# hoomd.tune

Overview

 CustomTuner User-defined tuner. GradientDescent Solves equations of $$min_x f(x)$$ using gradient descent. GridOptimizer Optimize by consistently narrowing the range where the extrema is. LoadBalancer Adjusts the boundaries of the domain decomposition. ManualTuneDefinition Class for defining y = f(x) relationships for tuning x for a set y target. Optimizer Abstract base class for optimizing $$f(x)$$. ParticleSorter Order particles in memory to improve performance. RootSolver Abstract base class for finding x such that $$f(x) = 0$$. ScaleSolver Solves equations of f(x) = y using a ratio of y with the target. SecantSolver Solves equations of f(x) = y using the secant method. SolverStep Abstract base class various solver types.

Details

Tuners.

Tuner operations make changes to the parameters of other operations (or the simulation state) that adjust the performance of the simulation without changing the correctness of the outcome. Every new hoomd.Simulation object includes a ParticleSorter in its operations by default. ParticleSorter rearranges the order of particles in memory to improve cache-coherency.

This package also defines the CustomTuner class and a number of helper classes. Use these to implement custom tuner operations in Python code.

..rubric:: Solver

Most tuners explicitly involve solving some sort of mathematical problem (e.g. root-finding or optimizationr). HOOMD provides infrastructure for solving these problems as they appear in our provided hoomd.operation.Tuner subclasses. All tuners that involve iteratively solving a problem compose a SolverStep subclass instance. The SolverStep class implements the boilerplate to do iterative solving given a simulation where calls to the “function” being solves means running potentially 1,000’s of steps.

Every solver regardless of type has a solve method which accepts a list of tunable quantities. The method returns a Boolean indicating whether all quantities are considered tuned or not. Tuners indicate they are tuned when two successive calls to SolverStep.solve return True unless otherwise documented.

Custom solvers can be created from inheriting from the base class of one of the problem types (RootSolver and Optimizer) or SolverStep if solving a different problem type. All that is required is to implement the SolverStep.solve_one method, and the solver can be used by any HOOMD tuner that expects a solver.

Custom Tuners

Through using SolverStep subclasses and ManualTuneDefinition most tuning problems should be solvable for a CustomTuner. To create a tuner define all ManualTuneDefinition interfaces for each tunable and plug into a solver in a CustomTuner.

class hoomd.tune.ManualTuneDefinition(get_y, target, get_x, set_x, domain=None)

Class for defining y = f(x) relationships for tuning x for a set y target.

This class is made to be used with hoomd.tune.SolverStep subclasses. Here y represents a dependent variable of x. In general, x and y should be of type float, but specific hoomd.tune.SolverStep subclasses may accept other types.

A special case for the return type of y is None. If the value is currently inaccessible or would be invalid, a ManualTuneDefinition object can return a y of None to indicate this. hoomd.tune.SolverStep objects will handle this automatically. Since we check for None internally in hoomd.tune.SolverStep objects, a ManualTuneDefinition object’s y property should be consistant when called multiple times within a timestep.

When setting x the value is clamped between the given domain via,

$\begin{split}x &= x_{max}, \text{ if } x_n > x_{max},\\ x &= x_{min}, \text{ if } x_n < x_{min},\\ x &= x_n, \text{ otherwise}\end{split}$
Parameters
• get_y (callable) – A callable that gets the current value for y.

• target (any) – The target y value to approach.

• get_x (callable) – A callable that gets the current value for x.

• set_x (callable) – A callable that sets the current value for x.

• domain (tuple [any, any], optional) – A tuple pair of the minimum and maximum accepted values of x, defaults to None. When, the domain is None then any value of x is accepted. Either the minimum or maximum can be set to None as well which means there is no maximum or minimum. The domain is used to wrap values within the specified domain when setting x.

Note

Placing domain restrictions on x can lead to the target y value being impossible to converge to. This will lead to the hoomd.tune.SolverStep object passed this tunable to never finish solving regardless if all other ManualTuneDefinition objects are converged.

__eq__(other)

Test for equality.

__hash__()

Compute a hash of the tune definition.

clamp_into_domain(value)

Return the closest value within the domain.

Parameters

value (any) – A value of the same type as x.

Returns

The value clamps within the domains of x. Clamping here refers to returning the value or minimum or maximum of the domain if value is outside the domain.

property domain

A tuple pair of the minimum and maximum accepted values of x.

