VIETNAM NATIONAL UNIVERSITY, HO CHI MINH CITY
UNIVERSITY OF TECHNOLOGY
FACULTY OF COMPUTER SCIENCE AND ENGINEERING
MATHEMATICAL MODELING
(CO2011)
Assignment (Semester: 221, Duration: 06 weeks)
Dynamics of Love
Instructor(s) : Nguyễn Tiến Thịnh
Nguyễn An Khương
Nguyễn Văn Minh Mẫn
Mai Xuân Toàn
Trần Hồng Tài
Student(s) : Đoàn Duy Tùng - 2112609 (Group L05 - Team 01)
Lương Thế Tổng - 2115040 (Group L05 - Team 01, Leader)
Đổng Hoàng Sơn - 2110507 (Group L05 - Team 01)
Nguyễn Trung Vương - 2115337 (Group L01 - Team 01)
HO CHI MINH CITY, 20/10/2022
University of Technology, Ho Chi Minh City
Faculty of Computer Science and Engineering
Contents
List of figures 1
List of Tables 1
1 Danh sách thành viên và phân công công việc 1
2 Exercise 1 1
2.1 Hệ phương trình giá trị ban đầu ................................ 1
2.2 Biểu thức nghiệm của hệ phương trình giá trị ban đầu .................... 2
2.3 Complete Tab. 2 ......................................... 7
3 Exercise 2 11
3.1 Tình yêu giữa Eager Beaver và Eager Beaver ......................... 11
3.2 Tình yêu giữa Eager Beaver và Narcissistic Nerd ....................... 14
3.3 Tình yêu giữa Eager Beaver và Cautious Lover ........................ 17
3.4 Tình yêu giữa Eager Beaver và Hermit ............................. 20
3.5 Tình yêu giữa Narcissistic Nerd và Narcissistic Nerd ..................... 23
3.6 Tình yêu giữa Narcissistic Nerd và Cautious Lover ...................... 26
3.7 Tình yêu giữa Narcissistic Nerd và Hermit ........................... 29
3.8 Tình yêu giữa Cautious Lover và Cautious Lover ....................... 32
3.9 Tình yêu giữa Cautious Lover và Hermit ............................ 35
3.10 Tình yêu giữa Hermit và Hermit ................................ 38
4 Exercise 3 42
4.1 Problem 1 ............................................. 42
4.1.1 Điều kiện có nghiệm của f, g .............................. 42
4.1.2 Ví dụ ........................................... 44
4.2 Problem 2 ............................................. 47
4.2.1 Định nghĩa: Lipschitz continuity ............................ 48
4.2.2 Định lý 1: Picard–Lindel¨of theorem ........................... 48
4.2.3 Ví dụ ........................................... 48
5 Exercise 4 50
5.1 Problem 1 ............................................. 50
5.1.1 Sơ lược về Explicit Euler ................................ 50
5.1.2 Công thức Taylor ..................................... 50
5.1.3 Ứng dụng công thức Taylor để chứng minh ...................... 51
5.2 Problem 2 ............................................. 51
5.2.1 Sơ lược về Implicit Euler ................................ 51
5.2.2 Ví dụ về Implicit Euler ................................. 51
5.3 Problem 3 ............................................. 55
5.3.1 Chứng minh ϵ(t1)tỉ lệ thuận với h2.......................... 55
5.3.2 Lợi thế và Nhược điểm khi sử dụng Implicit Euler .................. 56
6 Exercise 5 58
6.1 Ý tưởng .............................................. 58
6.2 Mạng neuron nhân tạo - Artificial Neural Network (ANN) .................. 58
6.2.1 Long short-term memory (LSTM) ........................... 58
6.2.2 Bidirectional LSTM - BiLSTM ............................. 60
6.3 Cấu trúc mô hình ......................................... 60
6.4 Xử lý dữ liệu và thông số mô hình ............................... 61
6.5 Kết quả và đánh giá mô hình .................................. 62
6.6 Thông số cấu hình ........................................ 63
Tài liệu tham khảo 64
Mathematical Modeling Assignment (CO2011), Semester 1, Academic year 2022-2023 Page i
University of Technology, Ho Chi Minh City
Faculty of Computer Science and Engineering
List of figures
1 The love between an eager beaver and an eager beaver .................... 12
2 The phase portrait of the love between an eager beaver and an eager beaver (Saddle Point)12
3 The love between an eager beaver and an eager beaver .................... 13
4 The phase portrait of the love between an eager beaver and an eager beaver (Unstable
Node) ............................................... 14
5 The love between an Eager beaver and a Narcissistic Nerd .................. 15
6 The phase portrait of the love between an eager beaver and a Narcissistic Nerd (Unstable
spiral) .............................................. 15
7 The love between an Eager beaver and a Narcissistic Nerd .................. 16
8 The phase portrait of the love between an eager beaver and a Narcissistic Nerd (Unstable
Improper Node) ........................................ 17
9 The love between an Eager beaver and a Cautious Lover ................... 18
10 The phase portrait of the love between an Eager beaver and a Cautious Lover (Saddle
Point) ............................................... 18
11 The love between an Eager beaver and a Cautious Lover ................... 19
12 The phase portrait of the love between an Eager beaver and a Cautious Lover (Saddle
Point) ............................................... 20
13 The love between an Eager beaver and a Hermit ....................... 21
