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Hi. How flexible/sensitive is this framework to the changes in geometries and meshes? For example, say I want to add/remove a feature, like a hole or a fillet, or place an obstacle to divert the flow or change the mesh resolution adaptively in an unsteady simulation.
This learns the operator of PDE. So it doesn't rely on mesh and is not resolution dependent. We see high fidelity super resolution capability in our method.
Thank you for your response! To understand how this works, I would like to use your trained model to run some simple CFD benchmarks, for example, flow past a cylinder shown in the attached Figure. Is the model available for use? Thanks!pic.twitter.com/ifuF7KSpbt
Great example. As @AnimaAnandkumar mentioned, the approaches are mesh independent. You may find it interesting to look at our generic deep operator learning framework as well,
https://arxiv.org/pdf/2003.03485.pdf …
which to the best of my knowledge is the first DL approach to learn operators
In the end, it's all the same. You have to use "some data" to train the NN model for the PDE operator, and that "data" must be based on some discretisation of the operator. So, whatever the discretion you used for generating the data is projected onto the operator NN model.
That's right. The discretization of the data does project into the model. For the graph-based methods, we sample random graphs from the data's discretization, in the hope to alleviate the effect of underlying discretization.
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