Population Annealing

Simulates a population of metropolis walkers with birth-death process resampling. The qiotoolkit implementation uses variable setpping in temperatures according to one of 4 available resampling strategies:

linear_schedule: Change the temperature according to a fixed schedule (non-adaptive).
friction_tensor: Estimate the next temperature step such that the friction tensor remains stable with a constant of friction_tensor_constant
energy_variance: Adjust culling such that the energy variance remains stable, using initial_culling_constant for the first step.
constant_culling: Adjust stepping such that a constant portion culling_fraction of the population is replaced each resampling step.

The initial number of replicas can be specified via initial_population_size. The solver will double the population size whenever

There is no remaining cost variance (all replicas are in an equal-cost state)
The ratio of families remaining in the population drops below alpha (indicating that one family dominates the population).

Additionally, you may increase the number of sweeps between resamplings using the sweeps_per_replica parameter.

Example

{
  "target": "population-annealing.cpu",
  "version": "1.0",
  "input_params": {
    "seed": 42,
    "population": 100
  },
  "input_data_uri": "..."
}

param	type	required/default	description
`seed`	integer	time-based
`population`	integer >1	number of threads	population size.
`constant_population`	bool	false	whether to keep the population constant between restarts
`resampling_strategy`	string	`linear_schedule`	resample by `linear_schedule`, `friction_tensor`, `energy_variance` or `constant_culling`.
`beta`	Schedule	linear `0..5`	The schedule by which to anneal the system.
`beta_start`	float >0	0.0	initial beta for the `linear_schedule`.
`beta_stop`	float >`beta_start`	5.0	final beta for the `linear_schedule`.
`friction_tensor_constant`	float >0.0	1.0	friction tensor constant (required for `friction_tensor`
`initial_culling_fraction`	float [0,1]	0.5	initial culling rate (for `energy_variance`)
`culling_fraction`	float [0,1]	0.2	constant culling rate (for `constant_culling`)
`alpha`	float >1.0	2.0	ratio to trigger a restart

{
  "$id": "solver/populationannealing.qiotoolkit.schema",
  "$schema": "http://json-schema.org/draft-07/schema#",
  "title": "qiotoolkit Population Annealing",
  "type": "object",
  "required": ["target", "input_params"],
  "properties": {
    "target": {
      "type": "string",
      "const": "populationannealing.qiotoolkit"
    },
    "input_params": {
      "type": "object",
      "required": ["resampling_strategy"],
      "properties": {
        "alpha": {
          "type": "number",
          "minimum": 1.0,
          "default": 2.0,
          "description": "ratio to trigger a restart"
        },
        "population": {
          "type": "number",
          "minimum": 2,
          "description": "desired population size (defaults to the number of threads)"
        },
        "constant_population": {
          "type": "boolean",
          "default": "false",
          "description": "whether to keep the population constant between restarts"
        },
        "beta": {
          "type": "object",
          "$ref": "../schedule/schedule.schema",
          "description": "How the temperature should be changed over time."
        },
        "beta_start": {
          "type": "number",
          "description": "float specifying the starting inverse temperature."
          "minimum": 0,
        },
        "beta_stop": {
          "type": "number",
          "description": "float specifying the stopping inverse temperature."
          "minimum": 0,
        },
        "resampling_strategy": {
          "type": "string",
          "enum": ["linear_schedule", "friction_tensor", "energy_variance", "constant_culling"],
          "default": 'linear_schedule',
          "description": "resample by 'linear_schedule', 'friction_tensor', 'energy_variance' or 'constant_culling'."
        },
        "friction_tensor_constant": {
          "type": "number",
          "minimum": 0.0,
          "default": 1.0,
          "description": "friction tensor constant"
        },
        "initial_culling_fraction": {
          "type": "number",
          "minimum": 0.0,
          "maximum": 1.0,
          "default": 0.5,
          "description": "initial culling rate"
        },
        "culling_fraction": {
          "type": "number",
          "minimum": 0.0,
          "maximum": 1.0,
          "default": 0.2,
          "description": "constant culling rate"
        },
        "sweeps_per_replica" {
          "type": "number",
          "minimum": 1,
          "multipleOf": 1,
          "default": 1,
          "sweeps per replica between resampling."
        }
      }
    }
  }
}