PySRRegressor Reference¶

PySRRegressor has many options for controlling a symbolic regression search. Let's look at them below.

PySRRegressor Parameters¶

The Algorithm¶

Creating the Search Space¶

binary_operators

List of strings for binary operators used in the search. See the operators page for more details.

Default: ["+", "-", "*", "/"]
unary_operators

Operators which only take a single scalar as input. For example, "cos" or "exp".

Default: None
maxsize

Max complexity of an equation.

Default: 20
maxdepth

Max depth of an equation. You can use both maxsize and maxdepth. maxdepth is by default not used.

Default: None

Setting the Search Size¶

niterations

Number of iterations of the algorithm to run. The best equations are printed and migrate between populations at the end of each iteration.

Default: 40
populations

Number of populations running.

Default: 15
population_size

Number of individuals in each population.

Default: 33
ncycles_per_iteration

Number of total mutations to run, per 10 samples of the population, per iteration.

Default: 550

The Objective¶

elementwise_loss

String of Julia code specifying an elementwise loss function. Can either be a loss from LossFunctions.jl, or your own loss written as a function. Examples of custom written losses include: myloss(x, y) = abs(x-y) for non-weighted, or myloss(x, y, w) = w*abs(x-y) for weighted. The included losses include: Regression: LPDistLoss{P}(), L1DistLoss(), L2DistLoss() (mean square), LogitDistLoss(), HuberLoss(d), L1EpsilonInsLoss(ϵ), L2EpsilonInsLoss(ϵ), PeriodicLoss(c), QuantileLoss(τ). Classification: ZeroOneLoss(), PerceptronLoss(), L1HingeLoss(), SmoothedL1HingeLoss(γ), ModifiedHuberLoss(), L2MarginLoss(), ExpLoss(), SigmoidLoss(), DWDMarginLoss(q).

Default: "L2DistLoss()"
loss_function

Alternatively, you can specify the full objective function as a snippet of Julia code, including any sort of custom evaluation (including symbolic manipulations beforehand), and any sort of loss function or regularizations. The default loss_function used in SymbolicRegression.jl is roughly equal to:
```
function eval_loss(tree, dataset::Dataset{T,L}, options)::L where {T,L}
    prediction, flag = eval_tree_array(tree, dataset.X, options)
    if !flag
        return L(Inf)
    end
    return sum((prediction .- dataset.y) .^ 2) / dataset.n
end
```
where the example elementwise loss is mean-squared error. You may pass a function with the same arguments as this (note that the name of the function doesn't matter). Here, both prediction and dataset.y are 1D arrays of length dataset.n. If using batching, then you should add an idx argument to the function, which is nothing for non-batched, and a 1D array of indices for batched.

Default: None
model_selection

Model selection criterion when selecting a final expression from the list of best expression at each complexity. Can be 'accuracy', 'best', or 'score'. 'accuracy' selects the candidate model with the lowest loss (highest accuracy). 'score' selects the candidate model with the highest score. Score is defined as the negated derivative of the log-loss with respect to complexity - if an expression has a much better loss at a slightly higher complexity, it is preferred. 'best' selects the candidate model with the highest score among expressions with a loss better than at least 1.5x the most accurate model.

Default: 'best'
dimensional_constraint_penalty

Additive penalty for if dimensional analysis of an expression fails. By default, this is 1000.0.
dimensionless_constants_only

Whether to only search for dimensionless constants, if using units.

Default: False

Working with Complexities¶

parsimony

Multiplicative factor for how much to punish complexity.

Default: 0.0032
constraints

Dictionary of int (unary) or 2-tuples (binary), this enforces maxsize constraints on the individual arguments of operators. E.g., 'pow': (-1, 1) says that power laws can have any complexity left argument, but only 1 complexity in the right argument. Use this to force more interpretable solutions.

Default: None
nested_constraints

Specifies how many times a combination of operators can be nested. For example, {"sin": {"cos": 0}}, "cos": {"cos": 2}} specifies that cos may never appear within a sin, but sin can be nested with itself an unlimited number of times. The second term specifies that cos can be nested up to 2 times within a cos, so that cos(cos(cos(x))) is allowed (as well as any combination of + or - within it), but cos(cos(cos(cos(x)))) is not allowed. When an operator is not specified, it is assumed that it can be nested an unlimited number of times. This requires that there is no operator which is used both in the unary operators and the binary operators (e.g., - could be both subtract, and negation). For binary operators, you only need to provide a single number: both arguments are treated the same way, and the max of each argument is constrained.

Default: None
complexity_of_operators

If you would like to use a complexity other than 1 for an operator, specify the complexity here. For example, {"sin": 2, "+": 1} would give a complexity of 2 for each use of the sin operator, and a complexity of 1 for each use of the + operator (which is the default). You may specify real numbers for a complexity, and the total complexity of a tree will be rounded to the nearest integer after computing.

Default: None
complexity_of_constants

Complexity of constants.

Default: 1
complexity_of_variables

Global complexity of variables. To set different complexities for different variables, pass a list of complexities to the fit method with keyword complexity_of_variables. You cannot use both.

