The top student must be diligent.

Chapter 207 Explosion Trend Discrimination Model
More than 300 TB of data is certainly a lot. However, for direct numerical simulation data of fluid mechanics, such a large amount of data is normal. After all, Xiao Yi tested too many things at one time, so the amount of data itself would be very large. Even in direct numerical simulation, it can be regarded as a large-scale simulation.

Those more than one hundred solid-state drives alone cost Xiao Yi a lot of money.

More data may even reach the PB level.

The simulation of fluid dynamics is so complex.
Otherwise, for scenes involving liquids in games, manufacturers often take opportunistic approaches to display the liquids in the game, and the performance of the liquids has become a major way for manufacturers to show off their muscles.

Of course, this was considered quite extravagant for Xiao Yi. Generally speaking, people would use mechanical hard disks for transportation. However, he took into account that the reading and writing speeds of mechanical hard disks were relatively slow, only about 100-200MB/s. Compared with the 2G/s reading and writing speeds of the hard disks he bought, it was still quite a difference. He didn't have time to waste waiting for data to be read and written.

It's just a few hundred thousand anyway, which is nothing. It just so happens that the price of SSDs is relatively low during this period. Maybe when he needs to calculate other things in the future, these SSDs can be used.

And so, back to the lab, the next step is the most important thing.

data analysis.

Looking at the box of solid-state drives in front of him, Xiao Yi shook his head with emotion.

"Director Zhao, Director Zhao, do you know how much gold coins I spent on your question?"

Then without further ado, he inserted ten of the SSDs into the specially prepared NAS nearby, connected them to the server, and started reading the data.

If you want to analyze so much data, you must first process it, discard some unnecessary data, then compile statistics for other useful data, and make corresponding charts or something.

This is a huge process, and it is naturally impossible for Xiao Yi to do it alone, so he also called some postdoctoral fellows and assistant researchers from the laboratory to give them guidance to help him process the data.

In this way, the data processing process alone took almost half a month.

In the end, Xiao Yi obtained complete statistical data.

Looking at the complicated charts displayed on the screen, Xiao Yi narrowed his eyes and began to analyze and think about the data.

From time to time, a peak will appear, and each peak represents the occurrence of an explosion.

Then, he can try to find the conditions for the formation of explosive cracks based on the occurrence patterns of these peaks.

Looking at these charts, if others were to look at them, they would simply think that these pictures had no pattern at all, but Xiao Yi quickly discovered quite a few points that were worth careful study.

"interesting……"

"The first is that in some cases, for some semilinear heat equations, if some norm of the initial data exceeds a certain critical value, such as the L^2 norm of the velocity field, the solution may become infinite in a finite time."

"Secondly, there is the influence of nonlinear terms, nonlinear convection terms, which is also a key factor leading to the explosion of these solutions, especially in three-dimensional cases, where the influence of nonlinear terms is more significant."

"There are also boundary conditions and external driving, which may also affect the stability of the solution under some periodic boundary conditions or complex boundary geometries, thereby increasing the possibility of solution explosion."

"Well, there is also the influence of vorticity..."

"The initial conditions, nonlinear terms, spatial dimensions, boundary conditions, and the concentration and growth of external driving vorticity, that is, the formation of the explosive solution, are basically closely related to these conditions."

"So what method should be used to reconcile these issues?"

Xiao Yi thought about it for a moment.

He took out a piece of draft paper and began to deduce on it.

【tu+(u)u=p+νΔu+f……】

As he deduced, the brainstorm that had been brewing in his mind gradually began to coalesce in the process of deduction, and gradually a common goal was formed, and then an attack was launched towards this common goal.

Time passed slowly.

……

For several days, Xiao Yi looked through all the data and analyzed a lot of information from it.

"The birth of explosive solutions is always caused by many different reasons."

"But these different reasons, from a mathematical point of view, ultimately have a unified reason."

"Um……"

Sitting in the office, Xiao Yi pondered.

Xiao Yi, who had not studied such difficult mathematical problems for a long time, gradually regained the original feeling.

It is impossible to simply solve this problem, which has been thoroughly studied by the academic community and has a history of hundreds of years.

As for the method that can perfectly prove the existence and smoothness of the solution to the NS equations in one go, it simply does not exist.

But at this moment, with so much information summarized, the storm in Xiao Yi's mind was like a centrifuge, stirring and centrifuging this information. And now, all the relationships that were connected like silk threads were also separated and precipitated in the centrifuge in his mind.

