I rather meant that Cuchulainn is a renown author in mathematics and economy, while you haven't revealed your credentials (and nobody seems to recognise your input to give you the benefit of the doubt). Anyway...

https://arxiv.org/pdf/1709.05963.pdf
https://arxiv.org/abs/1804.07010
https://arxiv.org/pdf/1707.02568.pdf
(I've seen similar attempts in physics and chemistry.)

You asked about a new field - microsimulations of complex systems are a new field. I also wrote where I would use it.

My guess is that TDA could become the 'next wave' 

https://en.wikipedia.org/wiki/Topological_data_analysis

https://arxiv.org/abs/1708.07469

Here were my questions at the time
When I first saw this "note' I thought it looked good but on deeper inspection it turned out to be a train wreck/horrror show. Part of my research back then was proving convergence of FEM (finite element) in Sobolev spaces, later in TV design, oil and gas. So, It is very interesting to see how someone uses maths to meet DL half way. 

The background of the authors is DL and business (nothing wrong with that) but the article is riddled with errors that I don't even know where to begin:
1. The Galerkin method fell into disuse around 1943. More seriously, the article is really the MESHLESS method which has its own issues.
2. It is not even DL imo; just because you use a stochastic gradient method does not make it as DL.
3. "DGM is a natural merging of ML and Galerkin". Yes?
4.Details are missing (e.g. Table 1!!!!!!). 
5. I seems DL applications need some kind of analytic solution for training? PDEs don't have this in general.
6. "Approximate the second derivatives using Monte Carlo". This is fiction.
7. Major numerical difficulties can't be swept under the carpet. In fact, DL will compound them, e.g how to choose an optimal learning rate alpha (usually use Brent's method).

Your serve, Tinman.  Cheers.

I rather meant that Cuchulainn is a renown author in mathematics and economy, while you haven't revealed your credentials (and nobody seems to recognise your input to give you the benefit of the doubt). Anyway...

https://arxiv.org/pdf/1709.05963.pdf
https://arxiv.org/abs/1804.07010
https://arxiv.org/pdf/1707.02568.pdf
(I've seen similar attempts in physics and chemistry.)

You asked about a new field - microsimulations of complex systems are a new field. I also wrote where I would use it.

These authors did not respond to my questions.

Your serve, Tinman.  Cheers.

You're like a broken record.  You brought up AI, and only so you could post your extended critique for the umpteenth time.  Nobody on this thread has proposed it as a solution to anything.

I rather meant that Cuchulainn is a renown author in mathematics and economy, while you haven't revealed your credentials (and nobody seems to recognise your input to give you the benefit of the doubt). Anyway...

https://arxiv.org/pdf/1709.05963.pdf
https://arxiv.org/abs/1804.07010
https://arxiv.org/pdf/1707.02568.pdf
(I've seen similar attempts in physics and chemistry.)

You asked about a new field - microsimulations of complex systems are a new field. I also wrote where I would use it.

So wait, are you proposing we use DL to solve PDEs??  Maybe I'm blind, but I didn't see where you said you would use 'microsimulations of complex systems'.
And no you probably wouldn't recognise me, and I don't need your benefit of the doubt, thanks very much.
Anyone who would remember me left this forum a long time ago, that's probably why it's usually just the same small group arguing about trump and Brexit. Ho hum.

I wrote that in my previous post, I just didn't use the exact same wording (you said that you left how many years ago??). No probs, I don't give strangers the benefit of the doubt, or anything for that matter - certainly not for free.

What about methods which reduce the dimensionality of the PDE by either exploiting the structure of the problem or some separable approximations?

These are possibilities indeed. But no matter what techniques are used we reach limitations of the human brain to cope with the complexity.We need to solve a PDE in a hypercube and associated boundary conditions etc. There are certain results in 4-5 dimensions But to be honest they are not trivial.

I think that the curse of dimensionality remains intact. Richard Bellman has a good discussion on this topic in his Dynamic Programming.

These are possibilities indeed. But no matter what techniques are used we reach limitations of the human brain to cope with the complexity.

Isn't it the moment where we often ask machines to help us? Even if the DL algorithms are worse on 2D or 3D problems, they may end up the only option on 100D problems. Especially that they're relatively easy to parallelise and run on GPU clusters - unlike standard PDE solvers.

This is the perfect place for me to namedrop...talking of machines, on Sunday I had breakfast with Arnold Schwarzenegger and James Cameron. Ok, not 'had breakfast with' exactly but they did sit at my table in Starbucks right next to me. They were discussing the next Terminator movie. There's no better warning about what happens when we let the machines help us! BTW Arnie is showing his age.

It could have been worse; what if it had been Rocky. BTW I don't understand why Paul should be hanging out in Starbucks.

All those weightlifters in the gym will become balls of flab in later years.

These are possibilities indeed. But no matter what techniques are used we reach limitations of the human brain to cope with the complexity.

Isn't it the moment where we often ask machines to help us? Even if the DL algorithms are worse on 2D or 3D problems, they may end up the only option on 100D problems. Especially that they're relatively easy to parallelise and run on GPU clusters - unlike standard PDE solvers.

I'm with Paul. This solution is trial and error from initial problem up to the pearly gates of  GPU.
The problem is people don't understand the problem. Hopping from solution to solution is soul-destroying.

It could have been worse; what if it had been Rocky. 

I know! (Although ships have been known to change direction!)

They were discussing the next Terminator movie. There's no better warning about what happens when we let the machines help us!

This ship has sailed long ago.

You're gonna need a bigger boat. And possibly a different cargo.

Did Arnold say "Hasta la vista, baby!" for goodbye?