How to: Run GP-NEB with OIE Acquisition

1 GP-Accelerated Nudged Elastic Band

The GP-NEB method reduces the number of oracle (energy/force) evaluations needed to converge a minimum energy path. Three modes are available:

Mode	Oracle calls/iter	Best for
Standard	All images	Cheap potentials, baseline
AIE	All images + GP inner relaxation	Moderate potentials
OIE	1-3 images (acquisition-selected)	Expensive DFT

1.1 Quick start (C++)

#include <gpr_optim/NEBPath.h>
#include <gpr_optim/AnalyticalPotentials.h>

// Muller-Brown oracle
auto oracle = [](const Eigen::VectorXd& x) {
    std::vector<double> xy = {x(0), x(1)};
    auto [e, g] = gpr::potentials::muller_brown_energy_gradient(xy);
    return std::make_pair(e, Eigen::Map<Eigen::VectorXd>(g.data(), 2));
};

// Set up GP-NEB
gpr::neb::GPNEBConfig config;
config.mode = gpr::neb::NEBMode::OIE;
config.max_outer_iter = 50;
config.conv_tol = 0.01;
config.evals_per_iter = 1;
config.acquisition = gpr::neb::AcquisitionType::ThompsonSampling;
config.climbing_image = true;

Eigen::VectorXd min1(2), min2(2);
min1 << -0.558, 1.442;  // Muller-Brown minimum 1
min2 << 0.623, 0.028;   // Muller-Brown minimum 2

auto result = gpr::neb::gpNEB(oracle, min1, min2, 7, config);

std::cout << "Converged: " << result.converged << "\n";
std::cout << "Oracle calls: " << result.oracle_calls << "\n";
std::cout << "Barrier energy: " << result.barrier_energy << "\n";

1.2 Acquisition strategies

The OIE mode selects which image to evaluate next. Four strategies:

ThompsonSampling is recommended for most cases. It naturally transitions from exploration (early, high uncertainty) to exploitation (late, low uncertainty).

1.3 IDPP path initialization

For molecular systems, use IDPP instead of linear interpolation:

gpr::neb::NEBPath path(initial, final_state, 7, 0.1);
path.initializeIDPP(n_atoms, false);   // per-image IDPP
path.initializeIDPP(n_atoms, true);    // collective S-IDPP with springs

1.4 Triplet evaluation

For better tangent accuracy in OIE mode, evaluate {i-1, i, i+1} instead of just image i:

config.use_triplet = true;
config.evals_per_iter = 3;