When the domain is None, any value of x is accepted. Either the minimum or maximum can be set to None as well which means there is no maximum or minimum. The domain is used to wrap values within the specified domain when setting x.

Type

tuple[any, any]

in_domain(value)

Check whether a value is in the domain.

Parameters

value (any) – A value that can be compared to the minimum and maximum of the domain.

Returns

Whether the value is in the domain of x.

Return type

bool

property max_x

Maximum allowed x value.

property min_x

Minimum allowed y value.

property target

The targetted y value, can be set.

property x

The dependent variable.

Can be set. When set the setting value is clamped within the provided domain. See clamp_into_domain for further explanation.

property y

The independent variable, and is unsettable.

class hoomd.tune.CustomTuner(trigger, action)

User-defined tuner.

Parameters

CustomTuner is a hoomd.operation.Tuner that wraps a user-defined hoomd.custom.Action object so the action can be added to a hoomd.Operations instance for use with hoomd.Simulation objects.

Tuners modify the parameters of other operations to improve performance. Tuners may read the system state, but not modify it.

class hoomd.tune.GradientDescent(alpha: float = 0.1, kappa: = None, tol: float = 1e-05, maximize: bool = True, max_delta: = None)

Bases: Optimizer

Solves equations of $$min_x f(x)$$ using gradient descent.

Derivatives are computed using the forward difference.

The solver updates x each step via,

$x_n = x_{n-1} - \alpha {\left (1 - \kappa) \nabla f + \kappa \Delta_{n-1} \right)}$

where $$\Delta$$ is the last step size. This gives the optimizer a sense of momentum which for noisy (stochastic) optimization can lead to smoother optimization. Due to the need for two values to compute a derivative, then first time this is called it makes a slight jump higher or lower to start the method.

The solver will stop updating when a maximum is detected (i.e. the step size is smaller than tol).

Parameters
• alpha (hoomd.variant.variant_like, optional) – Either a number between 0 and 1 used to dampen the rate of change in x or a variant that varies not by timestep but by the number of times solve has been called (i.e. the number of steps taken) (defaults to 0.1). alpha scales the corrections to x each iteration. Larger values of alpha lead to larger changes while a alpha of 0 leads to no change in x at all.

• kappa (numpy.ndarray, optional) – Real number array that determines how much of the previous steps’ directions to use (defaults to None which does no averaging over past step directions). The array values correspond to weight that the $$N$$ last steps are weighted when combined with the current step. The current step is weighted by $$1 - \sum_{i=1}^{N} \kappa_i$$.

• tol (float, optional) – The absolute tolerance for convergence of y, (defaults to 1e-5).

• maximize (bool, optional) – Whether or not to maximize function (defaults to True).

• max_delta (float, optional) – The maximum step size to allow (defaults to None which allows a step size of any length).

kappa

Real number array that determines how much of the previous steps’ directions to use. The array values correspond to weight that the $$N$$ last steps are weighted when combined with the current step. The current step is weighted by $$1 - \sum_{i=1}^{N} \kappa_i$$.

Type

numpy.ndarray

tol

The absolute tolerance for convergence of y.

Type

float

maximize

Whether or not to maximize function.

Type

bool

max_delta

The maximum step size to allow.

Type

float

__eq__(other)

Test for equality.

property alpha

Number between 0 and 1 that dampens of change in x.

Larger values of alpha lead to larger changes while a alpha of 0 leads to no change in x at all. The property returns the current alpha given the current number of steps.

The property can be set as in the constructor.

Type

float

reset()

Reset all solving internals.

solve(tunables)

Iterates towards a solution for a list of tunables.

If a y for one of the tunables is None then we skip that tunable. Skipping implies that the quantity is not tuned and solve will return False.

Parameters

tunables (list[hoomd.tune.ManualTuneDefinition]) – A list of tunable objects that represent a relationship f(x) = y.

Returns

Returns whether or not all tunables were considered tuned by the object.

Return type

bool

solve_one(tunable)

Solve one step.

class hoomd.tune.GridOptimizer(n_bins: int = 5, n_rounds: int = 1, maximize: bool = True)

Bases: Optimizer

Optimize by consistently narrowing the range where the extrema is.

