Find the answer in turn, it's not so easy

This article is produced by "Light Popular Popular Popularity"

Writing: Jiao Shuming (Pengcheng Lab)

Review expert: Zuo Chao (Nanjing University of Technology)

In a spacious kitchen, there are all kinds of kitchen utensils. Of course, there must be a superb chef. There is a potato, one eggplant, one green pepper, three onions, one onion, and one on the table. Two or two edible oils, two spoons of soy sauce, a spoon of starch, and a spoonful of salt. In a blink of an eye, all ingredients and seasonings are processed into a hot and delicious land. If these raw materials are regarded as the input of a mathematical function, the well -made land three is the output of the function. The process of using various tools to cook is the function itself.

Figure 1: A plate of authentic Northeast Sanxian

Photo source: Light Popular Popularity Square/Veer

Of course, there are many types of functions, and some are very simple. For example, just add two numbers together. The two inputs are 2 and 3, the output is 5, and some are very complicated. For example, the complex function model predicts the global climate change. The reverse relationship between the function input and output is also very delicate. If you give you a plate of fresh, you will probably be able to see that there are potatoes, eggplant and green pepper, and tell the raw materials of "function input". In other words, this function is basically reversible from output to input. Of course, if the chef encountered is dozens of generations with ancestral feasting recipe, it is really difficult to fully restore the input. But for the function of harmony, telling you that the output is 5, guessing that the input is not difficult, and you will find that there are many possibilities in input, not only 2 and 3 can, 1 and 4, 0 and 5 can also ...

But there are also such functions that tell you that after the output, it is very difficult to get the corresponding input. Even if you just find one of many correct answers, it is difficult to search for all the input possibilities. Such a function is a "one -way lane" that goes without returning, which is equivalent to making the chef into a super dark dish that the familiar raw materials can not see the original appearance, which will produce irreversible output results. Such functions often cannot be directly expressed by a simple equation, but a code running on the computer can indicate the calculation process from input to output. Essence

MD5 and SHA-1 are typical examples of one-way function [1]. This one -way function is not easy to design. It requires specialized mathematical principles. Researchers have been found for many years. They are very widely used.

For example, you must face the stone scissors with others face to face. Have you ever thought about how to play on the phone? Can I still play with each other? If you and the other party turn around on the phone, you talk about the stone first, the other party must say the cloth, the other party said the scissors first, you must say the stone, whoever "takes up the machine" will win. Of course, you can agree with the other party. We are all "honest and good children who don't lie". I think about something in my heart, and we cannot change at that time. We can't change when we hear what the other party is. But who exactly said the truth, who said false words, how do you know?

Figure 2: Stone scissors cloth (guessing game)

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One -way function can show magical powers here, such as stones, scissors, and cloths with numbers 1, 2, and 3, respectively. Everyone adds the gestures they want to produce. ) Or 20NS5HS54JS (indicating scissors), and then input your own digital letters into one -way functions, which will get different output results. When the two play, first say that their function output results are used as a "anti -counterfeiting" anti -counterfeit and counterfeit The label ", because the input cannot be seen from the output, it is impossible to temporarily change the idea according to the other party's information, and then take turns to say what gestures they originally wanted and what the password it was set. If someone is suspected to cheat for the victory, you can use a function to verify whether the input claimed in the function is the corresponding output, so it is possible to play stone scissors on the phone fairly.

If you say that you can play stone scissors on the phone, you only need to verify the user's authority without saving the real personal information of the user. In the blockchain digital currency, you must ensure that only users who really dug mines can get rewards. Functions can play an indispensable role in these practical applications.

And more often, the functions we face are not as difficult to restore as the one -way function mentioned above. Although it is difficult to get input from the output, it is not impossible. It is not necessary to spend tens of millions of years to achieve supercomputers. Using a ordinary laptop around us is enough to do the task, but the calculation time we hope that the faster, the better. It can be used for one week without one month.

In the design of optical device, there are many tasks in this type, such as this multi -layer thin film structure in Figure 2 below [2], which looks like the two adjacent -shaped color of the Cantonese -style morning tea. Essence The red and white layers of the thousand -layer cakes are added with brown sugar and coconut milk, while the film device is stacked by many layers of silicon and silicon nitrite. Although each layer is very thin (tens of hundreds of nanometers, smaller than the diameter of human hair), how to set the thickness of each layer can be "related". We do not need to make each layer of thin and uniform as a thousand layer of cakes and look beautiful. Instead, it is necessary to optimize the design into appropriate thin thickness. For example, the first layer of silicon dioxide is very thick, and the second layer of silicon nitride is thin. The third layer of silicon dioxide becomes thicker ... Figure 3: Multi -layer thin film optical devices alternating with silicon dioxide and silicon nitride materials

Picture source: ACS Photonics 5.4 (2018): 1365-1369, FIG.2

Figure 4: Thousand -layer cakes in Cantonese -style early tea

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When a bouquet of light is irradiated to such a multi -layer thin film structure and penetrates from the other side, the section of different frequencies (wavelengths) will be different. For example, for visible light, different frequencies means that red, green and blue are different. Light, the relationship between the transmission rate and the frequency is a curve, and this curve is closely related to the thickness distribution of each layer of film. The function input we face is the thickness distribution of the film per layer, and the output is the distribution of the transmission rate of the corresponding structure. From the input to obtain the output, it can be simulated by physical simulation on the computer. To get a set of target inputs that meet the requirements, it is a difficult task of "reverse design".