Default: 1
warmup_maxsize_by

Whether to slowly increase max size from a small number up to the maxsize (if greater than 0). If greater than 0, says the fraction of training time at which the current maxsize will reach the user-passed maxsize.

Default: 0.0
use_frequency

Whether to measure the frequency of complexities, and use that instead of parsimony to explore equation space. Will naturally find equations of all complexities.

Default: True
use_frequency_in_tournament

Whether to use the frequency mentioned above in the tournament, rather than just the simulated annealing.

Default: True
adaptive_parsimony_scaling

If the adaptive parsimony strategy (use_frequency and use_frequency_in_tournament), this is how much to (exponentially) weight the contribution. If you find that the search is only optimizing the most complex expressions while the simpler expressions remain stagnant, you should increase this value.

Default: 20.0
should_simplify

Whether to use algebraic simplification in the search. Note that only a few simple rules are implemented.

Default: True

Mutations¶

weight_add_node

Relative likelihood for mutation to add a node.

Default: 0.79
weight_insert_node

Relative likelihood for mutation to insert a node.

Default: 5.1
weight_delete_node

Relative likelihood for mutation to delete a node.

Default: 1.7
weight_do_nothing

Relative likelihood for mutation to leave the individual.

Default: 0.21
weight_mutate_constant

Relative likelihood for mutation to change the constant slightly in a random direction.

Default: 0.048
weight_mutate_operator

Relative likelihood for mutation to swap an operator.

Default: 0.47
weight_swap_operands

Relative likehood for swapping operands in binary operators.

Default: 0.1
weight_randomize

Relative likelihood for mutation to completely delete and then randomly generate the equation

Default: 0.00023
weight_simplify

Relative likelihood for mutation to simplify constant parts by evaluation

Default: 0.0020
weight_optimize

Constant optimization can also be performed as a mutation, in addition to the normal strategy controlled by optimize_probability which happens every iteration. Using it as a mutation is useful if you want to use a large ncycles_periteration, and may not optimize very often.

Default: 0.0
crossover_probability

Absolute probability of crossover-type genetic operation, instead of a mutation.

Default: 0.066
annealing

Whether to use annealing.

Default: False
alpha

Initial temperature for simulated annealing (requires annealing to be True).

Default: 0.1
perturbation_factor

Constants are perturbed by a max factor of (perturbation_factor*T + 1). Either multiplied by this or divided by this.

Default: 0.076
skip_mutation_failures

Whether to skip mutation and crossover failures, rather than simply re-sampling the current member.

Default: True

Tournament Selection¶

tournament_selection_n

Number of expressions to consider in each tournament.

Default: 10
tournament_selection_p

Probability of selecting the best expression in each tournament. The probability will decay as p*(1-p)^n for other expressions, sorted by loss.

Default: 0.86

Constant Optimization¶

optimizer_algorithm

Optimization scheme to use for optimizing constants. Can currently be NelderMead or BFGS.

Default: "BFGS"
optimizer_nrestarts

Number of time to restart the constants optimization process with different initial conditions.

Default: 2
optimize_probability

Probability of optimizing the constants during a single iteration of the evolutionary algorithm.

Default: 0.14
optimizer_iterations

Number of iterations that the constants optimizer can take.

Default: 8
should_optimize_constants

Whether to numerically optimize constants (Nelder-Mead/Newton) at the end of each iteration.

Default: True

Migration between Populations¶

fraction_replaced

How much of population to replace with migrating equations from other populations.

Default: 0.000364
fraction_replaced_hof

How much of population to replace with migrating equations from hall of fame.

Default: 0.035
migration

Whether to migrate.

Default: True
hof_migration

Whether to have the hall of fame migrate.

Default: True
topn

How many top individuals migrate from each population.

Default: 12

Data Preprocessing¶

denoise

Whether to use a Gaussian Process to denoise the data before inputting to PySR. Can help PySR fit noisy data.

Default: False
select_k_features

Whether to run feature selection in Python using random forests, before passing to the symbolic regression code. None means no feature selection; an int means select that many features.

Default: None

Stopping Criteria¶

max_evals

Limits the total number of evaluations of expressions to this number.

Default: None
timeout_in_seconds

Make the search return early once this many seconds have passed.

Default: None
early_stop_condition

Stop the search early if this loss is reached. You may also pass a string containing a Julia function which takes a loss and complexity as input, for example: "f(loss, complexity) = (loss < 0.1) && (complexity < 10)".

Default: None

Performance and Parallelization¶

procs

Number of processes (=number of populations running).

Default: cpu_count()
multithreading

Use multithreading instead of distributed backend. Using procs=0 will turn off both.

Default: True
cluster_manager

For distributed computing, this sets the job queue system. Set to one of "slurm", "pbs", "lsf", "sge", "qrsh", "scyld", or "htc". If set to one of these, PySR will run in distributed mode, and use procs to figure out how many processes to launch.

