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Comment by college_physics | Hacker News Reader

> Will ML models replace or just augment traditional simulations?

Its bizarre to even pose this. Where will the data on which the ML will be trained come from? First principles simulations might be "inefficient" but this is the price to pay for generating insights ex-nihilo.

The interesting question is indeed "augmentation": can we use ML models to improve the efficiency of first principles simulations via some sort of feedback process.

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> The interesting question is indeed "augmentation": can we use ML models to improve the efficiency of first principles simulations via some sort of feedback process.

Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations, https://arxiv.org/abs/2010.00072

very cool.

It's been quite a while but I have some very fuzzy memories of a lab I worked with in undergrad working on some sort of optimistic methods for solving PDEs, something along the lines of speculatively projecting into a lower dimension space where you can tell if the projection has become inaccurate.

This was well before neural nets were hot and the term 'machine learning' was fresh on the horizon. I believe the problem largely revolved around discovering the best set of basis functions to project onto.

I don't remember if there were provably 'best' projections but if not, there might be something interesting there

Using Neural Networks to solve differential equations have been a hot topic under Physics Informed Neural Networks at the last few NVIDIA GTCs. And arguably my work can also fall under a similar umbrella as well. So your lab was definitely before the curve.

There are ML models that solve hyperbolic and parabolic PDEs pretty well right? I’m aware of some interesting full-physics simulations that are modeled to be solved with this class of PDE.

I don't know how you would classify this for replace vs augment. However Neural Network force fields which replace traditional forcefields in simulations are and have been an active area of work. There are plenty of examples but I'd say most notable are Deep-MD by the Weinan E lab of Princeton (they even have a docker file on NGC), the work of Behler and derivatives, and probably more towards the direct replacement, TensorMol which I've seen some recent movement on.

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