USAAIO Round 1真题

USAAIO Round 2真题

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一、2025 USAAIO Round 1（部分真题）

第1题：Problem 1 (100 points)

Let us consider the following sequence:

$$F_n=F_{n-1}+F_{n-2},\forall n\ge 2.$$

Before starting this problem, make sure to run the following code first without any change:

# DO NOT CHANGE

import numpy as np

import matplotlib.pyplot as plt

""" END OF THIS PART """

$\text{WARNING !!!}$

Beyond importing libraries/modules/classes/functions in the preceeding cell, you are NOT allowed to import anything else for the following purposes:

• As a part of your final solution. For instance, if a problem asks you to build a model without using sklearn but you use it, then you will not earn points.
• Temporarily import something to assist you to get a solution. For instance, if a problem asks you to manually compute eigenvalues but you temporarily use np.linalg.eig to get an answer and then delete your code, then you violate the rule.

Rule of thumb: Each part has its particular purpose to intentionally test you something. Do not attempt to find a shortcut to circumvent the rule.

All coding tasks shall run on CPUs, not GPUs.

Part 1 (10 points, non-coding task)

Let $F_0=3$, $F_1=1$.

Manually write down $F_n$ for $n=2,3,4,5$.

Reasoning is not required.

Part 2 (10 points, non-coding task)

Part 3 (10 points, non-coding task)

Explain why $A$ is a symmetric matrix.

Part 4 (10 points, non-coding task)

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二、2025 USAAIO Round 2（部分真题）

Problem 1 (100 points)

The high level idea of PINN is as follows:

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