14 The phase portrait of the love between an Eager beaver and a Hermit (Center) ..... 21
15 The love between an Eager beaver and a Hermit ....................... 22
16 The phase portrait of the love between an Eager beaver and a Hermit (Unstable Spiral) 23
17 The love between a Narcissistic Nerd and a Narcissistic Nerd ................ 24
18 The phase portrait of the love between a Narcissistic Nerd and a Narcissistic Nerd (Un-
stable Saddle) ......................................... 24
19 The love between a Narcissistic Nerd and a Narcissistic Nerd ................ 25
20 The phase portrait of the love between a Narcissistic Nerd and a Narcissistic Nerd (Saddle
Point) ............................................... 26
21 The love between a Narcissistic Nerd and a Cautious Lover ................. 27
22 The phase portrait of the love between a Narcissistic Nerd and a Cautious Lover (Unstable
Node) ............................................... 27
23 The love between a Narcissistic Nerd and a Cautious Lover ................. 28
24 The phase portrait of the love between a Narcissistic Nerd and a Cautious Lover (Saddle
Point) ............................................... 29
25 The love between a Narcissistic Nerd and a Hermit ...................... 30
26 The phase portrait of the love between a Narcissistic Nerd and a Hermit (Saddle Point) 30
27 The love between a Narcissistic Nerd and a Hermit ...................... 31
28 The phase portrait of the love between a Narcissistic Nerd and a Hermit (Saddle Point) 32
29 The love between a Cautious Lover and a Cautious Lover .................. 33
30 The phase portrait of the love between a Cautious Lover and a Cautious Lover (Stable
Node) ............................................... 33
31 The love between a Cautious Lover and a Cautious Lover .................. 34
32 The phase portrait of the love between a Cautious Lover and a Cautious Lover (Stable
Node) ............................................... 35
33 The love between a Cautious Lover and a Hermit ....................... 36
34 The phase portrait of the love between a Cautious Lover and a Hermit (Stable Spiral) . 36
35 The love between a Cautious Lover and a Hermit ....................... 37
36 The phase portrait of the love between a Cautious Lover and a Hermit (Stable Improper
Node) ............................................... 38
37 The love between a Hermit and a Hermit ........................... 39
38 The phase portrait of the love between a Hermit and a Hermit (Stable Node) ...... 39
39 The love between a Hermit and a Hermit ........................... 40
40 The phase portrait of the love between a Hermit and a Hermit (Stable Node) ...... 41
41 Hàm implicit Euler ........................................ 52
42 Mô tả f(R, J, t)và g(R, J, t)cho ví dụ 1 ............................ 52
43 Kết quả ví dụ 1 .......................................... 52
Mathematical Modeling Assignment (CO2011), Semester 1, Academic year 2022-2023 Page ii
University of Technology, Ho Chi Minh City
Faculty of Computer Science and Engineering
44 Mô tả f(R, J, t)và g(R, J, t)cho ví dụ 2 ............................ 53
45 Kết quả ví dụ 2 .......................................... 53
46 Mô tả f(R, J, t)và g(R, J, t)cho ví dụ 3 ............................ 53
47 Kết quả ví dụ 3 .......................................... 54
48 Mô tả f(R, J, t)và g(R, J, t)cho ví dụ 4 ............................ 54
49 Kết quả ví dụ 4 .......................................... 54
50 Mô tả f(R, J, t)và g(R, J, t)cho ví dụ 5 ............................ 55
51 Kết quả ví dụ 5 .......................................... 55
52 Explicit Euler function ...................................... 57
53 Định nghĩa hàm tính LTE trong python ............................ 57
54 Cấu trúc một LSTM cell ..................................... 59
55 Recurrent Neural Network .................................... 59
56 Bidirectional LSTM ....................................... 60
57 Cấu trúc mô hình ......................................... 60
58 Minh họa bộ lọc Savitzky–Golay ................................ 62
59 Kết quả xấp xỉ a, b, c, d ..................................... 63
60 Kết quả đào tạo ......................................... 63
Mathematical Modeling Assignment (CO2011), Semester 1, Academic year 2022-2023 Page iii
University of Technology, Ho Chi Minh City
Faculty of Computer Science and Engineering
List of Tables
1 Romantic styles .......................................... 2
2 Phase-portrait classification ................................... 7
3 So sánh giá trị Local Truncation Error và thời gian thực thi của giải thuật (40 điểm) . . . 57
4 Bảng thống kê MAE cho từng giá trị m ............................ 62
5 Kết quả xấp xỉ a, b, c, d ..................................... 62
6 Kết quả cuối cùng của a, b, c, d ................................. 63
7 Thông số cấu hình ........................................ 63
Mathematical Modeling Assignment (CO2011), Semester 1, Academic year 2022-2023 Page iv