I was a top student in America.

Chapter 114 has run into problems again (Please subscribe)

Upon hearing this, Benjamin stared intently at him, his expression somewhat complicated.

Sigh, what was bound to happen has happened—

Ever since he witnessed Li Ao's amazing talent and learning efficiency, he knew that sooner or later Li Ao might turn around and explain problems to him.

I just didn't expect this day to come so soon.

But then I thought about it again, and the most important thing is to acquire the knowledge.

After a brief moment of surprise, Benjamin decisively handed over the exercise book: "Thanks, please take a look at it for me."

As he handed me the notebook, he couldn't resist asking out of curiosity, "Have you finished studying ordinary differential equations?"

Benjamin had known for a long time that Li Ao had been borrowed by Professor Rudy to help him, and when he first heard about it, he could hardly hide his envy.

Surprisingly, he didn't fall behind in his studies either.

"I finished learning it during the training camp a while ago, and I'm currently learning functional analysis," Li Ao answered truthfully, taking the exercise book and glancing at it.

After reading the question and conditions, I immediately realized that this was a comprehensive problem about linear differential equations, variable parameter formulas, and continuous dependence, and it was indeed quite difficult.

He quickly deconstructed and deduced the problem in his mind. After clarifying his thoughts, he picked up a pen and wrote down the formulas while explaining: "This problem is quite complicated. You can try to transform the non-homogeneous equation into a variable parameter formula under the basic matrix."

That is: "y(t) = Φ(t)y(0) + ∫—0^tΦ(t)Φ(s)^{—1}g(s)ds".

Li Ao listed the core steps on the paper, then said, "Then take the difference between the two sets of solutions, and use the matrix norm and Gronwald I..."

Inequalities control for errors. Finally, by estimating the initial term and the non-homogeneous term separately, the conclusion of continuous dependence can be derived.

Benjamin, after all, was an IMO gold medalist, and after a little guidance from Li Ao, he immediately understood.

When he took the exercise book, he was still amazed by Li Ao's quick thinking and couldn't help but give him a thumbs up and exclaim, "I'm really impressed. You don't look like you just finished studying during the summer vacation. Even when David was explaining problems to me, his thinking wasn't as clear as yours."

"At your current pace, once you actually get into university, you'll probably feel a lot of pressure compared to many graduate students."

After his reflection, Benjamin was about to continue working on his problems when he caught a glimpse of the document interface on Li Ao's screen. He paused slightly, then asked in surprise, "Are you—writing a paper again?"

"It's a paper from a project in the physics department. I'm just one of the collaborators," Li Ao explained calmly. "I derived a candidate local boundary weight, and Professor Rudy asked me and Amber to add this part so that we could complete the interim report as soon as possible."

These words carried a completely different weight in Benjamin's ears.

A project that was still struggling to overcome difficulties was able to prepare for a phased completion thanks to the new weights provided by Li Ao, which can be considered a key contribution.

Benjamin looked at him with envy: "Then you must have contributed a lot to this project, right?"

"It only provides a local weight, it's not that big," Li Ao replied casually.

That's really what he was thinking.

Benjamin, however, wanted to roll his eyes and internally ranted:

This has been written into the core content of the paper. Just how much of a contribution is considered significant?

Time flies by in the regular schedule, and before we knew it, it was the day before we were to officially attend the U.S. Department of Energy's interim report.

at this time.

In a project meeting room at Argonne National Laboratory, Rudy is leading the project team in final preparations for tomorrow's report.

Through the glass partition, you can see other small meeting rooms and visitor work areas where several competing teams from other schools are also busy preparing slides and debugging scripts.

"Tomorrow, each project team will give their progress reports here in turn, which will be jointly evaluated by the Department of Energy and Argonne." Rudy tapped the table to bring everyone's attention back. "Let's first do a final reproduction of the benchmark example and optimize the parameters as well."

Li Ao glanced down at his temporary pass on his chest, then looked at the high-spec workstation terminal on the conference table.

Even though he had prepared himself mentally before coming, when he actually stepped into the project site of the national laboratory and faced the operation of core scientific research, he still felt a sense of novelty and his heart couldn't help but fluctuate.

On the other side, Arjun and Carter acted swiftly.

Before long, they set up a validation branch in Argonne's local environment, imported several sets of irregular boundary and strong boundary coupling parameters, and prepared to collect stability margin data to improve the report.

Just as everyone was full of confidence and enthusiastically preparing to report, Nicole, who was sitting in front of the computer, suddenly spoke up.

"How could this happen?" She frowned, staring at the screen. "The worst-case scenario has gone back above 1.2, exceeding the safety threshold."

.

The meeting room immediately fell silent as everyone crowded around the computer to check the situation.

"This shouldn't be happening." Arjun quickly swiped the mouse, checking the feedback logs on the screen. "We used new local weights, and the worst Rboundary/EbuIk score had never exceeded 0.94 before."

Li Ao, who was checking the log on the side, remained relatively calm.

He noticed the abnormal boundary block numbers and casually arranged them in order on a piece of paper.

"13, 21, 42, 53——.——"

Looking at the numbers on the paper, Li Ao noticed a pattern and said, "The intervals between these adjacent anomaly numbers correspond exactly to the segment lengths of the irregular boundary in the benchmark example."

These anomalies are not randomly distributed along the entire boundary; rather, each one is precisely positioned at the junction of two adjacent segments, and without exception, they all fall on the concave angle where the normal change is most severe, while the smooth convex angles are completely normal.

After listening to Li Ao's analysis, Lu Di gave his judgment: "It should be a problem with the dataset."

"This is the robustness test set that Argonne just released the day before yesterday. They added irregular boundaries to the benchmark example, which strengthened the local patterns near the corners. Furthermore, this set of extreme data is very likely to be included in tomorrow's evaluation."

"Because the normal to the boundary is discontinuous, the constant of the local trace estimation is directly amplified," Li Ao added, following Rudy's line of thought.

Previous tests by the project team focused on regular boundaries and relatively smooth perturbation boundaries, which are standard scenarios.

In that case, the existing candidate weights are sufficient to guarantee lower bound stability.

However, once an extreme irregular boundary is introduced, the local energy at the corner will bypass the original jump index, causing the value of R-boundary/E-bulk to be raised again.

The root of the problem has been found, but the challenges ahead have become more daunting:

How can this be resolved?

"The formal report is tomorrow morning, and we only have less than a day left. We definitely won't have time to redo a complete plan," Arjun said with a serious tone.

"If it's because the test set changed, then we're probably not the only ones experiencing this problem," Carter added from the side.

After a brief moment of thought, Li Ao proposed his own strategy: "Since the anomalies are concentrated near the corners, we can try adding discrete curvature correction to the local weights and compensate separately for boundary blocks with large normal jumps. This should solve the stability relaxation problem under irregular boundaries."

He was very confident in his candidate local boundary weights, plus the corner correction term, which were theoretically sufficient to handle this type of non-smooth boundary.

Amber nodded after listening: "Yes, I think Leo's plan is feasible."

Rudy looked at Li Ao, a hint of surprise flashing in his eyes, but still reminded him, "But we don't have much time left."

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