Constitutive-model calibration¶

The motivating application of DEEM is the automatic calibration of advanced constitutive soil models with numgeo-ACT. Here a single objective evaluation runs finite-element simulations of laboratory element tests (oedometer, drained/undrained monotonic and cyclic triaxial), compares them with experimental data using a discrete Fréchet distance, and returns a weighted error \(\epsilon\). The cost function is rugged and discontinuous — for some parameter sets the model is not numerically stable — which makes it a hard optimisation problem and a good match for DEEM's restart and multi-population strategy.

This page is a usage pattern, not a runnable script: the objective wraps an external FE solver.

A calibration-style objective¶

import numpy as np
from DEEM.DEEMI import DEEM

def calibration_error(x):
    """
    Run the element-test simulations for the parameter vector x, compare with
    the experiments, and return the weighted error epsilon (to be minimised).
    Return a large penalty if the model fails to converge for these parameters.
    """
    try:
        eps = run_act_simulations(x)        # your numgeo-ACT evaluation
    except SimulationError:
        return 1e22                          # penalty (matches the `penalty` arg)
    return float(eps)

# parameter bounds for the model (e.g. Hypo-ISA: nD = 15)
LB = np.array([...])
UB = np.array([...])

optimizer = DEEM(
    function=calibration_error,
    lower_bound=LB, upper_bound=UB,
    nparticles_max=10 * len(LB), nparticles_min=10 * len(LB),
    npop_max=10, npop_min=4,
    maxiter=200,                 # calibrations use far fewer iterations than CEC
    nworkers=8,                  # evaluate the population in parallel
    method_reset="hybrid",       # correlation-aware restart (parameters interact)
    adapt=True,
    seed=0,
)
result = optimizer.update()
print("calibrated parameters:", result["x"])
print("final error epsilon  :", result["f"])

Parallel evaluation¶

With nworkers > 1, the population is evaluated through a process pool. On a workstation, the paper reports roughly 40 min per iteration for the Hypo-ISA calibration with parallelisation, so spreading the population over the available cores is essential.

Windows worker initialization¶

On Windows, worker processes are spawned and do not inherit the parent process state. The bundled evaluation.py starts the pool with an initializer that re-establishes the runtime state the objective needs (for numgeo-ACT, the ACT.globals module) in every worker:

# DEEM/evaluation.py (excerpt)
with futures.ProcessPoolExecutor(
        max_workers=nworkers,
        initializer=initialize_worker,
        initargs=(worker_data,)) as executor:
    ...

On Linux this state is inherited through fork, so no special handling is required. If your objective relies on state set at runtime in the main process, make sure that state is available to the workers — either through the initializer mechanism, or by running serially with nworkers=1.

Reducing expensive evaluations¶

For very costly objectives, DEEMI offers two opt-in mechanisms to spend the evaluation budget more carefully:

• Surrogate pre-screening (surrogate=SurrogateManager(LB, UB) for the RBF model, or surrogate=GPSurrogateManager(LB, UB) for the Gaussian process) — evaluate only the most promising trial vectors on the real objective each iteration.
• Evaluation cache (cache_tol=1e-6) — never re-simulate a position that has already been evaluated (useful when penalty-triggering points recur).

See the DEEMI overview for details.