The algorithm is as follows. Given a domain $$d = [a, b]$$, $$d$$ is broken up into n_bins subsequent bins. For the next n_bins calls, the optimizer tests the function value at each bin center. The next call does one of two things. If the number of rounds has reached n_rounds the optimization is done, and the center of the best bin is the solution. Otherwise, another round is performed where the bin’s extent is the new domain.

Warning

Changing a tunables domain during usage of a GridOptimizer results in incorrect behavior.

Parameters
• n_bins (int, optional) – The number of bins in the range to test (defaults to 5).

• n_rounds (int, optional) – The number of rounds to perform the optimization over (defaults to 1).

• maximize (bool, optional) – Whether to maximize or minimize the function (defaults to True).

__eq__(other)

Test for equality.

reset()

Reset all solving internals.

solve_one(tunable)

Perform one step of optimization protocol.

class hoomd.tune.LoadBalancer(trigger, x=True, y=True, z=True, tolerance=1.02, max_iterations=1)

Bases: Tuner

Adjusts the boundaries of the domain decomposition.

Parameters

LoadBalancer adjusts the boundaries of the MPI domains to distribute the particle load close to evenly between them. The load imbalance is defined as the number of particles owned by a rank divided by the average number of particles per rank if the particles had a uniform distribution:

$I = \frac{N_i}{N / P}$

where $$N_i$$ is the number of particles on rank $$i$$, $$N$$ is the total number of particles, and $$P$$ is the number of ranks.

In order to adjust the load imbalance, LoadBalancer scales by the inverse of the imbalance factor. To reduce oscillations and communication overhead, it does not move a domain more than 5% of its current size in a single rebalancing step, and not more than half the distance to its neighbors.

Simulations with interfaces (so that there is a particle density gradient) or clustering should benefit from load balancing. The potential speedup is $$I-1.0$$, so that if the largest imbalance is 1.4, then the user can expect a 40% speedup in the simulation. This is of course an estimate that assumes that all algorithms are linear in $$N$$, all GPUs are fully occupied, and the simulation is limited by the speed of the slowest processor. If you have a simulation where, for example, some particles have significantly more pair force neighbors than others, this estimate of the load imbalance may not produce the optimal results.

A load balancing adjustment is only performed when the maximum load imbalance exceeds a tolerance. The ideal load balance is 1.0, so setting tolerance less than 1.0 will force an adjustment every update. The load balancer can attempt multiple iterations of balancing on each update, and up to maxiter attempts can be made. The optimal values of update and maxiter will depend on your simulation.

Load balancing can be performed independently and sequentially for each dimension of the simulation box. A small performance increase may be obtained by disabling load balancing along dimensions that are known to be homogeneous. For example, if there is a planar vapor-liquid interface normal to the $$z$$ axis, then it may be advantageous to disable balancing along $$x$$ and $$y$$.

In systems that are well-behaved, there is minimal overhead of balancing with a small update. However, if the system is not capable of being balanced (for example, due to the density distribution or minimum domain size), having a small update and high maxiter may lead to a large performance loss. In such systems, it is currently best to either balance infrequently or to balance once in a short test run and then set the decomposition statically in a separate initialization.

Balancing is ignored if there is no domain decomposition available (MPI is not built or is running on a single rank).

trigger

Select the timesteps on which to perform load balancing.

Type

hoomd.trigger.Trigger

x

Balance the x direction when True.

Type

bool

y

Balance the y direction when True.

Type

bool

z

Balance the z direction when True.

Type

bool

tolerance

Type

float

max_iterations

Maximum number of iterations to attempt in a single step.

Type

int

class hoomd.tune.Optimizer

Bases: SolverStep

Abstract base class for optimizing $$f(x)$$.

class hoomd.tune.ParticleSorter(trigger=200, grid=None)

Bases: Tuner

Order particles in memory to improve performance.

Parameters
• trigger (hoomd.trigger.trigger_like) – Select the timesteps on which to sort. Defaults to a hoomd.trigger.Periodic(200) trigger.

• grid (int) – Resolution of the grid to use when sorting. The default value of None sets grid=4096 in 2D simulations and grid=256 in 3D simulations.

ParticleSorter improves simulation performance by sorting the particles in memory along a space-filling curve. This takes particles that are close in space and places them close in memory, leading to a higher rate of cache hits when computing pair potentials.

Note

New hoomd.Operations instances include a ParticleSorter constructed with default parameters.

trigger

Select the timesteps on which to sort.