"Professor, your water."

As a diligent assistant, Wang Hao refilled his empty cup with water and placed it next to him.

The jasmine tea inside is constantly rotating along with the vortex in the cup, and the effect of fluid mechanics is constantly at work between the collision and adhesion of microscopic water molecules.

Xiao Yi's eyes were fixed on the glass of water, but in his mind, there was another scene:
The water in the cup began to rotate slower and slower until it finally stopped completely, including the tea leaves inside. They also basically stopped, except for the tea leaves on the surface, which were still swirling.

Until finally everything came to a standstill.

However, at that moment of stillness, a certain volume of tea at the center suddenly exploded, instantly raising the air pressure in the entire cup a lot, and then with a "bang", the glass teacup exploded.

Liquid splashed on the desk and glass fragments flew everywhere.

And one of the fragments seemed to be about to rush towards Xiao Yi's eyes.

But as he blinked, the scene of the cup exploding disappeared.

All that was left was the boiling water and tea leaves that were still swirling slightly, and the white steam coming out of the cup.

"professor?"

Perhaps because he saw Xiao Yi suddenly had no reaction when looking at the cup of water he brought over, Wang Hao couldn't help but ask.

Xiao Yi came back to his senses, then smiled and nodded at him: "Thank you."

Wang Hao also smiled and was about to leave, but at this moment, Xiao Yi suddenly looked at the water in the cup and said, "Did you see it explode?"

Wang Hao was stunned: "What? Explosion? How could this cup explode?"

He didn't quite understand.

Xiao Yi smiled and nodded: "Yes, cups won't explode for no reason, and the same goes for water."

In the world of mathematics, it exploded, but in the real world that obeys various physical rules, it did not explode and still has the softness of water.

Then, he picked up the cup, shook it, and then took a sip to feel the temperature of the tea.

Then he put down the cup and looked at the computer again.

"It's time to take this crucial step."

Open LaTeX and enter the title.

《The formation mechanism of PDEs and blow-up solutions in dynamical systems》

Explosion problems are not unique to fluid mechanics, but exist in many other fields of nonlinear partial differential equations (PDEs) and dynamical systems.

The problem of explosive solution exists in many studies, such as nonlinear wave equations, nonlinear heat equations, Keller-Segel model, etc.

It can be said that this problem can basically be regarded as a chronic disease in many fields of academia, and has always been a key issue that has troubled people's research.

If this problem can be solved, it will be of great significance both in academia and in practical applications.

And now, Xiao Yi has such confidence.

……

Half a month passed quietly.
"nailed it."

"The most important thing about the formation of explosive solutions is a trend in the equation." "Under different initial conditions, a trend will inevitably appear. All fluid mechanics of the fluid model are moving towards this common goal."

"So, the most important thing is to set the initial conditions in a way that avoids such a trend."

Now, Xiao Yi has summarized all the rules in his paper, and at the end he gave a model that can simply determine whether there is a "trend" in the initial condition settings.

"Well, let's just name this trend the bursting trend, and this model is called the bursting trend discrimination model."

It is conceivable that his explosion trend identification model will play a huge role in relevant practical applications.

In any industrial technology research related to fluid mechanics, in the process of direct numerical simulation, there will be problems caused by explosion. Now, if they can use his explosion trend judgment model to calculate the initial conditions they set, they can easily determine whether their model has the possibility of explosion.

This model is of great significance. After all, every time direct numerical simulation is used, companies or research teams need to spend a part of the computing resources, and the cost of renting supercomputers is not small.

If their model runs and eventually fails to work properly, it not only wastes time but also costs.

However, if they can use this discriminant model to help them find problems in advance and modify their models accordingly, it will undoubtedly reduce the waste of time and cost.

By then, all these people will call him the savior of fluid mechanics.

"I'm a really nice guy."

Xiao Yi sighed slightly in his heart.

Of course, his model is only the initial version. If more direct numerical simulation data of fluid mechanics can be fed into this model, its judgment of explosion trends will be more accurate.

"Perhaps, I can call on laboratories or corporate institutions that study fluid mechanics to feed data to this model, so as to cultivate a more powerful discriminant model?"

This is what Xiao Yi thought in his heart.

Just like chatgpt, the more data you feed it, the stronger the model will be.

