Chapter 147 Running on the Computer

The meeting room was eerily quiet.

The sky outside the window was overcast, with low-hanging rain clouds. Even the cicadas in the trees had stopped chirping, and the sweltering air seemed to solidify inside the room. Zhang Yuan's originally bloodshot eyes were now somewhat dazed.

He lowered his head, his gaze fixed on the draft paper pushed in front of him.

His mind was filled with those despairing partial differential equations, grids, boundaries, and time steps.

So when his eyes fell on the neatly arranged symbols on the paper, his first reaction was bewilderment.

It doesn't have the curl symbol commonly found in fluid mechanics, nor does it have the divergence formula.

All I could see were square brackets filled with numbers and algebraic terms.

Zhang Yuan frowned and subconsciously picked up the paper.

He understood the first line; it was a transformation formula used for dimensionality reduction.

As he continued reading, his brows furrowed deeper and deeper, and his previously listless eyes were gradually replaced by a look of absurdity and bewilderment. "Xiao Zhuo."

Zhang Yuan's voice was very hoarse; when he spoke, it sounded like there was sandpaper grinding in his throat.

"What is this?"

He held the paper and waved it in mid-air, making a rustling sound.

"matrix?"

Zhang Yuan looked at Chen Zhuo sitting at the end of the long table, his tone carrying an instinctive sense of rejection.

"You're using algebraic matrices to calculate fluid dynamics?"

Chen Zhuo sat in the chair, his hands resting naturally on the table.

"Um."

Chen Zhuo nodded.

Discrete algebraic matrices.

What about the time variable?

Zhang Yuan's voice unconsciously rose a little as he pointed to a large blank space in the middle of the page.

"You removed the time derivative? Where did that 0.01-second physical process go?"

Zhang Yuan turned around and pointed to the formulas on the blackboard behind him that had been scribbled and messed up.

"Fluids are continuous media. When a car crashes into a tunnel, the air is violently compressed. This is a continuous physical process. Our Navier-Stokes equations, conservation of mass, and conservation of momentum are all based on the continuity of time."

Zhang Yuan turned around, stared at Chen Zhuo, his voice trembling with excitement.

"You're going to create a matrix that directly maps state A to state B, ignoring the entire process in between? That's physics-wise impossible. You can't just cover the equation with a cloth and pretend it doesn't exist because the equation is difficult to calculate."

This is the perseverance of a PhD in fluid mechanics.

Zhang Yuan wasn't targeting Chen Zhuo; he was simply defending the physics knowledge he had studied for over a decade and which was ingrained in his very being.

Chen Zhuo did not refute Zhang Yuan's excitement.

He simply listened quietly, looking into Zhang Yuan's red eyes, and then leaned back slightly.

"Senior brother."

Chen Zhuo's voice remained calm.

"Physical continuity certainly exists; air doesn't just disappear out of thin air."

He paused.

"But microcomputers don't understand this principle; they only recognize memory."

Chen Zhuo looked into Zhang Yuan's eyes.

"To simulate the continuous process you described, you divided time into one millionth of a second. In that 0.01-second time span, the variables explode exponentially. The computer doesn't understand your physical principles; it will simply cut off the power when the memory is full."

Zhang Yuan opened his mouth, wanting to speak, but found that he couldn't say anything.

Those few memory sticks with blackened edges are the most irrefutable evidence in the lab.

"Since it doesn't make sense."

Chen Zhuo pointed to the piece of paper.

"Why should we force it to calculate?"

"But...."

Zhang Yuan gripped the paper with a bit of force.

"Skipping the micro-processes, macro-data is like water without a source; it simply doesn't make sense."

Just as Zhang Yuan stubbornly wanted to continue arguing.

A hand reached out from the side and snatched the draft paper from Zhang Yuan's hand.

"show me."

The sorcerer's voice rang out from the top of the long table.

Zhang Yuan paused for a moment, swallowed the rest of his words, and stepped aside.

The sorcerer placed the paper flat on the table in front of him.

He reached into his shirt pocket, pulled out a somewhat worn glasses case, opened it, and took out a pair of reading glasses, putting them on.

The meeting room fell silent once again.

Lin Fang stopped wiping her tears, and the boy with glasses stopped biting his pen. Everyone held their breath, watching the sorcerer sitting in the main seat. The sorcerer read very slowly.

His index finger touched the paper, moving down little by little along the lines of writing Chen Zhuo had made.

The ceiling fan overhead creaked and groaned as it turned.

A minute passed.

Two minutes passed.

The cigarette between the alchemist's fingers had burned down to the filter, and the ash fell onto the table without him noticing.

His brows were initially furrowed tightly, just like Zhang Yuan's reaction.

But as his fingers moved downwards, his brow gradually relaxed, and his gaze lingered for a long time on a few key lines of conversion formulas. The old fox's academic intuition was extremely sharp.

He understood Chen Zhuo's intention.

This is not fluid mechanics at all; it is a purely, unscrupulous mathematical tool.

The sorcerer's finger stopped at the bottom of the page.

