Lyapunov-sign-preserving neural time stepping / results.json

Mechanism confirmed, baseline not beaten

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  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}