However, for this kind of thing, he just needs to make a call. If he is asked to do it himself, forget it. At least he should find someone to help him.

"Who are you looking for..."

At this moment, there was a knock on the office door, and then Wang Hao walked in and said, "Professor, Dean Tang Fucheng of the School of Mathematics and Dean Shen Gensheng of the School of Physics are here to see you."

Xiao Yi was stunned, and then his eyes lit up.

Isn’t this a coincidence!
He immediately said, "Okay, please let the two deans come in."

Afterwards, Deans Tang Fucheng and Shen Gensheng walked in.

Xiao Yi took the initiative to greet them and said with a smile: "President Tang and President Shen, welcome, welcome. I just happened to have something to talk to you two about, but I didn't expect you two to come to me first."

Tang Fucheng and Shen Gensheng were both stunned.

Tang Fucheng said, "Professor Xiao actually has something else to ask us?"

Xiao Yi smiled and then asked, "Have you two done research on partial differential equations?"

Hearing this question, the two were stunned again.

Shen Gensheng said: "I have studied this and understand a little bit."

Tang Fucheng smiled reservedly, "I know a little bit."

Although his main research is not partial differential equations, he still has some understanding of it.

"That's good!"

Xiao Yi nodded, then turned his computer towards them.

"Please take a look at this paper on partial differential equations."

The two deans looked over curiously.

As a result, no one said a word.

After a long time, Xiao Yi asked, "You two, how is the paper?"

"Uh...well..."

Shen Gensheng opened his mouth with difficulty, but after hesitating for a long time, he said nothing.

The mathematical methods used here were still a bit too difficult for him, a physicist.

Tang Fucheng hesitated for a moment, then said, "Although I don't fully understand the derivation process, but... the final model can determine whether the fluid mechanics model has the possibility of an explosive solution under certain initial conditions?"

Xiao Yi nodded: "Yes."

Tang Fucheng took a breath of cold air.

“Then this model is incredible!”

Shen Gensheng beside him roughly understood what Tang Fucheng meant, and he also widened his eyes: "Are you sure? This is really incredible!"

Even if they are not specialized in fluid mechanics, they can understand the significance of this matter through their daily understanding.
This can be regarded as a major technological innovation for the entire fluid mechanics industry.

Xiao Yi nodded, and then expressed his previous thoughts.

"Of course, you two shouldn't be so happy. This model is currently only a preliminary version, 1.0. If we can use machine learning methods to feed this model with enough data, like ChatGPT, then this model will be able to play a more critical role."

"To do this, we need to do it in an organized way, and that's why I want to find you two."

"So, I propose..."

Then, Xiao Yi expressed his thoughts, and the two deans' eyes became brighter and brighter as they listened.

In general, the Science Island Laboratory reached a cooperation with the two colleges and, of course, the University of Science and Technology of China, and took the lead in establishing a large model organization for blasting trend discrimination to train the model and call on various research teams to feed the model with relevant model data. As the model grows, it will feed back to the industrial field.

As long as the model is accurate enough in the end, their organization is bound to gain a certain influence in the global industrial field.

Xiao Yi may not care about such influence, but for HKUST, it must be very happy to do this.

After some discussion, the two deans agreed immediately. For them, this was an achievement during their tenure. If it could really become an organization with great influence on a global scale in the future, it would be even more amazing.

"Okay, Professor Xiao, it's decided. We'll go back and talk to Principal Bao about this. He will definitely agree then."

Tang Fucheng said, and Shen Gensheng nodded.

They were full of energy at this time.

"That's good."

Xiao Yi smiled and said, "I'll trouble you to worry about this matter. I'm just playing the role of a rallying cry."

"Of course, we have to thank you!" Tang Fucheng laughed.

"Yeah." Xiao Yi nodded, and then he asked: "But speaking of which, I still don't know why you two came to see me?"

The two deans were stunned, and then they slapped their heads.

"I almost forgot about this."

"Professor Xiao, you have been a professor at our school for such a long time. Isn't it time to consider teaching students?"

The two said helplessly.

Xiao Yi has been a professor at their university for more than a year, but because he has been busy with the affairs of the Science Island Laboratory, he has never had any students.

Now that so much time has passed and the Science Island Laboratory has become stable, we should also consider the issue of supervising students, right?

Xiao Yi was stunned.

“This… is indeed true!”

(End of this chapter)