Type

hoomd.trigger.Trigger

grid

Set the resolution of the space-filling curve. grid rounds up to the nearest power of 2 when set. Larger values of grid provide more accurate space-filling curves, but consume more memory (grid**D * 4 bytes, where D is the dimensionality of the system).

Type

int

class hoomd.tune.RootSolver

Bases: SolverStep

Abstract base class for finding x such that $$f(x) = 0$$.

For solving for a non-zero value, $$f(x) - y_t = 0$$ is solved.

class hoomd.tune.ScaleSolver(max_scale=2.0, gamma=2.0, correlation='positive', tol=1e-05)

Bases: RootSolver

Solves equations of f(x) = y using a ratio of y with the target.

Each time this solver is called it takes updates according to the following equation if the correlation is positive:

$x_n = \min{\left(\frac{\gamma + t}{y + \gamma}, s_{max}\right)} \cdot x$

and

$x_n = \min{\left(\frac{y + \gamma}{\gamma + t}, s_{max}\right)} \cdot x$

if the correlation is negative, where $$t$$ is the target and $$x_n$$ is the new x.

The solver will stop updating when $$\lvert y - t \rvert \le tol$$.

Parameters
• max_scale (float, optional) – The maximum amount to scale the current x value with, defaults to 2.0.

• gamma (float, optional) – nonnegative real number used to dampen or increase the rate of change in x. gamma is added to the numerator and denominator of the y / target ratio. Larger values of gamma lead to smaller changes while a gamma of 0 leads to scaling x by exactly the y / target ratio.

• correlation (str, optional) – Defines whether the relationship between x and y is of a positive or negative correlation, defaults to ‘positive’. This determines which direction to scale x in for a given y.

• tol (float, optional) – The absolute tolerance for convergence of y, defaults to 1e-5.

Note

This solver is only usable when quantities are strictly positive.

__eq__(other)

Test for equality.

reset()

Reset all solving internals.

solve_one(tunable)

Solve one step.

class hoomd.tune.SecantSolver(gamma=0.9, tol=1e-05)

Bases: RootSolver

Solves equations of f(x) = y using the secant method.

The solver updates x each step via,

$x_n = x - \gamma \cdot (y - t) \cdot \frac{x - x_{o}}{y - y_{old}}$

where $$o$$ represent the old values, $$n$$ the new, and $$t$$ the target. Due to the need for a previous value, then first time this is called it makes a slight jump higher or lower to start the method.

The solver will stop updating when $$\lvert y - t \rvert \le tol$$.

Parameters
• gamma (float, optional) – real number between 0 and 1 used to dampen the rate of change in x. gamma scales the corrections to x each iteration. Larger values of gamma lead to larger changes while a gamma of 0 leads to no change in x at all.

• tol (float, optional) – The absolute tolerance for convergence of y, defaults to 1e-5.

Note

Tempering the solver with a smaller than 1 gamma value is crucial for numeric stability. If instability is found, then lowering gamma accordingly should help.

__eq__(other)

Test for equality.

reset()

Reset all solving internals.

solve_one(tunable)

Solve one step.

class hoomd.tune.SolverStep

Bases: object

Abstract base class various solver types.

Requires a single method solve_one that steps forward one iteration in solving the given variable relationship. Users can use subclasses of this with hoomd.tune.ManualTuneDefinition to tune attributes with a functional relation.

Note

A SolverStep object requires manual iteration to converge. This is to support the use case of measuring quantities that require running the simulation for some amount of time after one iteration before remeasuring the dependent variable (i.e. the y). SolverStep object can be used in hoomd.custom.Action subclasses for user defined tuners and updaters.

abstract reset()

Reset all solving internals.

This should put the solver in its initial state as if it has not seen any tunables or done any solving yet.

solve(tunables)

Iterates towards a solution for a list of tunables.

If a y for one of the tunables is None then we skip that tunable. Skipping implies that the quantity is not tuned and solve will return False.

Parameters

tunables (list[hoomd.tune.ManualTuneDefinition]) – A list of tunable objects that represent a relationship f(x) = y.

Returns

Returns whether or not all tunables were considered tuned by the object.

Return type

bool

abstract solve_one(tunable)

Takes in a tunable object and attempts to solve x for a specified y.

Parameters

tunable (hoomd.tune.ManualTuneDefinition) – A tunable object that represents a relationship of f(x) = y.

Returns

Whether or not the tunable converged to the target.

Return type

bool