Default: None
heap_size_hint_in_bytes

For multiprocessing, this sets the --heap-size-hint parameter for new Julia processes. This can be configured when using multi-node distributed compute, to give a hint to each process about how much memory they can use before aggressive garbage collection.
batching

Whether to compare population members on small batches during evolution. Still uses full dataset for comparing against hall of fame.

Default: False
batch_size

The amount of data to use if doing batching.

Default: 50
precision

What precision to use for the data. By default this is 32 (float32), but you can select 64 or 16 as well, giving you 64 or 16 bits of floating point precision, respectively. If you pass complex data, the corresponding complex precision will be used (i.e., 64 for complex128, 32 for complex64).

Default: 32
fast_cycle

Batch over population subsamples. This is a slightly different algorithm than regularized evolution, but does cycles 15% faster. May be algorithmically less efficient.

Default: False
turbo

(Experimental) Whether to use LoopVectorization.jl to speed up the search evaluation. Certain operators may not be supported. Does not support 16-bit precision floats.

Default: False
bumper

(Experimental) Whether to use Bumper.jl to speed up the search evaluation. Does not support 16-bit precision floats.

Default: False
enable_autodiff

Whether to create derivative versions of operators for automatic differentiation. This is only necessary if you wish to compute the gradients of an expression within a custom loss function.

Default: False

Determinism¶

random_state

Pass an int for reproducible results across multiple function calls. See :term:Glossary <random_state>.

Default: None
deterministic

Make a PySR search give the same result every run. To use this, you must turn off parallelism (with procs=0, multithreading=False), and set random_state to a fixed seed.

Default: False
warm_start

Tells fit to continue from where the last call to fit finished. If false, each call to fit will be fresh, overwriting previous results.

Default: False

Monitoring¶

verbosity

What verbosity level to use. 0 means minimal print statements.

Default: 1
update_verbosity

What verbosity level to use for package updates. Will take value of verbosity if not given.

Default: None
print_precision

How many significant digits to print for floats.

Default: 5
progress

Whether to use a progress bar instead of printing to stdout.

Default: True

Environment¶

temp_equation_file

Whether to put the hall of fame file in the temp directory. Deletion is then controlled with the delete_tempfiles parameter.

Default: False
tempdir

directory for the temporary files.

Default: None
delete_tempfiles

Whether to delete the temporary files after finishing.

Default: True
update

Whether to automatically update Julia packages when fit is called. You should make sure that PySR is up-to-date itself first, as the packaged Julia packages may not necessarily include all updated dependencies.

Default: False

Exporting the Results¶

equation_file

Where to save the files (.csv extension).

Default: None
output_jax_format

Whether to create a 'jax_format' column in the output, containing jax-callable functions and the default parameters in a jax array.

Default: False
output_torch_format

Whether to create a 'torch_format' column in the output, containing a torch module with trainable parameters.

Default: False
extra_sympy_mappings

Provides mappings between custom binary_operators or unary_operators defined in julia strings, to those same operators defined in sympy. E.G if unary_operators=["inv(x)=1/x"], then for the fitted model to be export to sympy, extra_sympy_mappings would be {"inv": lambda x: 1/x}.

Default: None
extra_torch_mappings

The same as extra_jax_mappings but for model export to pytorch. Note that the dictionary keys should be callable pytorch expressions. For example: extra_torch_mappings={sympy.sin: torch.sin}.

Default: None
extra_jax_mappings

Similar to extra_sympy_mappings but for model export to jax. The dictionary maps sympy functions to jax functions. For example: extra_jax_mappings={sympy.sin: "jnp.sin"} maps the sympy.sin function to the equivalent jax expression jnp.sin.

Default: None

PySRRegressor Functions¶

`fit(X, y, Xresampled=None, weights=None, variable_names=None, complexity_of_variables=None, X_units=None, y_units=None)` ¶

Search for equations to fit the dataset and store them in self.equations_.

Parameters:

Name	Type	Description	Default
`X`	`ndarray \| DataFrame`	Training data of shape (n_samples, n_features).	required
`y`	`ndarray \| DataFrame`	Target values of shape (n_samples,) or (n_samples, n_targets). Will be cast to X's dtype if necessary.	required
`Xresampled`	`ndarray \| DataFrame`	Resampled training data, of shape (n_resampled, n_features), to generate a denoised data on. This will be used as the training data, rather than `X`.	`None`
`weights`	`ndarray \| DataFrame`	Weight array of the same shape as `y`. Each element is how to weight the mean-square-error loss for that particular element of `y`. Alternatively, if a custom `loss` was set, it will can be used in arbitrary ways.	`None`
`variable_names`	`list[str]`	A list of names for the variables, rather than "x0", "x1", etc. If `X` is a pandas dataframe, the column names will be used instead of `variable_names`. Cannot contain spaces or special characters. Avoid variable names which are also function names in `sympy`, such as "N".	`None`
`X_units`	`list[str]`	A list of units for each variable in `X`. Each unit should be a string representing a Julia expression. See DynamicQuantities.jl https://symbolicml.org/DynamicQuantities.jl/dev/units/ for more information.	`None`
`y_units`	`str \| list[str]`	Similar to `X_units`, but as a unit for the target variable, `y`. If `y` is a matrix, a list of units should be passed. If `X_units` is given but `y_units` is not, then `y_units` will be arbitrary.	`None`

Returns:

Name	Type	Description
`self`	`object`	Fitted estimator.

