Prediction

Prediction in Interfere empowers you to translate fitted forecasting methods into precise counterfactual system trajectories. By leveraging the same simulate interface, you can compare baseline dynamics to intervention-driven responses with minimal code changes.

API Reference: fit() & predict()

fit()

fit(
    self,
    t: np.ndarray,
    endog_states: np.ndarray,
    exog_states: Optional[np.ndarray] = None,
) -> ForecastMethod

• t (np.ndarray): 1D array of time points with shape (n,), strictly increasing.
• endog_states (np.ndarray): 2D array (n, d) of endogenous variable observations.
• exog_states (Optional[np.ndarray]): 2D array (n, k) of exogenous signals; defaults to no exogenous inputs.

Returns: The fitted forecasting method instance (self).

predict()

predict(
    self,
    t: np.ndarray,
    prior_endog_states: np.ndarray,
    prior_exog_states: Optional[np.ndarray] = None,
    prior_t: Optional[np.ndarray] = None,
    prediction_exog: Optional[np.ndarray] = None,
    prediction_max: float = 1e9,
    rng: np.random.RandomState = DEFAULT_RANGE
) -> np.ndarray

• t (np.ndarray): 1D array (m,) of future time points to predict.
• prior_endog_states (np.ndarray): 2D array (p, d) of historic endogenous observations used as initial conditions or lagged values.
• prior_exog_states (Optional[np.ndarray]): 2D array (p, k) of historic exogenous signals.
• prior_t (Optional[np.ndarray]): 1D array (p,) of times corresponding to prior_*_states. If None, inferred from t spacing.
• prediction_exog (Optional[np.ndarray]): 2D array (m, k) of future exogenous inputs.
• prediction_max (float): Threshold to cap predictions and prevent overflow.
• rng (np.random.RandomState): Random state for reproducible stochastic forecasts.

Returns: A 2D array (m, d) of predicted endogenous states, including the first row as the initial condition.

Prediction Methods

Use any forecasting method that inherits from ForecastMethod.

Method	Description
AverageMethod	Baseline forecast using average historical data
VAR	Vector autoregression forecast using statsmodels
SINDy	Sparse model identification for nonlinear dynamics
ResComp	Reservoir computing forecast with Tikhonov regularization
ARIMA	Classical time series ARIMA model via Nixtla StatsForecast
LSTM	Long Short-Term Memory RNN forecaster via Nixtla NeuralForecast
NHITS	NHITS deep learning forecaster via Nixtla NeuralForecast

Example

import numpy as np
import interfere

# Pre-intervention simulation
t = np.arange(0, 10, 0.1)
x0 = np.random.rand(2)
dynamics = interfere.dynamics.Lorenz(sigma=0.2)
states = dynamics.simulate(t, x0)

# Define intervention
interv = interfere.PerfectIntervention(0, 2.0)

# Generate pre-intervention data
t0 = t
n_endog, n_exog = states.shape[1]-len(interv.iv_idxs), len(interv.iv_idxs)
endog, exog = interv.split_exog(states)

# Fit SINDy to pre-intervention data
method = interfere.SINDy()
method.fit(t0, endog, exog)

# Forecast with intervention
t_pred = np.arange(t[-1], t[-1]+5, 0.1)
pred_states = method.simulate(t_pred, states, intervention=interv)

# Inspect predicted states shape
print(pred_states.shape)  # (50, endog+exog dims)