FYI, Matlab can train NN with Levenberg- Marquardt. There’s also a 90s software called neuralLab which has some interesting optimizer for NN. I just realized that  for engineers it’s beneficial to  take a look at some older tools. Framework like pytorch/tensorflow are more tailored for modern DNN applications. They might not be suitable for engineers (I mean, non-CS engineers). The only second order optimizer in pytorch is LBFGS. The reason why they don’t implement algorithms like Levenberg- Marquardt is they have DNN applications in mind, which these algorithms are not suitable for. But it could be a different story in some other fields.