Source code in pysr/sr.py

def fit(
    self,
    X,
    y,
    Xresampled=None,
    weights=None,
    variable_names: Optional[ArrayLike[str]] = None,
    complexity_of_variables: Optional[
        Union[int, float, List[Union[int, float]]]
    ] = None,
    X_units: Optional[ArrayLike[str]] = None,
    y_units: Optional[Union[str, ArrayLike[str]]] = None,
) -> "PySRRegressor":
    """
    Search for equations to fit the dataset and store them in `self.equations_`.

    Parameters
    ----------
    X : ndarray | pandas.DataFrame
        Training data of shape (n_samples, n_features).
    y : ndarray | pandas.DataFrame
        Target values of shape (n_samples,) or (n_samples, n_targets).
        Will be cast to X's dtype if necessary.
    Xresampled : ndarray | pandas.DataFrame
        Resampled training data, of shape (n_resampled, n_features),
        to generate a denoised data on. This
        will be used as the training data, rather than `X`.
    weights : ndarray | pandas.DataFrame
        Weight array of the same shape as `y`.
        Each element is how to weight the mean-square-error loss
        for that particular element of `y`. Alternatively,
        if a custom `loss` was set, it will can be used
        in arbitrary ways.
    variable_names : list[str]
        A list of names for the variables, rather than "x0", "x1", etc.
        If `X` is a pandas dataframe, the column names will be used
        instead of `variable_names`. Cannot contain spaces or special
        characters. Avoid variable names which are also
        function names in `sympy`, such as "N".
    X_units : list[str]
        A list of units for each variable in `X`. Each unit should be
        a string representing a Julia expression. See DynamicQuantities.jl
        https://symbolicml.org/DynamicQuantities.jl/dev/units/ for more
        information.
    y_units : str | list[str]
        Similar to `X_units`, but as a unit for the target variable, `y`.
        If `y` is a matrix, a list of units should be passed. If `X_units`
        is given but `y_units` is not, then `y_units` will be arbitrary.

    Returns
    -------
    self : object
        Fitted estimator.
    """
    # Init attributes that are not specified in BaseEstimator
    if self.warm_start and hasattr(self, "julia_state_stream_"):
        pass
    else:
        if hasattr(self, "julia_state_stream_"):
            warnings.warn(
                "The discovered expressions are being reset. "
                "Please set `warm_start=True` if you wish to continue "
                "to start a search where you left off.",
            )

        self.equations_ = None
        self.nout_ = 1
        self.selection_mask_ = None
        self.julia_state_stream_ = None
        self.julia_options_stream_ = None
        self.complexity_of_variables_ = None
        self.X_units_ = None
        self.y_units_ = None

    self._setup_equation_file()

    runtime_params = self._validate_and_modify_params()

    (
        X,
        y,
        Xresampled,
        weights,
        variable_names,
        complexity_of_variables,
        X_units,
        y_units,
    ) = self._validate_and_set_fit_params(
        X,
        y,
        Xresampled,
        weights,
        variable_names,
        complexity_of_variables,
        X_units,
        y_units,
    )

    if X.shape[0] > 10000 and not self.batching:
        warnings.warn(
            "Note: you are running with more than 10,000 datapoints. "
            "You should consider turning on batching (https://ai.damtp.cam.ac.uk/pysr/options/#batching). "
            "You should also reconsider if you need that many datapoints. "
            "Unless you have a large amount of noise (in which case you "
            "should smooth your dataset first), generally < 10,000 datapoints "
            "is enough to find a functional form with symbolic regression. "
            "More datapoints will lower the search speed."
        )

    random_state = check_random_state(self.random_state)  # For np random
    seed = cast(int, random_state.randint(0, 2**31 - 1))  # For julia random

    # Pre transformations (feature selection and denoising)
    X, y, variable_names, complexity_of_variables, X_units, y_units = (
        self._pre_transform_training_data(
            X,
            y,
            Xresampled,
            variable_names,
            complexity_of_variables,
            X_units,
            y_units,
            random_state,
        )
    )

    # Warn about large feature counts (still warn if feature count is large
    # after running feature selection)
    if self.n_features_in_ >= 10:
        warnings.warn(
            "Note: you are running with 10 features or more. "
            "Genetic algorithms like used in PySR scale poorly with large numbers of features. "
            "You should run PySR for more `niterations` to ensure it can find "
            "the correct variables, and consider using a larger `maxsize`."
        )

    # Assertion checks
    use_custom_variable_names = variable_names is not None
    # TODO: this is always true.

    _check_assertions(
        X,
        use_custom_variable_names,
        variable_names,
        complexity_of_variables,
        weights,
        y,
        X_units,
        y_units,
    )

    # Initially, just save model parameters, so that
    # it can be loaded from an early exit:
    if not self.temp_equation_file:
        self._checkpoint()

    # Perform the search:
    self._run(X, y, runtime_params, weights=weights, seed=seed)

    # Then, after fit, we save again, so the pickle file contains
    # the equations:
    if not self.temp_equation_file:
        self._checkpoint()

    return self

`predict(X, index=None)` ¶

Predict y from input X using the equation chosen by model_selection.

