Lyapunov-sign-preserving neural time stepping / results.json
Mechanism confirmed, baseline not beaten
1{
2 "continuous_scalar": -1.0,
3 "predicted_euler_boundary": 2.0,
4 "observed_first_positive_grid_h": 2.01,
5 "boundary_parameter_sweep": [
6 {
7 "a": 0.5,
8 "predicted_h_star": 4.0,
9 "observed_grid_h_star": 4.004,
10 "relative_grid_error": 0.0009999999999998899
11 },
12 {
13 "a": 1.0,
14 "predicted_h_star": 2.0,
15 "observed_grid_h_star": 2.002,
16 "relative_grid_error": 0.0009999999999998899
17 },
18 {
19 "a": 2.0,
20 "predicted_h_star": 1.0,
21 "observed_grid_h_star": 1.001,
22 "relative_grid_error": 0.0009999999999998899
23 },
24 {
25 "a": 4.0,
26 "predicted_h_star": 0.5,
27 "observed_grid_h_star": 0.5005,
28 "relative_grid_error": 0.0009999999999998899
29 }
30 ],
31 "scalar": [
32 {
33 "h": 0.25,
34 "euler": -1.1507282898071236,
35 "implicit": -0.8925742052568391,
36 "euler_sign": -1,
37 "implicit_sign": -1,
38 "euler_error": 0.1507282898071236,
39 "implicit_error": 0.10742579474316094
40 },
41 {
42 "h": 0.5,
43 "euler": -1.3862943611198906,
44 "implicit": -0.8109302162163288,
45 "euler_sign": -1,
46 "implicit_sign": -1,
47 "euler_error": 0.3862943611198906,
48 "implicit_error": 0.18906978378367123
49 },
50 {
51 "h": 1.0,
52 "euler": -Infinity,
53 "implicit": -0.6931471805599453,
54 "euler_sign": -1,
55 "implicit_sign": -1,
56 "euler_error": Infinity,
57 "implicit_error": 0.3068528194400547
58 },
59 {
60 "h": 1.5,
61 "euler": -0.46209812037329684,
62 "implicit": -0.6108604879161034,
63 "euler_sign": -1,
64 "implicit_sign": -1,
65 "euler_error": 0.5379018796267032,
66 "implicit_error": 0.38913951208389663
67 },
68 {
69 "h": 1.9,
70 "euler": -0.05545290297780337,
71 "implicit": -0.5603740721012781,
72 "euler_sign": -1,
73 "implicit_sign": -1,
74 "euler_error": 0.9445470970221966,
75 "implicit_error": 0.4396259278987219
76 },
77 {
78 "h": 2.01,
79 "euler": 0.0049504133597850115,
80 "implicit": -0.5482288949058629,
81 "euler_sign": 1,
82 "implicit_sign": -1,
83 "euler_error": 1.004950413359785,
84 "implicit_error": 0.4517711050941371
85 },
86 {
87 "h": 2.5,
88 "euler": 0.16218604324326574,
89 "implicit": -0.5011051873981472,
90 "euler_sign": 1,
91 "implicit_sign": -1,
92 "euler_error": 1.1621860432432658,
93 "implicit_error": 0.49889481260185276
94 },
95 {
96 "h": 3.0,
97 "euler": 0.23104906018664842,
98 "implicit": -0.46209812037329684,
99 "euler_sign": 1,
100 "implicit_sign": -1,
101 "euler_error": 1.2310490601866484,
102 "implicit_error": 0.5379018796267032
103 }
104 ],
105 "jvp_log_error_for_known_linear_map": 0.0,
106 "error_ratios_h_to_h2": [
107 2.3943089429396647,
108 2.1587056909740094,
109 2.072426707108348
110 ],
111 "oscillator_true": -0.2,
112 "oscillator": [
113 {
114 "h": 0.05,
115 "euler": -0.0994933085366799,
116 "implicit": -0.29655884907510516,
117 "euler_error": 0.10050669146332011,
118 "implicit_error": 0.09655884907510515,
119 "euler_sign": -1,
120 "implicit_sign": -1
121 },
122 {
123 "h": 0.1,
124 "euler": 0.001999600106635902,
125 "implicit": -0.38665671468161716,
126 "euler_error": 0.20199960010663592,
127 "implicit_error": 0.18665671468161715,
128 "euler_sign": 1,
129 "implicit_sign": -1
130 },
131 {
132 "h": 0.2,
133 "euler": 0.19610356576640556,
134 "implicit": -0.5410021761170432,
135 "euler_error": 0.3961035657664056,
136 "implicit_error": 0.34100217611704314,
137 "euler_sign": 1,
138 "implicit_sign": -1
139 },
140 {
141 "h": 0.4,
142 "euler": 0.4954463613467962,
143 "implicit": -0.7391698930165755,
144 "euler_error": 0.6954463613467963,
145 "implicit_error": 0.5391698930165756,
146 "euler_sign": 1,
147 "implicit_sign": -1
148 },
149 {
150 "h": 0.8,
151 "euler": 0.7396521956709019,
152 "implicit": -0.8515071379103495,
153 "euler_error": 0.9396521956709019,
154 "implicit_error": 0.6515071379103494,
155 "euler_sign": 1,
156 "implicit_sign": -1
157 }
158 ],
159 "controller": [
160 {
161 "h": 2.5,
162 "lambda_hat": 0.16218604324326574,
163 "action": "halve"
164 },
165 {
166 "h": 1.25,
167 "lambda_hat": -1.1090354888959124,
168 "action": "keep"
169 }
170 ]
171}