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Why do you need a neural network when you have the Hamiltonian mechanics of the system modeled? I've always understood Langrangian/Hamiltonian mechanics to be

Why do you need a neural network when you have the Hamiltonian mechanics of the system modeled? I've always understood Langrangian/Hamiltonian mechanics to be methods of modeling the behavior of a system through the decomposition of the external constraints and forces acting on a body. In other words you can understand a complex model by doing some calculus on the less complex constituents of the model. I'm probably misunderstanding what the accomplished, but it sounds like they've increased the accuracy of a neural network model of a system, notably for edge cases, by training it on complete a complete model of said system.

joshlk 6y ago
For some systems even with the Lagrangian/Hamiltonian setup your solving differential equations with numerical techniques that has error. It might be that the neural networks has less error than the standard techniques. This is a guess.
- seesawtron 6y ago
  Hamiltonian NNs are not a new thing. There was a NIPS 2019 paper [0] that attempted to do that same for some toy problems. In general the idea of including model or context-based information into neural networks goes along the line of Kahneman's System I and System II of the human mind. System I is the "emotional" brain that is fast and makes decisions quickly while System II is the "rational" brain that is slow and expensive and takes time to compute a response. Researchers have been trying to develop ML models that utilize this dichotomy by building corresponding dual modules but the major challenge remains in efficiently embedding the assumptions of the world dynamics into the models. [0] https://arxiv.org/abs/1906.01563 https://arxiv.org/abs/1906.01563 [1] https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow
- deleted 6y ago
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- noobermin 6y ago
  To be frank, this should be the reference, compare to numerical integration and see which is better.
deleted 6y ago
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gajomi 6y ago
> it sounds like they've increased the accuracy of a neural network model of a system, notably for edge cases, by training it on complete a complete model of said system. Not quite. It's really just that they require the dynamics to be Hamiltonian, which would be highly atypical of the kind of dynamics an otherwise unconstrained neural network would learn. This is reflected in their loss function, the first of which learn an arbitrary second order differential equation, the second of which enforces Hamiltonian dynamics. I don't understand how this was considered novel enough to warrant at PRE paper. Here is a link to the paper: https://journals.aps.org/pre/pdf/10.1103/PhysRevE.101.062207 https://journals.aps.org/pre/pdf/10.1103/PhysRevE.101.062207
DrAwdeOccarim 6y ago
I love your comment. I follow, and appreciate it, but I could not help but think of this xkcd: https://xkcd.com/793/ https://xkcd.com/793/

joshlk 6y ago

For some systems even with the Lagrangian/Hamiltonian setup your solving differential equations with numerical techniques that has error. It might be that the neural networks has less error than the standard techniques. This is a guess.

seesawtron 6y ago
Hamiltonian NNs are not a new thing. There was a NIPS 2019 paper [0] that attempted to do that same for some toy problems. In general the idea of including model or context-based information into neural networks goes along the line of Kahneman's System I and System II of the human mind. System I is the "emotional" brain that is fast and makes decisions quickly while System II is the "rational" brain that is slow and expensive and takes time to compute a response. Researchers have been trying to develop ML models that utilize this dichotomy by building corresponding dual modules but the major challenge remains in efficiently embedding the assumptions of the world dynamics into the models. [0] https://arxiv.org/abs/1906.01563 https://arxiv.org/abs/1906.01563 [1] https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow
deleted 6y ago
[deleted]
noobermin 6y ago
To be frank, this should be the reference, compare to numerical integration and see which is better.

deleted 6y ago

[deleted]

gajomi 6y ago

> it sounds like they've increased the accuracy of a neural network model of a system, notably for edge cases, by training it on complete a complete model of said system. Not quite. It's really just that they require the dynamics to be Hamiltonian, which would be highly atypical of the kind of dynamics an otherwise unconstrained neural network would learn. This is reflected in their loss function, the first of which learn an arbitrary second order differential equation, the second of which enforces Hamiltonian dynamics. I don't understand how this was considered novel enough to warrant at PRE paper. Here is a link to the paper: https://journals.aps.org/pre/pdf/10.1103/PhysRevE.101.062207 https://journals.aps.org/pre/pdf/10.1103/PhysRevE.101.062207

DrAwdeOccarim 6y ago

I love your comment. I follow, and appreciate it, but I could not help but think of this xkcd: https://xkcd.com/793/ https://xkcd.com/793/