You may see what equation is used by printing this object. X should have the same columns as the training data.

Parameters:

Name	Type	Description	Default
`X`	`ndarray \| DataFrame`	Training data of shape `(n_samples, n_features)`.	required
`index`	`int \| list[int]`	If you want to compute the output of an expression using a particular row of `self.equations_`, you may specify the index here. For multiple output equations, you must pass a list of indices in the same order.	`None`

Returns:

Name	Type	Description
`y_predicted`	`ndarray of shape (n_samples, nout_)`	Values predicted by substituting `X` into the fitted symbolic regression model.

Raises:

Type	Description
`ValueError`	Raises if the `best_equation` cannot be evaluated.

Source code in pysr/sr.py

def predict(self, X, index=None):
    """
    Predict y from input X using the equation chosen by `model_selection`.

    You may see what equation is used by printing this object. X should
    have the same columns as the training data.

    Parameters
    ----------
    X : ndarray | pandas.DataFrame
        Training data of shape `(n_samples, n_features)`.
    index : int | list[int]
        If you want to compute the output of an expression using a
        particular row of `self.equations_`, you may specify the index here.
        For multiple output equations, you must pass a list of indices
        in the same order.

    Returns
    -------
    y_predicted : ndarray of shape (n_samples, nout_)
        Values predicted by substituting `X` into the fitted symbolic
        regression model.

    Raises
    ------
    ValueError
        Raises if the `best_equation` cannot be evaluated.
    """
    check_is_fitted(
        self, attributes=["selection_mask_", "feature_names_in_", "nout_"]
    )
    best_equation = self.get_best(index=index)

    # When X is an numpy array or a pandas dataframe with a RangeIndex,
    # the self.feature_names_in_ generated during fit, for the same X,
    # will cause a warning to be thrown during _validate_data.
    # To avoid this, convert X to a dataframe, apply the selection mask,
    # and then set the column/feature_names of X to be equal to those
    # generated during fit.
    if not isinstance(X, pd.DataFrame):
        X = check_array(X)
        X = pd.DataFrame(X)
    if isinstance(X.columns, pd.RangeIndex):
        if self.selection_mask_ is not None:
            # RangeIndex enforces column order allowing columns to
            # be correctly filtered with self.selection_mask_
            X = X[X.columns[self.selection_mask_]]
        X.columns = self.feature_names_in_
    # Without feature information, CallableEquation/lambda_format equations
    # require that the column order of X matches that of the X used during
    # the fitting process. _validate_data removes this feature information
    # when it converts the dataframe to an np array. Thus, to ensure feature
    # order is preserved after conversion, the dataframe columns must be
    # reordered/reindexed to match those of the transformed (denoised and
    # feature selected) X in fit.
    X = X.reindex(columns=self.feature_names_in_)
    X = self._validate_data_X(X)

    try:
        if isinstance(best_equation, list):
            assert self.nout_ > 1
            return np.stack(
                [eq["lambda_format"](X) for eq in best_equation], axis=1
            )
        else:
            return best_equation["lambda_format"](X)
    except Exception as error:
        raise ValueError(
            "Failed to evaluate the expression. "
            "If you are using a custom operator, make sure to define it in `extra_sympy_mappings`, "
            "e.g., `model.set_params(extra_sympy_mappings={'inv': lambda x: 1/x})`, where "
            "`lambda x: 1/x` is a valid SymPy function defining the operator. "
            "You can then run `model.refresh()` to re-load the expressions."
        ) from error

`from_file(equation_file, *, binary_operators=None, unary_operators=None, n_features_in=None, feature_names_in=None, selection_mask=None, nout=1, **pysr_kwargs)` `classmethod` ¶

Create a model from a saved model checkpoint or equation file.

Parameters:

Name	Type	Description	Default
`equation_file`	`str or Path`	Path to a pickle file containing a saved model, or a csv file containing equations.	required
`binary_operators`	`list[str]`	The same binary operators used when creating the model. Not needed if loading from a pickle file.	`None`
`unary_operators`	`list[str]`	The same unary operators used when creating the model. Not needed if loading from a pickle file.	`None`
`n_features_in`	`int`	Number of features passed to the model. Not needed if loading from a pickle file.	`None`
`feature_names_in`	`list[str]`	Names of the features passed to the model. Not needed if loading from a pickle file.	`None`
`selection_mask`	`NDArray[bool_]`	If using `select_k_features`, you must pass `model.selection_mask_` here. Not needed if loading from a pickle file.	`None`
`nout`	`int`	Number of outputs of the model. Not needed if loading from a pickle file. Default is `1`.	`1`
`**pysr_kwargs`	`dict`	Any other keyword arguments to initialize the PySRRegressor object. These will overwrite those stored in the pickle file. Not needed if loading from a pickle file.	`{}`

Returns:

Name	Type	Description
`model`	`PySRRegressor`	The model with fitted equations.

