it could work for me. Do you have any thoughts on an ML based approach or method to incorporate this correlation between neighbouring nodes? Any suggestions or ideas would be very welcome. Thanks in advance for your help.