Agreed, this paper did not show any meaningful generalization and is sorely short on baselines. If you wanted to train a neural network model that would genera

Agreed, this paper did not show any meaningful generalization and is sorely short on baselines. If you wanted to train a neural network model that would generalize, you would need build in physical constraints into the model architecture. For example, dynamics are governed by a Hamiltonian based on pairwise interactions, which should be integrated as an ODE. A nice recent example of this from folks at DeepMind is this paper “Hamiltonian Graph Networks with ODE Integrators”: https://arxiv.org/abs/1909.12790 https://arxiv.org/abs/1909.12790. That said, if you go down this road too far you may find that you are just learning an approximation to Newton’s law of gravity, which we already know exactly! The interesting work in this space is finding appropriate interpolation problems inside the context of state of the art physics based models. In any complex simulation, there are tunable parameters and approximations that are suitable to replace with ML. If I were working on this problem, I would start by making a differentiable version of Brutus, and try to deeply understand its strengths and weaknesses. Neural nets are just high dimensional interpolation. The only reason why they are more powerful than “classical” ML is that you can fit them when embedded in an arbitrary computational graph, in which it is easy to embed prior knowledge (“differentiable programming” style). If you’re not doing that, you might as well just stick with the blackbox algorithms of Scikit-Learn.