optimizer

class GradientDescent(learning_rate: float, convergence_tolerance: float, max_cycle: int)

Simple gradient descent optimizer.

__init__(learning_rate: float, convergence_tolerance: float, max_cycle: int)

Initialize the gradient descent optimizer.

Parameters:

• max_cycle – Maximum number of optimization cycles.

• convergence_tolerance – Optimization stops if the gradient norm is below this value.

• learning_rate – The learning rate.

optimize(sample: OFData, energy_functional: Callable, callback: Callable | None = None, disable_pbar: bool = False) → tuple[Energies, bool]

Perform gradient descent optimization.

class Optimizer

Base class for optimization algorithms for density optimization.

__str__() → str

Return a string representation of the optimizer.

abstractmethod optimize(sample: OFData, energy_functional: Callable[[OFData], tuple[Energies, Tensor]], callback: Callable | None = None, disable_pbar: bool = False) → tuple[Energies, bool]

Perform density optimization.

Parameters:

• sample – The OFData containing the initial coefficients.

• energy_functional – Callable which returns the energy and gradient vector.

• callback – Optional callback function.

• disable_pbar – Whether to disable the progress bar.

Returns:

Final energy.

class SLSQP(max_cycle: int, convergence_tolerance: float, grad_scale: float, use_projected_gradient: bool = True)

Wrapper for the SLSQP (Sequential Least Squares Programming) optimizer from scipy.

__init__(max_cycle: int, convergence_tolerance: float, grad_scale: float, use_projected_gradient: bool = True)

Initialize the SLSQP optimizer.

Parameters:

• max_cycle – Maximum number of optimization cycles. Note that this is not the same as the number of functional evaluations.

• convergence_tolerance – Optimization stops if the gradient norm is below this value.

• grad_scale – Scaling factor for the gradient vector.

• use_projected_gradient – Whether to use the projected gradient for the optimization step.

optimize(sample: OFData, energy_functional: Callable, callback: Callable | None = None, disable_pbar: bool = False) → tuple[Energies, bool]

Perform density optimization using the SLSQP optimizer.

class TorchOptimizer(torch_optimizer: Type[Optimizer], convergence_tolerance: float, max_cycle: int, **optimizer_kwargs)

Wrapper for torch optimizers to be used in the optimization loop.

__init__(torch_optimizer: Type[Optimizer], convergence_tolerance: float, max_cycle: int, **optimizer_kwargs)

Initialize the torch optimizer.

Parameters:

• torch_optimizer – The torch optimizer to use. To be able to apply the optimizer with hydra, the class is partially applied without any arguments.

• convergence_tolerance – Optimization stops if the gradient norm is below this value.

• max_cycle – Maximum number of optimization cycles.

• optimizer_kwargs – Additional keyword arguments for the optimizer.

__str__() → str

Return a string representation of the optimizer.

This method is overwritten since the torch optimizer can either be a class via direct instantiation or via hydra with a partial.

optimize(sample: OFData, energy_functional: Callable, callback: Callable | None = None, disable_pbar: bool = False) → tuple[Energies, bool]

Optimization loop for a torch optimizer.

class TrustRegionConstrained(max_cycle: int, convergence_tolerance: float, initial_tr_radius: float, initial_constr_penalty: float, use_projected_gradient: bool = True)

Wrapper for the trust region constrained optimizer from scipy.

__init__(max_cycle: int, convergence_tolerance: float, initial_tr_radius: float, initial_constr_penalty: float, use_projected_gradient: bool = True)

Initialize the trust region constrained optimizer.

Parameters:

• convergence_tolerance

• max_cycle – Maximum number of optimization cycles.

• convergence_tolerance – Optimization stops if the gradient norm is below this value.

• initial_tr_radius – Initial trust radius. Affects the size of the first steps.

• initial_constr_penalty – Initial constraint penalty.

• use_projected_gradient – Whether to use the projected gradient for the optimization step.

optimize(sample: OFData, energy_functional: Callable, callback: Callable | None = None, disable_pbar: bool = False) → tuple[Energies, bool]

Perform trust region constrained optimization.

class VectorAdam(max_cycle: int, learning_rate: float, convergence_tolerance: float, betas: tuple[float, float] = (0.9, 0.999), epsilon: float = 1e-08)

Equivariant version of the Adam optimizer.

__init__(max_cycle: int, learning_rate: float, convergence_tolerance: float, betas: tuple[float, float] = (0.9, 0.999), epsilon: float = 1e-08)

Initialize the equivariant version of the Adam optimizer.

Parameters:

• max_cycle – Maximum number of optimization cycles.

• learning_rate – Learning rate function.

• convergence_tolerance – Optimization stops if the gradient norm is below this value.

• betas – Exponential decay rates for the moment estimates.

• epsilon – Small value to avoid division by zero.

optimize(sample: OFData, energy_functional: Callable, callback: Callable | None = None, disable_pbar: bool = False) → tuple[Energies, bool]

Perform equivariant VectorAdam optimization.

get_pbar_str(sample: OFData, energy: Energies, gradient_norm: float) → str

Return a string for the tqdm progress bar.

Parameters:

• sample – The OFData containing the current coefficients. If the ground state energy is available, the energy difference to the ground state is calculated.

• energy – The current energy.

• gradient_norm – The norm of the gradient vector.

Returns:

A string for the tqdm progress bar.

scipy_functional(coeffs: ndarray, sample: OFData, energy_functional: Callable, convergence_tolerance: float, use_projected_gradient: bool, pbar: tqdm, callback: Callable | None = None) → tuple[float, ndarray]

Functional for scipy optimizers.

Make the energy functional compatible with scipy optimizers.

Parameters:

• coeffs – Input coefficients.

• sample – OFData containing the basis functions and integrals.

• energy_functional – Callable which returns the energy and gradient vector.

• convergence_tolerance – Optimization stops if the gradient norm is below this value.

• use_projected_gradient – Whether to use the projected gradient for the optimization step.

• pbar – tqdm progress bar.

• callback – Optional callback function.

Returns:

Energy and gradient vector.