Source code in pysr/sr.py

@classmethod
def from_file(
    cls,
    equation_file: PathLike,
    *,
    binary_operators: Optional[List[str]] = None,
    unary_operators: Optional[List[str]] = None,
    n_features_in: Optional[int] = None,
    feature_names_in: Optional[ArrayLike[str]] = None,
    selection_mask: Optional[NDArray[np.bool_]] = None,
    nout: int = 1,
    **pysr_kwargs,
):
    """
    Create a model from a saved model checkpoint or equation file.

    Parameters
    ----------
    equation_file : str or Path
        Path to a pickle file containing a saved model, or a csv file
        containing equations.
    binary_operators : list[str]
        The same binary operators used when creating the model.
        Not needed if loading from a pickle file.
    unary_operators : list[str]
        The same unary operators used when creating the model.
        Not needed if loading from a pickle file.
    n_features_in : int
        Number of features passed to the model.
        Not needed if loading from a pickle file.
    feature_names_in : list[str]
        Names of the features passed to the model.
        Not needed if loading from a pickle file.
    selection_mask : NDArray[np.bool_]
        If using `select_k_features`, you must pass `model.selection_mask_` here.
        Not needed if loading from a pickle file.
    nout : int
        Number of outputs of the model.
        Not needed if loading from a pickle file.
        Default is `1`.
    **pysr_kwargs : dict
        Any other keyword arguments to initialize the PySRRegressor object.
        These will overwrite those stored in the pickle file.
        Not needed if loading from a pickle file.

    Returns
    -------
    model : PySRRegressor
        The model with fitted equations.
    """

    pkl_filename = _csv_filename_to_pkl_filename(equation_file)

    # Try to load model from <equation_file>.pkl
    print(f"Checking if {pkl_filename} exists...")
    if os.path.exists(pkl_filename):
        print(f"Loading model from {pkl_filename}")
        assert binary_operators is None
        assert unary_operators is None
        assert n_features_in is None
        with open(pkl_filename, "rb") as f:
            model = pkl.load(f)
        # Change equation_file_ to be in the same dir as the pickle file
        base_dir = os.path.dirname(pkl_filename)
        base_equation_file = os.path.basename(model.equation_file_)
        model.equation_file_ = os.path.join(base_dir, base_equation_file)

        # Update any parameters if necessary, such as
        # extra_sympy_mappings:
        model.set_params(**pysr_kwargs)
        if "equations_" not in model.__dict__ or model.equations_ is None:
            model.refresh()

        return model

    # Else, we re-create it.
    print(
        f"{pkl_filename} does not exist, "
        "so we must create the model from scratch."
    )
    assert binary_operators is not None or unary_operators is not None
    assert n_features_in is not None

    # TODO: copy .bkup file if exists.
    model = cls(
        equation_file=str(equation_file),
        binary_operators=binary_operators,
        unary_operators=unary_operators,
        **pysr_kwargs,
    )

    model.nout_ = nout
    model.n_features_in_ = n_features_in

    if feature_names_in is None:
        model.feature_names_in_ = np.array([f"x{i}" for i in range(n_features_in)])
        model.display_feature_names_in_ = np.array(
            [f"x{_subscriptify(i)}" for i in range(n_features_in)]
        )
    else:
        assert len(feature_names_in) == n_features_in
        model.feature_names_in_ = feature_names_in
        model.display_feature_names_in_ = feature_names_in

    if selection_mask is None:
        model.selection_mask_ = np.ones(n_features_in, dtype=np.bool_)
    else:
        model.selection_mask_ = selection_mask

    model.refresh(checkpoint_file=equation_file)

    return model

`sympy(index=None)` ¶

Return sympy representation of the equation(s) chosen by model_selection.

Parameters:

Name	Type	Description	Default
`index`	`int \| list[int]`	If you wish to select a particular equation from `self.equations_`, give the index number here. This overrides the `model_selection` parameter. If there are multiple output features, then pass a list of indices with the order the same as the output feature.	`None`

Returns:

Name	Type	Description
`best_equation`	`str, list[str] of length nout_`	SymPy representation of the best equation.

Source code in pysr/sr.py

def sympy(self, index=None):
    """
    Return sympy representation of the equation(s) chosen by `model_selection`.

    Parameters
    ----------
    index : int | list[int]
        If you wish to select a particular equation from
        `self.equations_`, give the index number here. This overrides
        the `model_selection` parameter. If there are multiple output
        features, then pass a list of indices with the order the same
        as the output feature.

    Returns
    -------
    best_equation : str, list[str] of length nout_
        SymPy representation of the best equation.
    """
    self.refresh()
    best_equation = self.get_best(index=index)
    if isinstance(best_equation, list):
        assert self.nout_ > 1
        return [eq["sympy_format"] for eq in best_equation]
    else:
        return best_equation["sympy_format"]

`latex(index=None, precision=3)` ¶

Return latex representation of the equation(s) chosen by model_selection.