He looked up, took off his reading glasses, and placed them on the table.

The Taoist priest looked at Chen Zhuo at the end of the long table. There was no anger or mockery in his eyes, but rather an extremely complex scrutiny.

"Xiao Zhuo."

The sorcerer spoke, his voice calm and steady.

"Use discrete matrix reduction to bypass the exhaustive problem in calculus, treat the 0.01-second continuous fluid motion as a black box, and only calculate the initial conditions and the final result." Fang Shi paused for a moment.

"The idea is ingenious, extremely ingenious."

Zhang Yuan, listening nearby, was stunned. He hadn't expected his usually meticulous mentor to use the word "ingenious" to describe such a physically unorthodox approach. But the sorcerer didn't finish his sentence.

He abruptly changed the subject, posing an extremely knowledgeable yet fatal question.

"but."

The sorcerer tapped the table with his finger, making a tapping sound.

"The air is violently compressed in the tunnel, which will generate tremendous internal friction and heat dissipation. You packaged this process into a black box, and you skipped the time derivative." Fang Shi stared at Chen Zhuo.

"What guarantees that the energy at the entrance and exit of the black box is conserved on a macroscopic level?"

This is a very insightful question.

"In mathematics, if there is even the slightest gap in your boundary conditions that cannot converge, after hundreds or thousands of iterations of the matrix, this error will diverge explosively." The strategist's tone became serious.

"After a hundred calculations, the error might exceed five percent. Using that kind of data to build a high-speed rail would lead to a derailment. Without a mechanism to lock in the error, this matrix is ​​just a piece of waste paper." Zhang Yuan nodded repeatedly beside him.

The tutor voiced his deepest concern, which was why he was unwilling to use pure algebra to gloss over the process—because once the constraints of the process were lost, the results often became wildly wrong. All eyes turned to Chen Zhuo once again.

Everyone was waiting for his answer.

Chen Zhuo sat there, looking at the alchemist, and then at Zhang Yuan beside him, whose face was full of disapproval.

Chen Zhuo stood up.

He pushed his chair back and left that secluded corner.

Under the watchful eyes of the entire research group, Chen Zhu strode forward along the long conference table toward the front of the room.

Chen Zhuo walked to the blackboard.

The large blackboard was covered with Zhang Yuan's hard work over the past few days.

Those complex partial differential equations, boundary conditions, and mesh partitioning parameters were densely packed together, like a huge, unsolvable net. Chen Zhuo lowered his head.

On the floor lay half a piece of white chalk that Zhang Yuan had just dropped.

Chen Zhuo bent down and picked up the broken piece of chalk.

There was some dust on the chalk, so he gently rubbed it between his fingers to remove the dust.

Then, Chen Zhuo turned around and faced the blackboard.

"Senior brother."

Chen Zhuo looked at the blackboard full of writing and then turned to look at Zhang Yuan behind him.

His tone was gentle, with a touch of casual banter.

"You've filled the blackboard quite a bit with writing."

Zhang Yuan stood there, speechless, unsure what to say. What time was it? This kid still had the mind to joke around? Chen Zhuo turned around and his gaze fell on a partial differential equation on the far left of the blackboard.

That was the source of the crash that caused all the microcomputers to freeze, plunging the entire research group into despair: the Navier-Stokes equations with continuous time terms. Chen Zhuo raised his hand and drew a heavy circle on the time derivative term of this equation with chalk.

Then, starting from the circle, he drew a long arrow that led to a relatively clean blank area in the lower right corner of the blackboard. The chalk landed on the blackboard.

The crisp sound of chalk striking the chalk rang out in the deathly silent conference room, without the slightest pause or hesitation.

Chen Zhuo began to speak as he wrote.

"Dean Fang, you are right. If internal friction and heat dissipation are ignored, the error will indeed spread."

Chen Zhuo wrote the beginning of a matrix.

This is a standard Jacobian matrix.

"If it's just a simple state mapping, then this set of matrices is indeed worthless."

Chen Zhuo's chalk moved across the blackboard.

"Therefore, we cannot let it spread out; we must forcibly bring it back together."

Zhang Yuan stood a few steps away, his eyes fixed on the equations that appeared on the blackboard.

When he saw Chen Zhuo add a complex logarithmic term to the end of the Jacobian matrix, his pupils contracted slightly.

"What is that?"

Zhang Yuan couldn't help but ask a question.

Chen Zhuo's chalk never stopped.

"Nonlinear compensation term".

Chen Zhuo answered without turning his head.

"I looked at the wind tunnel test report of the German ICE train a few years ago. When they were dealing with the boundary layer peeling of irregular tunnel walls, they did not exhaustively list the specific fluid disturbances." Chen Zhuo drew a straight line on the blackboard, connecting the kinetic energy term at the entrance and the potential energy term at the exit.

"I reversed their approach to wall compensation and embedded it into this matrix."

The people in the conference room were somewhat bewildered.

Chen Zhuo ignored the silence behind him.

He took the chalk and drew a heavy horizontal line under that compensation item.