Figure 5: Volume spectrum distribution curve of multi -layer thin film optical devices

Picture source: ACS Photonics 5.4 (2018): 1365-1369, FIG.2

In various optical applications, we will specialize in the light of certain frequencies through, and at the same time do not allow other frequencies to pass through. In advance, there will be a target transmission spectrum distribution curve like Figure 4. It is to find the corresponding input using a function, that is, the structure of the best "thousand layer of cake" in reverse design. Suppose that the "Thousand Layers Cake" has a total of 10 layers, and the thickness of each layer is available in 10 different sizes. The random combination is randomly combined. The final possible structure is as many as 10 billion, which is 10 billion. The structure input can be given to the function, which can get the corresponding output curve, but try all the possible inputs with huge quantities one by one. "Traversing the full search" to see which output is the closest goal, it is a "Yugong Yishan" -type inefficient clumsy method. And there are more intelligent algorithms on the computer to help us find answers in the opposite direction. Like genetic evolution algorithms and deep learning, the correct answer can be obtained with as few search times as possible.

In Darwin's theory of evolution, various creatures in the world can become what they are today because of the mutations of genes and the screening of the environment, the survival of the fittest, the survival of the fittest, and the uncomfortable people are eliminated. After the evolution of many generations, some animals will never fly and fly. From stupidity to being able to hide in the jungle easily, it becomes lighter and fast from the body shape. Everything is because of the pressure of survival. On the surface, it seems that the problem we are going to solve is "eight poles can not be played together", but it is actually "the same work". The imitation of the evolution process has also become a weapon for solving functions in the opposite direction.

The genetic evolution algorithm moves the process of natural evolution to the computer, which can be used to solve the problem of the reverse design of optical devices. Assuming the structure formed by each thin film layer thickness is regarded as an animal individual. At first, a considerable number of different individuals were generated at first. The corresponding output, that is, the distribution of transmission rate spectrum. Some of them are relatively close to the design goals. Destinists, adapters have a relatively large chance to stay, and the uncomfortable person has a relatively large chance to be eliminated. Then we will also make the individual mating with high scores produce offspring. Of course, there is no real mating here, but the thickness of the different thin film layers of the two structures takes the intermediate value. adaptability. In addition, we will have some random changes, such as letting a better structure suddenly thicker or thinner, depending on whether the adaptation will increase to explore new possibilities.

In fact, the above process is just like we look for food. One way is to continue to discover the dishes that have not been tried on the menu that we have visited. ，另一种方式是去光顾没去过的新餐厅，虽然有不确定踩雷的风险，但也许会有更好的发现，最优的策略就是将这两种所谓的“局部搜索”和“ Global search "combined. The genetic evolution algorithm through continuous screening, crossing and mutation of a large number of individuals, after generation and generation of evolution, finally search for the optimal structure of the optimal structure obtained by the searches will be very close to the target. Device design task. In the process of finding the "Best Thousand Layers Cake", only a few of the possible combinations of 10 billion kinds of possible combinations are tried. Reverse design results. Figure 6: Natural evolutionary process

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In recent years, another intelligent algorithm for the reverse design of optical devices is deep learning. It originally passed the physical simulation function. It was easy to obtain output from the input, and it could not be realized directly. However, it doesn't matter. In the spirit of "there is no way in the world, there are more people walking, and it becomes the spirit of the road." We can try a lot of different inputs (of course, compared to 10 billion possible possibilities) The result of the corresponding output obtained from the known function is also recorded. Then we use a black box model that imitates the human brain neuron connection as deep learning. For the reverse relationship from output to input to establish a data model, use a large amount of output and input corresponding data to train deep learning networks, so that the parameters in the network have the parameters in the network to have the parameters in the network. The optimal value, such a well -trained artificial intelligence model also has the ability to speculate the input structure from a given output, which means that the required passage spectrum distribution curve, the output of deep learning can be possible. Tell you how to design each layer in the film directly, which is also much smarter than traversing the full search method.

Figure 7: Deep learning is used in the reverse design of optical devices

Picture source: ACS Photonics 5.4 (2018): 1365-1369, FIG.1

In fact, we have to design a variety of optical devices, not only like thousands of cakes, but also a variety of structures such as chocolate squares, deformation fudge. With various reverse design intelligent algorithms, they can always obediently obediently obediently obedient You come and go with you in the way you are expected.

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Reference materials:

[1] Gandhi U, Sinha MP, Kulhare Mr.. A Review Towards Various Hash Mms and Their Comparative Analysis. Int. Res. Res. J. ENG. Technol. 2017; 4 (2). 1316-9.

[2] LIU D, Tan Y, Khoram E, Yu Z. Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures. AcS Photonics. 2018 Feb 25; 5 (4): 1365-9.

About the Author

Jiao Shuming, assistant researcher at Pengcheng Laboratory, Ph.D. in Electronic Engineering, Hong Kong University, engaged in the holographic three -dimensional display algorithm, single pixel imaging, optical computing, image processing, information security, machine learning and other studies. With the "Pearl River Talent Program" overseas youth introduction plan (post -doctoral funding project) in Guangdong Province. In the Optics Letters, Optics Express, IEEE Transactions on Industrial Informatics, Engineering and other journals, more than 20 papers were published in the first or communication authors to win the 2020 International Display Technology Conference (ICDT 2020) Excellent Paper Award. He served as the youth editor of "Application Optics" and "LCD and Display", a member of the Professional Committee of the Chinese Optical Society holographic and optical information processing, a member of the 3D imaging and display professional committee of the Chinese Image and Graphics Society Member. He is a member of the Chinese Popular Science Writers Association, a member of the Light Popular Popular Popular Fang scientist consultant group. Why "Book Mathematics Book and Electronic Information Book Author.

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Source: Chinese Optics

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