The top student must be diligent.

Chapter 145: Just a Harder Question

Hearing Xiao Yi's idea was truly a shock to Luo Mingya.

Why is it that he can come up with such insightful thoughts after only studying computational materials science for such a short period of time?
However, Luo Mingya didn't know how to answer this question for a moment.

She is indeed a genius, otherwise she wouldn't have been able to start working on this kind of topic after only half a year of studying computational materials science.
But the same thing is that although she is talented enough, it is still within the normal range. She cannot think of an idea like Xiao Yi's.

After thinking for a moment, she said, "Can you explain in detail the principle of your idea?"

Xiao Yi nodded and said, "The core principle is to use the microscopic motion trajectory of electrons to accurately calculate the state function of electrons through the path integral method. This method can bypass the approximation of the exchange-correlation potential in DFT and directly calculate the interaction and overall behavior of electrons."

"We then introduced Markov Chain Monte Carlo technology to optimize the calculation path and improve calculation efficiency."

"This allows us to predict the properties of materials by accurately predicting the behavior of electrons."

"It basically combines the advantages of multiple methods including density functional theory, first principles calculations, and Monte Carlo methods."

After listening to what Xiao Yi said, Luo Mingya pondered for a moment, then nodded and said, "Anyway, if I were to explain it from the perspective of materials science, your idea is completely credible."

"If we can really calculate the trajectory and laws of electrons, it will certainly help us predict the various properties of materials. After all, the different properties of different materials are ultimately the result of the different distributions of electrons in them."

"Just like the experimental data from Zhao Yuanyuan that day, the defects in the lattice led to changes in the reaction."

Zhao Yuanyuan's head squeezed over at this time: "Did I hear you mention me?"

"It's none of your business." Luo Mingya rolled her eyes at her.

"Hmm..." After a pause, she continued, "But no matter what, it is still a huge problem to achieve what you said. Let me briefly talk about path integrals. I have some understanding of this."

"You just said that the method of computational materials science needs to balance the calculation accuracy and the amount of calculation, but the calculation complexity of path integral is extremely high, especially when dealing with multi-electron systems, the amount of calculation increases exponentially."

“So how do you control the amount of computation?”
Facing the question raised by Luo Mingya, Xiao Yi just smiled and said, "Use machine learning technology."

"I don't know if you have heard of variational autoencoder technology, or VAE technology. This is a generative network structure based on variational Bayesian inference. When I was thinking about it these days, I made some simple optimizations to this technology from a mathematical perspective, combined it with machine learning to train a neural network, and it can automatically optimize the generated electron trajectory."

"This not only reduces the amount of calculation, but also achieves high-precision requirements."

Listening to their conversation, Zhao Yuanyuan began to feel dizzy and quickly moved away from them. She felt like she had suffered a nuclear attack on her IQ.

However, Luo Mingya is no different from her.

This genius from the Department of Materials Science finally heard something he didn't understand.

"VAE technology?" She thought about it carefully for a long time, and finally shook her head and said, "I have never heard of this. If it involves machine learning, it is indeed not within the scope of my professional studies."

"However, I do know that applying machine learning to materials research has become a hot topic in the past two years, just like the two-dimensional materials we are studying now."

"Anyway," Luo Mingya said, "your idea does seem to be a good one, although it may be difficult to implement. Just from what you said, you want to introduce the Markov Chain Monte Carlo technique to optimize the calculation path. I can almost imagine how difficult it is mathematically."

"Not to mention your initial idea of ​​how to establish the relationship between path integrals and electron orbitals."

"I don't think I can help you with how to achieve these points. Maybe you can look for that woman Sun Lina... But I don't think she would understand much. Her math is worse than mine."

As she spoke, Luo Mingya expressed her envy for the first time: "To be honest, sometimes I really envy you mathematicians for being able to master mathematics so thoroughly. For those of us who study other subjects, it is really hard to understand what kind of thinking realm that is. No matter how I studied mathematics in the past, I could not reach that realm."

Looking at her expression, Xiao Yi smiled and said gently: "That's because even if you don't need to learn math well, you can still do everything well enough. No one needs to restrict themselves to something, and the same is true for life."

After hearing Xiao Yi's words, Luo Mingya was silent for a long time. Finally, she looked at Xiao Yi deeply and said, "Thank you. I understand."

