Checklist NOAI China 2024 Round 2 (China Stage) · Task 4
Solving the Pendulum Motion with Missing Data
English title: 求解部分数据丢失的单摆运动
Use PyTorch to regress the parameters of a damped pendulum with a hidden change of forcing from an interrupted angle recording, then extrapolate its motion.
The task
A unit-mass pendulum on a rope of length l is released from rest at angle theta_0 < pi/2 under gravity g = 9.8 and air resistance proportional to velocity (coefficient mu). A sensor records theta(t) but stops for at least 1 s in the middle and stops again before the motion ends. At an unknown time t_Fput during the gap, a constant downward force F starts to act. The motion obeys a(t) = -alpha * omega(t) - beta * sin(theta(t)), with alpha = mu/m, beta_1 = g/l before t_Fput and beta_2 = g/l + F/(m l) afterwards.
From the recorded (t, theta) data the contestant must determine: the rope length l, the air resistance mu, the force F, the time t_nextzerotheta at which theta next equals 0 after the recording ends (after the force is applied), and t_Fput. The training set and test sets A and B have different parameters, so the submitted method must work on unseen data. An appendix shows an example of regressing a damped linear oscillator with PyTorch.
Abridged by SOTA from the official materials. The official statement has the exact rules, and it wins wherever this summary differs.
At a glance
- You get
pendulum_train.csv(columns t, theta) from the Bohrium datasets tab;pendulum_testA.csvandpendulum_testB.csvare hidden.- You submit
submission.ipynbcontaining the full training and parameter-solving process, producingsubmission_train.csv,submissionA.csvandsubmissionB.csvwith columns l, miu, F,t_nextzerotheta, t_Fput (unsolved values filled with a default such as 1).- Scoring
- S1 = exp(-10|
l_pre-l_real|), S2 = exp(-10|mu_pre-mu_real|), S3 = exp(-|F_pre - F_real|), S4 = exp(-10|t_nextzerotheta_pre-t_nextzerotheta_real|), S5 = exp(-10|t_Fput_pre - t_Fput_real|); Score = (S1 + S2 + 2 S3 + 2 S4 + 2 S5) / 8. A submission in the wrong format scores 0. - Rules
- PyTorch is required for the regression.
- Format
- NOAI 2024 Round 2 (China Stage), a one-day practical round in Beijing on 10 June 2024 (date and place from a third-party overview page). Republished on Bohrium as the 'NOAI2025 teaching test (NOAI2024 real problems)' and, in English, as the 'APOAI2025 Mock Competition' (10 Nov 2024 - 31 May 2025). Leaderboard A uses 50% of the test set during the contest; leaderboard B (the remaining 50%) is final. Question 4.