Parameters:

Name	Type	Description	Default
`index`	`int \| list[int]`	If you wish to select a particular equation from `self.equations_`, give the index number here. This overrides the `model_selection` parameter. If there are multiple output features, then pass a list of indices with the order the same as the output feature.	`None`
`precision`	`int`	The number of significant figures shown in the LaTeX representation. Default is `3`.	`3`

Returns:

Name	Type	Description
`best_equation`	`str or list[str] of length nout_`	LaTeX expression of the best equation.

Source code in pysr/sr.py

def latex(self, index=None, precision=3):
    """
    Return latex representation of the equation(s) chosen by `model_selection`.

    Parameters
    ----------
    index : int | list[int]
        If you wish to select a particular equation from
        `self.equations_`, give the index number here. This overrides
        the `model_selection` parameter. If there are multiple output
        features, then pass a list of indices with the order the same
        as the output feature.
    precision : int
        The number of significant figures shown in the LaTeX
        representation.
        Default is `3`.

    Returns
    -------
    best_equation : str or list[str] of length nout_
        LaTeX expression of the best equation.
    """
    self.refresh()
    sympy_representation = self.sympy(index=index)
    if self.nout_ > 1:
        output = []
        for s in sympy_representation:
            latex = sympy2latex(s, prec=precision)
            output.append(latex)
        return output
    return sympy2latex(sympy_representation, prec=precision)

`pytorch(index=None)` ¶

Return pytorch representation of the equation(s) chosen by model_selection.

Each equation (multiple given if there are multiple outputs) is a PyTorch module containing the parameters as trainable attributes. You can use the module like any other PyTorch module: module(X), where X is a tensor with the same column ordering as trained with.

Parameters:

Name	Type	Description	Default
`index`	`int \| list[int]`	If you wish to select a particular equation from `self.equations_`, give the index number here. This overrides the `model_selection` parameter. If there are multiple output features, then pass a list of indices with the order the same as the output feature.	`None`

Returns:

Name	Type	Description
`best_equation`	`Module`	PyTorch module representing the expression.

Source code in pysr/sr.py

def pytorch(self, index=None):
    """
    Return pytorch representation of the equation(s) chosen by `model_selection`.

    Each equation (multiple given if there are multiple outputs) is a PyTorch module
    containing the parameters as trainable attributes. You can use the module like
    any other PyTorch module: `module(X)`, where `X` is a tensor with the same
    column ordering as trained with.

    Parameters
    ----------
    index : int | list[int]
        If you wish to select a particular equation from
        `self.equations_`, give the index number here. This overrides
        the `model_selection` parameter. If there are multiple output
        features, then pass a list of indices with the order the same
        as the output feature.

    Returns
    -------
    best_equation : torch.nn.Module
        PyTorch module representing the expression.
    """
    self.set_params(output_torch_format=True)
    self.refresh()
    best_equation = self.get_best(index=index)
    if isinstance(best_equation, list):
        return [eq["torch_format"] for eq in best_equation]
    else:
        return best_equation["torch_format"]

`jax(index=None)` ¶

Return jax representation of the equation(s) chosen by model_selection.

Each equation (multiple given if there are multiple outputs) is a dictionary containing {"callable": func, "parameters": params}. To call func, pass func(X, params). This function is differentiable using jax.grad.

Parameters:

Name	Type	Description	Default
`index`	`int \| list[int]`	If you wish to select a particular equation from `self.equations_`, give the index number here. This overrides the `model_selection` parameter. If there are multiple output features, then pass a list of indices with the order the same as the output feature.	`None`

Returns:

Name	Type	Description
`best_equation`	`dict[str, Any]`	Dictionary of callable jax function in "callable" key, and jax array of parameters as "parameters" key.

Source code in pysr/sr.py

def jax(self, index=None):
    """
    Return jax representation of the equation(s) chosen by `model_selection`.

    Each equation (multiple given if there are multiple outputs) is a dictionary
    containing {"callable": func, "parameters": params}. To call `func`, pass
    func(X, params). This function is differentiable using `jax.grad`.

    Parameters
    ----------
    index : int | list[int]
        If you wish to select a particular equation from
        `self.equations_`, give the index number here. This overrides
        the `model_selection` parameter. If there are multiple output
        features, then pass a list of indices with the order the same
        as the output feature.

    Returns
    -------
    best_equation : dict[str, Any]
        Dictionary of callable jax function in "callable" key,
        and jax array of parameters as "parameters" key.
    """
    self.set_params(output_jax_format=True)
    self.refresh()
    best_equation = self.get_best(index=index)
    if isinstance(best_equation, list):
        assert self.nout_ > 1
        return [eq["jax_format"] for eq in best_equation]
    else:
        return best_equation["jax_format"]

`latex_table(indices=None, precision=3, columns=['equation', 'complexity', 'loss', 'score'])` ¶

Create a LaTeX/booktabs table for all, or some, of the equations.

