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Overview

History matching is an iterative calibration technique that progressively rules out regions of parameter space that are implausible — i.e., where simulated outputs are inconsistent with observations. Rather than finding a single "best fit," it identifies the set of all parameter combinations that could plausibly have produced the observed data.

How it works

Each iteration of the algorithm:

  1. Sample points from the current non-implausible parameter space
  2. Simulate the model at each sample point
  3. Select features — choose which model outputs to emulate
  4. Train emulators — build fast statistical surrogates (e.g., Gaussian Process Regression) of the simulation
  5. Filter — use emulator predictions and implausibility scores to discard implausible regions

The parameter space shrinks with each iteration until it converges on the region consistent with observations.

Key features

  • Single-constructor API: Configure an entire workflow in one HistoryMatching(...) call
  • Interactive engine: Step-by-step control with step() / commit_step() / revert_step(), or fully automated execution with run()
  • Multiple emulators: Linear, GLM, and Gaussian Process Regression (GPflow-based with ARD kernels)
  • Pluggable strategies: Swap sampling (LHS, grid, random), feature selection (auto Fano-factor, manual), and emulator types at any point
  • Domain objects: ParameterSpace, ObservationData, EmulatorBank, and IterationResult for clean data management
  • Checkpoint/resume: Save and restore engine state for long-running workflows

Architecture

HistoryMatching                 # Configure and execute the workflow
    ├── ParameterSpace          # Parameter bounds
    ├── ObservationData         # Target observations (mean, std)
    ├── SamplingStrategy        # How to generate samples (LHS, grid, random)
    ├── FeatureSelectionStrategy # Which outputs to emulate (auto, manual)
    ├── EmulatorFactory         # Which emulator to use (linear, glm, gpr)
    ├── step()                  # Run one iteration
    ├── commit_step()           # Accept the iteration
    ├── revert_step()           # Reject and retry
    └── run()                   # Fully automated multi-iteration
            │
            ▼
IterationResult                 # Immutable results per iteration
    ├── samples                 # Parameter samples used
    ├── simulation_results      # Model outputs
    ├── emulators               # Trained emulators
    └── nroy_fraction           # Fresh-LHS acceptance rate (convergence diagnostic)

When to use history matching

History matching is well-suited for:

  • Expensive simulations where each run takes minutes to hours
  • Multiple uncertain parameters (2-20+ dimensions)
  • Multiple output features to match against observations
  • Uncertainty quantification — you want the set of plausible parameters, not just a point estimate
  • Iterative refinement — you want to progressively learn which regions of parameter space are viable

It complements other calibration approaches like MCMC (which finds posterior distributions) and optimization (which finds point estimates).