Xiao Yi was stunned for a moment, then waved his hand and said with a smile: "You're welcome. As a person who studies mathematics, it is necessary to explain this to those who are confused about mathematics."

"I think you are different from those who study mathematics. You are a gentle mathematician." Luo Mingya said.

"Really?" This compliment caught Xiao Yi off guard. Xiao Yi said shyly, "Thank you for the compliment."

Luo Mingya smiled and said, "Anyway, if you plan to study the ideas you just mentioned, I can help you with any material science questions within my ability. In addition, you just said that you may need to use machine learning, which should require a lot of data, which I can also provide you with."

Xiao Yi nodded: "Thank you very much."

At this moment, Xu Ming shouted: "The results are out!"

Xiao Yi and Luo Mingya turned their heads to look, and the latter immediately walked over. Soon, her eyes lit up.

"So that's it!"

“Comparable band structures are found for the 2H and 2H/3R polytypes, where the valence band top of the 2H/3R polytype is located at a high symmetry point… so the volume plasmon peaks for all polytypes occur at similar energy loss values,” he said. “This allows us to further determine the energy loss strengths for different valence and conduction bands for different energy loss regions.”

"Great! Now we are one step closer to the final conclusion!"

Luo Mingya clapped her hands and said, "What we have to do next is very simple. Find those TMD-based heterostructures. Now let's go back to the lab!"

Afterwards, she took her fellow juniors and sisters away from here. Before leaving, she said to Xiao Yi: "There should be nothing for you to do next. You can study your idea with peace of mind."

"I'll contact you when our project is completed. By then, you will be able to take the position of first author."

Then she left with her people.

Xiao Yi watched them leave and raised his eyebrows.

In other words, you won’t have anything to do with the next topic?

That's fine, this way he can focus on his research.

By accurately predicting the trajectory and laws of electrons in materials, a new theoretical model is constructed...

Sitting back in his original seat, he took out the draft paper he had used during this period and reviewed the previous related derivations.

On the first piece of draft paper, there was a line of words written: [Absolute Electronic Computation (AEC)]

This is the name he gave to this method.

All materials need to follow the principle, that is, the chemical bonds between atoms formed by electrons, and these chemical bonds form the most basic structure of the material.

The properties of materials all derive from this point, nothing more than this.

Just like the saying goes, structure determines properties, and properties determine function.

For example, there is a material technology called single crystal casting technology, which can make the material only have a single crystal structure. This means that the atomic arrangement inside the entire casting is continuous and there are no grain boundaries. Therefore, it can enable the material to obtain extremely strong mechanical properties and creep resistance, especially in high temperature environments. Therefore, it is also widely used in the field of aviation engines, such as turbine blades.

Absolute electronic calculation is to calculate the structure of electrons by predicting the behavior of electrons, and then predict the properties of materials.

However, in order to predict the behavior of electrons, we must first introduce path integrals.

[qf, tf|qi, ti=∫D[q(t)]exp(iS[q(t)])】

Write down the formula for the path integral on a piece of scratch paper.

Xiao Yi knocked his head.

Unlike the Schrödinger equation, the path integral method calculates the behavior of a quantum system by summing over all possible quantum paths, a method that is particularly suitable for dealing with many-body problems and strongly interacting systems.

So obviously, from the perspective of predicting material properties, the path integral has a very good effect in this regard.

"In addition, in electronic structure calculations, the path integral method can be used to calculate the distribution function and correlation function of particles, which is particularly advantageous when dealing with electron correlation effects and thermal effects."

He narrowed his eyes, and his thoughts began to wander infinitely.

"The properties of materials are also affected by different scales, from the atomic scale to the macroscopic scale. How to achieve a unified description of multiple scales in the calculation of absolute electronic properties has become another major challenge."

Thinking of this, he wrote down the five words "multi-scale modeling" on the draft paper.

"If we can combine molecular dynamics and finite element analysis to build a unified computational framework from micro to macro, it should be very effective in solving multi-scale problems."

"And then there's..."

There are many difficulties, but difficulties are meant to be solved.

If proving conjectures in mathematics requires theoretical innovation, then solving such application difficulties requires more of his flexible combination of existing methods and finding completely new methods from them.

"It's just a more difficult problem."

Xiao Yi raised the corner of his mouth, without frowning at all.

On the contrary, I enjoy such difficulties more and more.

(End of this chapter)