for random homohaus equations.

This is a joint work with Professor Bao

from Zhejiang University and Chao

from Urban University of US.

And one of my former PhD students

and Gao is the current PhD student.

The talk have two parts.

First, we introduce random interface grading.

We propose some new macro method

to give the fashion of preservation

and also the variance of preservation.

Second, we use the machine learning

for the inverse acoustic scaling problems.

We use the CNN to solve this obstacle problem.

Then we give the conclusion going work.

First, we introduce the motivation for the grading problems.

The design of grading is in an army scale

while during the factory process,

there exists a small perturbation on the interface.

For example, the left-hand side picture.

On the right-hand side of the model, in the nature,

mirrors always take the form of layers.

The interface of layers always across several meters.

Which is a small perturbation

with respect to a whole minor else.

So we consider the small perturbation around the interface.

For the deterministic grading problems,

Professor Bao set up the mathematical models in 1995

and several worker continue on these topics.

On the other hand side, for the random interface,

CNN-K firstly introduced the so-called fiction domain

to deal with random interface equations.

And several worker on this topic,

we only consider the grading problems

and the Maxwell equations.

In this talk, we present the work of these grading problems.

This is the geometry of the grading problems.

From the left to the right,

we have the periodic constructions.

And the theta is the insidious wave from the omega one

into the omega, omega zero,

and then transparent to the omega two.

We zoom in the omega zero domain, like this way.

We have an interface on this domain.

Substituting the two domains,

one is omega minus and the other is,

one is D minus and the other is D plus.

And we have a boundary condition on gamma one, gamma two.

And the periodic boundary condition on gamma three

and gamma four.