Resources for Project Neural Nets – PDEs

Added November 2020

The file neural-networks-pdes.pdf is a draft of a supplemental Chapter 28 on neural networks for solving PDEs. It is pretty complete but it has no citations to the literature. See neural-nets-odes.html for a couple of references.

The files demo-square-with-hole-fragment.c and demo-L-shaped-fragment.c contains the definitions of the functions my_pde() and my_phi() for the the demos “Square with a hole” and “L-shaped”. Calculating the first and second derivatives of those domains' φ and u_exact functions by hand would be tedious and error-prone, therefore some of the code in those files were generated through symbolic calculation in Maple.

To produce graphical output out of this chapter's Project Neural Nets – PDEs, you will need the following files:

	plot-with-maple.c    plot-with-matlab.c

The plotting scripts produced by these files work fine if the domain's edges are parallel with the coordinate axes, otherwise they produce visible edge artifacts. Correcting these requires some effort. I will get around to it when find some free time.

---

Programming Projects in C