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Thanks for the comment Hamza, It's hard to say. I think it's unlikely you'll find many particularly useful direct applications of Dirichlet energy minimisation in data science, but the general problem of energy minimisation can be used to solve a whole range of tasks. Check out this video for an example: ruclips.net/video/-uXFYpVumh4/видео.html It's possible you could also use gradient flows as a theoretical tool to understand neural networks. See for example this paper from Michael Bronstein's lab on GNNs: arxiv.org/pdf/2206.10991.pdf

Thanks for the comment Hamza, To address your question: It depends on the particular scenario you are applying inverse optimisation to. In this example I show an algorithm for solving the inverse knapsack problem with the infinity norm penalty. Depending on the application it may be undesirable to use the infinity norm to measure distance from your estimate y vector. But this is really an implementation detail, so really this could be changed to suit the problem. In more general inverse optimisation problems, it's unlikely that you will have a perfect understanding of the constraints (i.e. the forwards feasible set). The consequence of this is that you have to also estimate the constraints in some way which could mean the forwards feasible set ends up being empty (and therefore the inverse problem won't work either). Typically inverse optimisation problems are also more computationally expensive than their forwards counterparts (since usually you solve the forwards problem during the running of your inverse algorithm). In the video you can see at the end how the time complexity of this IKP-infty algorithm is O(nC * log kmax) rather than the forwards problem which is just O(nC). So that's another consideration.