Parameters:

Name	Type	Description	Default
`indices`	`list[int] \| list[list[int]]`	If you wish to select a particular subset of equations from `self.equations_`, give the row numbers here. By default, all equations will be used. If there are multiple output features, then pass a list of lists.	`None`
`precision`	`int`	The number of significant figures shown in the LaTeX representations. Default is `3`.	`3`
`columns`	`list[str]`	Which columns to include in the table. Default is `["equation", "complexity", "loss", "score"]`.	`['equation', 'complexity', 'loss', 'score']`

Returns:

Name	Type	Description
`latex_table_str`	`str`	A string that will render a table in LaTeX of the equations.

Source code in pysr/sr.py

def latex_table(
    self,
    indices=None,
    precision=3,
    columns=["equation", "complexity", "loss", "score"],
):
    """Create a LaTeX/booktabs table for all, or some, of the equations.

    Parameters
    ----------
    indices : list[int] | list[list[int]]
        If you wish to select a particular subset of equations from
        `self.equations_`, give the row numbers here. By default,
        all equations will be used. If there are multiple output
        features, then pass a list of lists.
    precision : int
        The number of significant figures shown in the LaTeX
        representations.
        Default is `3`.
    columns : list[str]
        Which columns to include in the table.
        Default is `["equation", "complexity", "loss", "score"]`.

    Returns
    -------
    latex_table_str : str
        A string that will render a table in LaTeX of the equations.
    """
    self.refresh()

    if isinstance(self.equations_, list):
        if indices is not None:
            assert isinstance(indices, list)
            assert isinstance(indices[0], list)
            assert len(indices) == self.nout_

        table_string = sympy2multilatextable(
            self.equations_, indices=indices, precision=precision, columns=columns
        )
    elif isinstance(self.equations_, pd.DataFrame):
        if indices is not None:
            assert isinstance(indices, list)
            assert isinstance(indices[0], int)

        table_string = sympy2latextable(
            self.equations_, indices=indices, precision=precision, columns=columns
        )
    else:
        raise ValueError(
            "Invalid type for equations_ to pass to `latex_table`. "
            "Expected a DataFrame or a list of DataFrames."
        )

    return with_preamble(table_string)

`refresh(checkpoint_file=None)` ¶

Update self.equations_ with any new options passed.

For example, updating extra_sympy_mappings will require a .refresh() to update the equations.

Parameters:

Name	Type	Description	Default
`checkpoint_file`	`str or Path`	Path to checkpoint hall of fame file to be loaded. The default will use the set `equation_file_`.	`None`

Source code in pysr/sr.py

def refresh(self, checkpoint_file: Optional[PathLike] = None) -> None:
    """
    Update self.equations_ with any new options passed.

    For example, updating `extra_sympy_mappings`
    will require a `.refresh()` to update the equations.

    Parameters
    ----------
    checkpoint_file : str or Path
        Path to checkpoint hall of fame file to be loaded.
        The default will use the set `equation_file_`.
    """
    if checkpoint_file is not None:
        self.equation_file_ = checkpoint_file
        self.equation_file_contents_ = None
    check_is_fitted(self, attributes=["equation_file_"])
    self.equations_ = self.get_hof()

PySRRegressor Reference¶

PySRRegressor Parameters¶

The Algorithm¶

Creating the Search Space¶

Setting the Search Size¶

The Objective¶

Working with Complexities¶

Mutations¶

Tournament Selection¶

Constant Optimization¶

Migration between Populations¶

Data Preprocessing¶

Stopping Criteria¶

Performance and Parallelization¶

Determinism¶

Monitoring¶

Environment¶

Exporting the Results¶

PySRRegressor Functions¶

fit(X, y, Xresampled=None, weights=None, variable_names=None, complexity_of_variables=None, X_units=None, y_units=None) ¶

predict(X, index=None) ¶

from_file(equation_file, *, binary_operators=None, unary_operators=None, n_features_in=None, feature_names_in=None, selection_mask=None, nout=1, **pysr_kwargs) classmethod ¶

sympy(index=None) ¶

latex(index=None, precision=3) ¶

pytorch(index=None) ¶

jax(index=None) ¶

latex_table(indices=None, precision=3, columns=['equation', 'complexity', 'loss', 'score']) ¶

refresh(checkpoint_file=None) ¶

`fit(X, y, Xresampled=None, weights=None, variable_names=None, complexity_of_variables=None, X_units=None, y_units=None)` ¶

`predict(X, index=None)` ¶

`from_file(equation_file, *, binary_operators=None, unary_operators=None, n_features_in=None, feature_names_in=None, selection_mask=None, nout=1, **pysr_kwargs)` `classmethod` ¶

`sympy(index=None)` ¶

`latex(index=None, precision=3)` ¶

`pytorch(index=None)` ¶

`jax(index=None)` ¶

`latex_table(indices=None, precision=3, columns=['equation', 'complexity', 'loss', 'score'])` ¶

`refresh(checkpoint_file=None)` ¶