PDE Sinkhorn with asymmetric geometric boundaries / results.json

Mechanism confirmed, baseline not beaten

Raw ⬇ ZIP
  1{
  2  "seed": 1094,
  3  "oblique_geometry": {
  4    "correlations": [
  5      0.0,
  6      0.2,
  7      0.5,
  8      0.8,
  9      0.95
 10    ],
 11    "oblique_residual": [
 12      0.0,
 13      0.0,
 14      0.0,
 15      0.0,
 16      0.0
 17    ],
 18    "normal_bc_residual": [
 19      0.0,
 20      0.2,
 21      0.5,
 22      0.8,
 23      0.95
 24    ],
 25    "oblique_flux_residual": [
 26      0.0,
 27      0.0,
 28      0.0,
 29      0.0,
 30      0.0
 31    ],
 32    "normal_bc_flux_residual": [
 33      0.0,
 34      0.2,
 35      0.5,
 36      0.8,
 37      0.95
 38    ]
 39  },
 40  "finite_volume_no_flux": [
 41    {
 42      "D": 0.0,
 43      "mass_error": 2.220446049250313e-16,
 44      "min_density": 2.0101186545820862e-53,
 45      "boundary_flux_left": 0.0,
 46      "boundary_flux_right": 0.0
 47    },
 48    {
 49      "D": 0.001,
 50      "mass_error": 1.3322676295501878e-15,
 51      "min_density": 1.2749254882107288e-36,
 52      "boundary_flux_left": 0.0,
 53      "boundary_flux_right": 0.0
 54    },
 55    {
 56      "D": 0.03,
 57      "mass_error": 2.886579864025407e-14,
 58      "min_density": 4.278259484180719e-07,
 59      "boundary_flux_left": 0.0,
 60      "boundary_flux_right": 0.0
 61    },
 62    {
 63      "D": 0.3,
 64      "mass_error": 2.0961010704922955e-13,
 65      "min_density": 0.006343464843167625,
 66      "boundary_flux_left": 0.0,
 67      "boundary_flux_right": 0.0
 68    },
 69    {
 70      "D": 1.0,
 71      "mass_error": 8.777423232686488e-13,
 72      "min_density": 0.012019163968891133,
 73      "boundary_flux_left": 0.0,
 74      "boundary_flux_right": 0.0
 75    }
 76  ],
 77  "explicit_stability": {
 78    "lambda_min": -25590.13166388125,
 79    "predicted_positivity_dt": 7.812500000000002e-05,
 80    "predicted_spectral_dt": 7.815512738540793e-05,
 81    "sweep": [
 82      {
 83        "ratio_to_positivity_bound": 0.5,
 84        "dt": 3.906250000000001e-05,
 85        "min_after_80": 0.011791476903648481,
 86        "l1_norm": 1.0,
 87        "nonnegative_observed": true
 88      },
 89      {
 90        "ratio_to_positivity_bound": 0.9,
 91        "dt": 7.031250000000002e-05,
 92        "min_after_80": 0.011972631497932828,
 93        "l1_norm": 1.0,
 94        "nonnegative_observed": true
 95      },
 96      {
 97        "ratio_to_positivity_bound": 1.0,
 98        "dt": 7.812500000000002e-05,
 99        "min_after_80": 0.0012501272648350811,
100        "l1_norm": 0.9999999999999998,
101        "nonnegative_observed": true
102      },
103      {
104        "ratio_to_positivity_bound": 1.05,
105        "dt": 8.203125000000002e-05,
106        "min_after_80": -23.031859208155673,
107        "l1_norm": 1522.2312585533655,
108        "nonnegative_observed": false
109      },
110      {
111        "ratio_to_positivity_bound": 1.5,
112        "dt": 0.00011718750000000002,
113        "min_after_80": -1.3600411825068436e+22,
114        "l1_norm": 9.200083731731275e+23,
115        "nonnegative_observed": false
116      }
117    ]
118  },
119  "sinkhorn_demo": [
120    {
121      "method": "reflected_PDE",
122      "initial_KL": 3.9631580800459455e-17,
123      "terminal_KL": 4.77791235308488e-16,
124      "boundary_mass_initial": 0.0009829825534952367,
125      "boundary_mass_terminal": 0.0009829817821124017
126    },
127    {
128      "method": "unconstrained_kernel",
129      "initial_KL": 1.2291990088734708e-17,
130      "terminal_KL": 5.031197839284198e-15,
131      "boundary_mass_initial": 0.0009829825477668782,
132      "boundary_mass_terminal": 0.0009829799777868512
133    }
134  ]
135}