Module optimizer

Expand description

Optimization algorithms for MECP calculations.

This module implements various optimization algorithms used in Minimum Energy Crossing Point (MECP) calculations, including:

BFGS: Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method
GDIIS: Geometry-based Direct Inversion in Iterative Subspace
GEDIIS: Energy-Informed DIIS with improved convergence
Hessian Updates: PSB (Powell-Symmetric-Broyden) formula
Convergence Checking: Multiple criteria for optimization termination

The module also provides functions to compute MECP effective gradients that combine the energy difference minimization and energy perpendicular components according to the Harvey et al. algorithm.

§Optimization Strategy

OpenMECP uses a hybrid optimization strategy:

Initialization: BFGS for the first 3 steps to build curvature information
Convergence Acceleration: Switch to GDIIS or GEDIIS for faster convergence
Adaptive Step Control: Automatic step size limiting prevents overshooting
Checkpointing: Save optimization state for restart capability

§Implementation Improvements (v2.0)

Recent enhancements ensure mathematical rigor and numerical stability:

Adaptive GEDIIS Parameters: α scales with 1/|g| for better stability
PSB Curvature Check: Validates s^T y > 0 before Hessian update
Improved MECP Gradient: Uses minimum norm vector to prevent premature convergence
Better Fallback Handling: Steepest descent properly scaled in BFGS
High-Precision Thresholds: Tighter convergence criteria for research use

§MECP Gradient Calculation

The MECP effective gradient combines two components:

G_MECP = (E1 - E2) * x_norm + (f1 - (x_norm · f1) * x_norm)

Where:

E1, E2: Energies of the two electronic states
f1, f2: Gradients (forces) of the two states
x_norm = (f1 - f2) / |f1 - f2|: Normalized gradient difference

The first term drives the energy difference to zero (f-vector). The second term minimizes energy perpendicular to the gradient difference (g-vector).

Re-exports§

pub use crate::gdiis::CosineCheckMode;
pub use crate::gdiis::CoeffCheckMode;
pub use crate::gdiis::GdiisError;
pub use crate::gdiis::GdiisOptimizer;
pub use crate::gediis::compute_dynamic_gediis_weight as gediis_dynamic_weight;
pub use crate::gediis::EnergyRiseTracker;
pub use crate::gediis::GediisConfig;
pub use crate::gediis::GediisOptimizer;
pub use crate::gediis::GediisVariant;
pub use crate::hessian_update::HessianUpdateMethod;

Structs§

ConvergenceStatus: Tracks convergence status for each optimization criterion.
MecpGradient: Holds the decomposed MECP effective gradient.
OptimizationState: Tracks optimization state and history for adaptive optimization algorithms.
OptimizationState_blend: Holds optimization state for the GDIIS_blend and GEDIIS_blend implementations.

Functions§

adjust_trust_radius: Adjusts the trust radius based on the actual energy change from QM.
bfgs_step: Performs a BFGS optimization step.
bfgs_step_direct: Performs a BFGS step using a direct Hessian (matching exactly).
build_b_matrix 🔒: Builds the B matrix for GDIIS optimization.
build_gediis_b_matrix 🔒: Computes enhanced error vectors for GEDIIS optimization.
build_gediis_b_matrix_taylor 🔒: Builds the GEDIIS B-matrix using the Taylor expansion formula.
check_convergence: Checks convergence criteria for MECP optimization.
compute_adaptive_scale: Computes adaptive step scaling based on optimization progress.
compute_error_vectors 🔒: Computes error vectors for GDIIS optimization.
compute_mecp_gradient: Computes the MECP effective gradient for optimization.
fixed_blend_step: Hybrid GEDIIS/GDIIS step.
fixed_sequential_blend_step: Fixed-then-GDIIS sequential blend step.
gdiis_blend_step: GDIIS_blend step: interpolate geometry, apply Newton correction via INVERTED mean true Hessian, with step control.
gdiis_step: Performs a GDIIS (Geometry-based Direct Inversion in Iterative Subspace) optimization step.
gdiis_step_direct: Performs a simplified GDIIS step matching exactly.
gediis_blend_step: GEDIIS_blend step: pure interpolation using Taylor expansion B-matrix.
gediis_step: Performs a GEDIIS (Energy-Informed Direct Inversion in Iterative Subspace) optimization step.
gradient_blend_step: Gradient-weighted hybrid GEDIIS/GDIIS blend step.
initialize_direct_hessian: Initializes the direct Hessian matrix for direct Hessian BFGS optimization.
initialize_inverse_hessian: Updates the Hessian matrix using the PSB (Powell-Symmetric-Broyden) formula.
initialize_true_hessian: Creates an identity matrix as the initial true Hessian approximation.
parse_coeff_mode: Converts config string to CoeffCheckMode.
parse_cosine_mode: Performs a hybrid GEDIIS optimization step (50% GDIIS + 50% GEDIIS).
parse_gediis_variant: Converts config string to GediisVariant.
parse_hessian_update_method: Converts config string to HessianUpdateMethod.
robust_gdiis_step: Performs a robust GDIIS step using the new GdiisOptimizer.
robust_gediis_step: Performs a robust GEDIIS step using the new GediisOptimizer.
select_blend_step: Dispatcher for the blend experiment methods.
select_diis_step: Selects and runs the appropriate DIIS/GEDIIS step based on configuration.
sequential_blend_step: Smart sequential hybrid GEDIIS/GDIIS blend step.
sequential_hybrid_gediis_step: Computes dynamic GEDIIS weight based on energy trend and oscillation detection.
solve_constrained_step: Solves the augmented Hessian system for a constrained optimization step.
stepsize_blend: Applies step size reduction and capping.
update_hessian: Updates the inverse Hessian matrix using the BFGS formula.
update_hessian_advanced: Updates the Hessian matrix using the specified method from the hessian_update module.
update_hessian_by_method: Updates the Hessian matrix using the specified method.
update_hessian_psb: Updates the Hessian matrix using the PSB (Powell-Symmetric-Broyden) formula.
update_inverse_hessian_advanced: Updates the inverse Hessian using the BFGS formula from the hessian_update module.