{
"cells": [
{
"cell_type": "markdown",
"id": "693439e4",
"metadata": {},
"source": [
"# Example 8: Model Calibration — Approximate Bayesian Computation (ABC-SMC) \n",
"\n",
"[(GitHub link)](https://github.com/heberlr/UQ_PhysiCell/tree/main/examples/virus-mac-new/ex8_ABC_Calib.ipynb)\n",
"\n",
"This notebook calibrates the [virus-mac-new](https://github.com/heberlr/UQ_PhysiCell/tree/main/examples/virus-mac-new) model using **ABC-SMC (Approximate Bayesian Computation — Sequential Monte Carlo)**. Unlike BO (ex7) which finds point estimates, ABC-SMC returns a full **posterior distribution** over parameters, quantifying how uncertain we are about each parameter given the observed data.\n",
"\n",
"**BO (ex7) vs ABC-SMC (ex8):**\n",
"| | Bayesian Optimization (ex7) | ABC-SMC (ex8) |\n",
"|---|---|---|\n",
"| Output | Pareto front (point estimates) | Posterior distribution |\n",
"| Tells you | Best-fit parameter values | Full uncertainty over parameters |\n",
"| Requires | Acquisition function + GP | Prior distribution + distance function |\n",
"| Best for | Finding optimal parameters | Uncertainty quantification |\n",
"\n",
"**What you will learn:**\n",
"- How to define prior distributions using pyABC's `Distribution` and `RV`\n",
"- How distance functions replace the objective function from BO\n",
"- How ABC-SMC progressively tightens the tolerance (epsilon) across populations\n",
"- How to read the posterior: width reflects identifiability, coverage of the true value reflects accuracy\n",
"\n",
"**Ground truth (same observed data as ex7):**\n",
"- `mac_phag_rate_infected` = 1.0\n",
"- `epi2infected_hfm` = 0.4"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a3574ae4",
"metadata": {},
"outputs": [],
"source": [
"import warnings, logging\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"from uq_physicell.abc import CalibrationContext, run_abc_calibration\n",
"from pyabc import RV, Distribution, visualization\n",
"\n",
"logging.basicConfig(level=logging.INFO)\n",
"logger = logging.getLogger(__name__)\n",
"\n",
"db_path = \"ex8_ABC_Calib.db\"\n",
"obs_data_path = \"ex7_ObsData.csv\"\n",
"dic_real_value = {\"mac_phag_rate_infected\": 1.0, \"epi2infected_hfm\": 0.4}\n",
"\n",
"model_config = {\"ini_path\": \"uq_pc_struc.ini\", \"struc_name\": \"Model_struc_Calib\"}\n",
"\n",
"# df_cell → cell DataFrame (see ex1 for the full dispatch table)\n",
"qoi_functions = {\n",
" \"epi_\": lambda df_cell: len(df_cell[df_cell['cell_type'] == 'epithelial']),\n",
" \"epi_infected\": lambda df_cell: len(df_cell[df_cell['cell_type'] == 'epithelial_infected']),\n",
"}\n",
"\n",
"obs_data_columns = {\n",
" \"time\": \"Time\",\n",
" \"epi_\": \"Healthy Epithelial Cells\",\n",
" \"epi_infected\": \"Infected Epithelial Cells\",\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "69566ab1",
"metadata": {},
"source": [
"## Distance functions, prior, and ABC options"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f7129ddc",
"metadata": {},
"outputs": [],
"source": [
"def euclidean_distance_epi(data1, data2):\n",
" obs_vals = np.array(data1['epi_'])\n",
" sim_vals = np.array(data2['epi_'])\n",
" return np.sum((obs_vals - sim_vals) ** 2)\n",
"\n",
"def euclidean_distance_epi_infected(data1, data2):\n",
" obs_vals = np.array(data1['epi_infected'])\n",
" sim_vals = np.array(data2['epi_infected'])\n",
" return np.sum((obs_vals - sim_vals) ** 2)\n",
"\n",
"distance_functions = {\n",
" \"epi_\": {\"function\": euclidean_distance_epi},\n",
" \"epi_infected\": {\"function\": euclidean_distance_epi_infected},\n",
"}\n",
"\n",
"# Uniform priors over the same bounds as ex7 for direct comparison\n",
"prior = Distribution(\n",
" mac_phag_rate_infected=RV(\"uniform\", 0.7, 0.8), # uniform on [0.7, 1.5]\n",
" epi2infected_hfm=RV(\"uniform\", 0.1, 0.4), # uniform on [0.1, 0.5]\n",
")\n",
"\n",
"abc_options = {\n",
" \"max_populations\": 2,\n",
" \"max_simulations\": 100,\n",
" \"population_strategy\": \"adaptive\",\n",
" \"min_population_size\": 10,\n",
" \"max_population_size\": 50,\n",
" \"adaptive_distance\": True,\n",
" \"sampler\": \"multicore\",\n",
" \"num_workers\": 6,\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "8f6006a0",
"metadata": {},
"source": [
"## Create context and run ABC-SMC calibration"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "fe38de9a",
"metadata": {},
"outputs": [],
"source": [
"calib_context = CalibrationContext(\n",
" db_path=db_path,\n",
" obsData=obs_data_path,\n",
" obsData_columns=obs_data_columns,\n",
" model_config=model_config,\n",
" qoi_functions=qoi_functions,\n",
" distance_functions=distance_functions,\n",
" prior=prior,\n",
" abc_options=abc_options,\n",
" logger=logger,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "fd73d229",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"ABC.Sampler INFO: Parallelize sampling on 1 processes.\n",
"INFO:ABC.Sampler:Parallelize sampling on 1 processes.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Completed — 1 populations, 158 total simulations\n"
]
}
],
"source": [
"history = run_abc_calibration(calib_context=calib_context)\n",
"print(f\"Completed — {history.n_populations} populations, {history.total_nr_simulations} total simulations\")"
]
},
{
"cell_type": "markdown",
"id": "f7855bf7",
"metadata": {},
"source": [
"## Posterior analysis\n",
"\n",
"The posterior distribution shows how much each parameter value is supported by the observed data. A narrow posterior means the data is informative about that parameter; a wide posterior means it is hard to identify from this QoI alone."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b571d9fc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | name | \n",
" epi2infected_hfm | \n",
" mac_phag_rate_infected | \n",
"
\n",
" \n",
" | id | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" | 2 | \n",
" 0.346153 | \n",
" 1.159550 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.354043 | \n",
" 0.920385 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.401899 | \n",
" 1.447023 | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.451707 | \n",
" 1.355795 | \n",
"
\n",
" \n",
" | 6 | \n",
" 0.366163 | \n",
" 0.875740 | \n",
"
\n",
" \n",
"
\n",
"