API Reference

Least-Squares estimators

Ridge([n_components, lag_time, ...])

Linear model minimizing the \(L^{2}\) loss.

Kernel-based estimators

KernelRidge([n_components, lag_time, ...])

Kernel model minimizing the \(L^{2}\) loss.

NystroemKernelRidge([n_components, ...])

Nyström-accelerated Kernel model minimizing the \(L^{2}\) loss.

GeneratorDirichlet(diffusion[, ...])

Kernel-based estimator for the infinitesimal generator of diffusion processes using the Dirichlet-form method.

Preprocessing utilities

TimeDelayEmbedding(history_length[, stride])

A scikit-learn compatible transformer that constructs time-delay embeddings (temporal windows) from trajectory data, with a configurable stride.

FeatureFlattener()

A scikit-learn compatible transformer that flattens multi-dimensional trajectories into a 2D array, and restores them to their original shape when inverted.

Datasets

compute_prinz_potential_eig(gamma, sigma, dt)

Computes the eigenvalues and eigenfunctions of the Generator of the Overdamped Langevin dynamics for the Prinz potential.

fetch_ordered_mnist(*[, num_digits, ...])

Fetch the MNIST dataset and return an ordered subset interleaving samples from each digit class.

make_duffing(X0[, n_steps, dt, alpha, beta, ...])

Generate a trajectory from the Duffing oscillator.

make_linear_system(X0, A[, n_steps, noise, ...])

Generate a trajectory from a discrete-time linear dynamical system.

make_logistic_map(X0[, n_steps, r, M, dt, ...])

Generate a trajectory from the logistic map with optional trigonometric noise Ostruszka et al. [1].

make_lorenz63(X0[, n_steps, dt, sigma, mu, beta])

Generate a trajectory from the Lorenz-63 system.

make_prinz_potential(X0[, n_steps, dt, ...])

Generate a 1D Langevin trajectory for the "Prinz potential" Prinz et al. [1].

make_regime_switching_var(X0, phi1, phi2, ...)

Generate a trajectory from a regime-switching vector autoregressive (VAR) process.

PyTorch Integration

SpectralContrastiveLoss()

Spectral contrastive loss based originally introduced by HaoChen et al. [1], and adopted for evolution operators in Turri et al. [2], Jeong et al. [3]

VampLoss([schatten_norm, center_covariances])

Variational Approach for learning Markov Processes (VAMP) score by Wu and Noé [1].

AutoEncoderLoss([alpha_rec, alpha_lin, ...])

Single-step Dynamic Autoencoder (DAE) loss introduced by Lusch et al. [1].

JAX Integration

spectral_contrastive_loss(x, y)

Spectral contrastive loss for self-supervised learning.

vamp_loss(x, y[, schatten_norm, ...])

Variational Approach for learning Markov Processes (VAMP) score.

autoencoder_loss(x, y, x_rec, y_enc, x_evo, ...)

Single-step Dynamic Autoencoder (DAE) loss.