• C++ Programming for Financial Engineering
    Highly recommended by thousands of MFE students. Covers essential C++ topics with applications to financial engineering. Learn more Join!
    Python for Finance with Intro to Data Science
    Gain practical understanding of Python to read, understand, and write professional Python code for your first day on the job. Learn more Join!
    An Intuition-Based Options Primer for FE
    Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models. Learn more Join!

Deep Learning (DL) and Partial Differential Equations (PDE)

Daniel Duffy

Daniel Duffy

C++ author, trainer
Joined
10/4/07
Messages
10,335
Points
648
PDE are not immune to the DL revolution it seems.

Here is a random example.

Neural networks for solving differential equations – Becoming Human

My suspicions is DL for PDE is a solution looking for a problem. Both articles has major major issues on many levels.

A certain amount of intellectual rigor and honesty is needed. Caveat: part of my research was (and still is) PDE/FEM/FDM both in academia (convergence in Sobolev spaces) and industry (oil/gas etc.) in this area.

I just don't get this stuff. Much of it is very confused. (e.g. The Galerkin method went out of fashion around 1943).
 

Attachments

Last edited:
Daniel Duffy said:
PDE are not immune to the DL revolution it seems.

Here is a random example.

Neural networks for solving differential equations – Becoming Human

My thesis is DL for PDE is a solution looking for a problem. Both articles has major major issues on many levels.

A certain amount of intellectual rigor and honesty is needed. Caveat: part of my research was (and still is) PDE/FEM/FDM both in academia (convergence in Sobolev spaces) and industry (oil/gas etc.) in this area.

I just don't get this stuff. Much of it is very confused. (e.g. The Galerkin method went out of fashion around 1943).
Click to expand...
I was in a CNN + PDE seminar today at NYU and basically this guy was describing how we can view deep learning as an ODE (stability and numerical ODE problem) as a PDE when the feature space is an image.

I couldn't grasp the full gravity of it, but here is some relevant input from the seminar:
[1705.03341] Stable Architectures for Deep Neural Networks
[1703.02009] Learning across scales - A multiscale method for Convolution Neural Networks
https://arxiv.org/pdf/1704.04932.pdf

You can also contact the guy who gave the lecture -- he is assistant professor from uni of Emory in Atlanta, he was young and very friendly. His name is Lars Ruthotto:
Lars Ruthotto | about

This might not address your question directly, but by looking into NN-PDE connections maybe you can get a better idea how to approach your problem?

Hope this is helpful.
 
Paul Lopez said:
@Daniel Duffy has deep learning come up very often in PDE solving from what you've seen? I wonder if the implementation gap in your view has improved any. Is it a decent/interesting enough path for research?
Click to expand...
I don't think so; it is not based on reality.
No future, at least not the way CS is approaching it.

I am not a betting man, but my money would not be on it.
 
Back
Top