Is Differentiable Programming Actually Necessary? Can't you just train the neural networks separately?

Is differentiable programming actually necessary, or can you just train the neural network in isolation against data and then stick the trained neural network into the simulation? We looked at this problem in detail in our new manuscript titled Capturing missing physics in climate model parameterizations using neural differential equations. The goal of this project is to understand temperature mixing in large eddy simulations, essentially columns of water in the ocean. I.e., can we take a "true"...

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