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by JohnLeM
April 4th, 2019, 7:34 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

CMIIW, but your method looks to me like a meshfree method with a kernel function used for regression (couldn't you replace it with another universal approximator? NNs?).  CMIIW?  It is a meshfree method with a kernel function, hence you are right, this is nothing else but a regression model. But wh...
by JohnLeM
April 3rd, 2019, 12:28 pm
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

I see. Thus Lagrangian Meshfree methods are Neural Networks ones ? I was just saying that I can design finite difference schemes with NNs approach. But I sincerely  hope that this bridge between NNs and finite difference methods has already been noticed before. Backpropagation is simply automatic d...
by JohnLeM
April 3rd, 2019, 12:17 pm
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

If you want publicity then you need to show that your ML could negotiate with the EU.
We have a chance, Brexit is a finite difference problem !
by JohnLeM
April 3rd, 2019, 7:24 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

All right guys, but can your FD scheme play chess?
No, cuchullain and I are about to launch finite-difference skynet. Bye human kind !
by JohnLeM
April 2nd, 2019, 8:34 pm
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

I was just saying that I can design finite difference schemes with NNs approach. But I sincerely  hope that this bridge between NNs and finite difference methods has already been noticed before. Remind us again. I missed it. The last time the details were missing AFAIR. Are you referring to approxi...
by JohnLeM
April 2nd, 2019, 7:19 pm
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

The crucial difference between NNs and kernel functions is that the first are parameterised and the second aren't (NNs can change shape). I quoted the chapter because it relates backpropagation to finite-difference method, AFAIR. You seemed to have said that ML is unaware of this correspondence. I ...
by JohnLeM
April 2nd, 2019, 4:23 pm
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

Good Heavens! For more than forty years I have been speaking NNs without knowing it.   Your conclusions are not only not right, they are not even wrong. That's not exactly what I am saying. I am saying that NNs are speaking about finite difference schemes without knowing it ! For instance, what I c...
by JohnLeM
April 2nd, 2019, 9:17 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

Good Heavens! For more than forty years I have been speaking NNs without knowing it.   Your conclusions are not only not right, they are not even wrong. That's not exactly what I am saying. I am saying that NNs are speaking about finite difference schemes without knowing it ! For instance, what I c...
by JohnLeM
April 2nd, 2019, 8:46 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

Never say that in ;public.
Flattery will get nowhere with me .. you say that to everyone.
Ok, I am apologizing. Me bad :/
But the conclusion is correct: NNs are just finite difference methods.
by JohnLeM
April 2nd, 2019, 8:05 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

This thread has lost focus. Some issues 1. NNs are rarely used in finance 2. NNs do not respond well to noisy data (gradient is all over the place). 3. Models get stuck in  local minima. 4. Models are too complex. 5. Finance data != 1024X1024X3 image. Cuchullain, NNs are nothing else but finite dif...
by JohnLeM
April 2nd, 2019, 6:39 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

I understand your last paragraph as saying that I could price different derivative payoffs for the same underlying price process, right? Yes. For instance in this post , you can see this effect: the samples points are computed within 20 secs (a 12-th dimensional process AFAIR). Then a portfolio of ...
by JohnLeM
April 2nd, 2019, 6:34 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

What do the sample points depend on?  I can here use NNs vocabulary : samples points mainly depend on choosing a RELU or a Radial Basis function, or whatever basis AI guys could invent to compute your sample points (or grid point, or NNs). Interestingly enough, this choice also determine the capaci...
by JohnLeM
April 2nd, 2019, 6:24 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

Another question: what about the greeks? ISayMoo, for the same price (I mean the same number of CPU operations), we can compute all the greeks you are able to dream about. We can also propose new sensitivity indicators: for instance some kind of reverse deltas or reverse gammas, that are the sensit...
by JohnLeM
April 2nd, 2019, 6:15 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

What do I need the PDE solution for, once I have my valuation? 1) Valuating means solving a Kolmogorov PDE equation. The link between Monte-Carlo methods and PDE is the Feynman Kac Theorem. 2) Monte-Carlo methods can't handle non-linear behavior (eg american options, or complex strategies). A PDE c...
by JohnLeM
April 2nd, 2019, 6:01 am
Forum: Numerical Methods Forum
Topic: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?
Replies: 327
Views: 12503

Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

I see. OTOH using Sobol numbers would cost me \epsilon^{-1}, so your method is in between the two? There are a number of problems occuring while using Sobol numbers. You mainly can't rely on them for low-number of samples (small N). Quite interestingly, we can compute efficiently low numbers of Sob...
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