"I didn't calculate how much energy was lost in that black box."

Chen Zhuo turned around and looked at the Taoist priest sitting in the main seat, his voice clear and firm.

"I've imposed a strong constraint on the export process."

He tapped the blackboard with chalk, making two muffled sounds.

"I used the initial kinetic energy of the train as it entered the tunnel to forcefully apply the potential energy and pressure after it was fully inside the tunnel to do work."

Chen Zhuo looked into the alchemist's eyes.

"In that 0.01 seconds, the air can be as chaotic as it wants, and it doesn't matter how much heat is generated by internal friction. As long as the energy difference between the initial state and the final state is swallowed up by this nonlinear compensation term," Chen Zhuo pointed to the formula on the blackboard.

"This matrix will not diverge."

The Taoist priest sat in his chair, his gaze shifting from Chen Zhuo's face to the lines of writing on the blackboard.

His hand rested on the table, his fingers unconsciously tapping lightly on the surface.

This is a unique habit he has when he's thinking.

Chen Zhuo's logic is extremely domineering.

He's unreasonable; he doesn't follow the rigid cause-and-effect relationships of physics. He uses pure mathematical methods, like adding two welded iron gates to both ends of a pipe. No matter how turbulent things are inside, as long as the data at both ends match, the score is even.

"What about the margin of error?"

The sorcerer stopped tapping on the table and looked at Chen Zhuo, asking.

This is a forced method of balancing the accounts, which will inevitably produce errors. Engineering projects allow for errors, but they must be within a safe range.

Chen Zhuo turned around and faced the blackboard.

He picked up the chalk and wrote down the convergence limit he had derived at 2 a.m. last night under the dormitory light after repeatedly verifying it. After writing this line, Chen Zhuo put his hand down.

Instead of throwing away the remaining half of the chalk, he walked back to the side of the classroom and gently placed it next to the chalk box.

He patted the chalk dust off his hands, the sound of his clapping clear and crisp in the quiet room.

"The total error is locked."

Chen Zhuo clapped his hands clean, turned around, and looked at everyone in the conference room.

His tone returned to its usual calmness, as if he were talking about something trivial.

"Seventeen out of ten thousand".

Chen Zhuo looked at Zhang Yuan.

"Far below the safety threshold of 0.2%."

Chen Zhuo let his hands hang down naturally.

"Most importantly, the computational power consumption of this matrix is ​​only one percent of that of the original partial differential equation. We can use it as a patch for the underlying logic." Chen Zhuo smiled.

"Even the Pentium microcomputers in our lab, which have huge fans blowing, will never crash."

The meeting room was extremely quiet.

There was no discussion, nor any gasp of surprise.

Zhang Yuan stood blankly beside the teacher, staring at the blackboard.

A striking image appeared on the blackboard.

On the left, occupying most of the blackboard, were messy partial differential equations, representing a dead end and endless despair in physics, covered with scribbles and corrections, like a ruin. On the right, in that tiny corner...

There are only a few lines of neatly written, extremely regular discrete algebraic matrices.

It is clean, concise, and free of unnecessary words; the logic forms a perfect closed loop from beginning to end.

It was like an extremely sharp knife that easily sliced ​​through that vast ruin.

Zhang Yuan felt his head buzzing.

Looking at the convergence limit of 17 ten-thousandths on the blackboard, he wanted to say something but couldn't utter a word.

He knew very well that Chen Zhuo was right.

This seemingly crude algebraic matrix is ​​perfectly feasible in engineering applications.

Lin Fang and the bespectacled boy sitting on either side exchanged glances. Although they hadn't fully understood the complex steps of the rank reduction process, they understood the final sentence that the system wouldn't crash. The Taoist priest remained seated.

He looked at the matrix on the blackboard, then at Chen Zhuo, who stood calmly by the lecture hall.

The sorcerer did not speak, nor did he immediately give any instructions.

He simply leaned back slowly in his chair and let out a long sigh.

In that breath, it seemed as if he had exhaled all the weight that had been pressing on his heart for the past two weeks.

Outside the window, a gust of wind blew by, making the window, which wasn't closed properly, rattle loudly.

The sound broke the silence in the conference room.

The sorcerer withdrew his gaze and clasped his hands together on the table.

He looked at Zhang Yuan, and a trace of the authority and decisiveness he usually displayed as the vice dean slowly appeared on his originally aged and tired face.

"Zhang Yuan".

The sorcerer's voice was not loud, but every word carried immense weight.

Zhang Yuan suddenly came to his senses and stood up straight.

"Fangyuan".

The sorcerer pointed to the blackboard with his chin.

"Erase those partial differential equations of yours."

The sorcerer did not use a tone of negotiation.

"Copy down this matrix code written by Chen Zhuo."

The Taoist priest stood up and picked up the cigarettes and lighter from the table.

"Forget about the physical process. Treat it as a patch, and install it into the underlying program to replace the 0.01-second critical point model." Fang Shi looked at Zhang Yuan and gave the final instruction.

"Let's go run it on the plane now."