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Getting Started with scHopfield

Network Inference

scHopfield infers gene regulatory networks (GRNs) from RNA velocity data using gradient descent optimization.

Theory

The Hopfield network dynamics are:

\[\frac{dx}{dt} = W \cdot \sigma(x) - \gamma \cdot x + I\]

Where RNA velocity approximates \(dx/dt\). By fitting W (interactions) and I (biases) to minimize the difference between observed and predicted velocity, we infer the GRN structure.

Basic Usage

Preprocessing

Sigmoid Function Fitting

scHopfield uses sigmoid activation functions to model gene expression:

\[\sigma(x; \theta, \alpha, \beta) = \frac{\alpha}{1 + e^{-\beta(x - \theta)}} + \text{offset}\]

Where:

\(\theta\) is the threshold parameter
\(\alpha\) is the amplitude (typically 1)
\(\beta\) is the exponent (steepness)
offset is a baseline value

Fitting Process

The fit_all_sigmoids() function fits these parameters to each gene’s expression distribution:

scHopfield models gene regulatory networks (GRNs) as continuous Hopfield

networks, where gene expression dynamics follow:

\[\frac{dx}{dt} = W \cdot \sigma(x) - \gamma \cdot x + I\]

W: Interaction matrix encoding gene-gene regulatory relationships
σ(x): Sigmoid activation function fitted to expression data
γ: Degradation rates (mRNA decay)
I: Bias vector representing external inputs / basal expression

This notebook walks through the full setup: data loading, sigmoid fitting,

network inference (with and without a scaffold), and saving/loading the model.

1.1 Setup & Imports

[1]:

import numpy as np
import scanpy as sc
import scHopfield as sch
import matplotlib.pyplot as plt

# Analysis parameters (update for your dataset)
DATA_PATH = './scratch/Data/'
DATASET_FILE = 'hematopoiesis.h5ad'

CLUSTER_KEY = 'cell_type'
VELOCITY_KEY = 'velocity_alpha_minus_gamma_s'
SPLICED_KEY  = 'M_t'
DEGRADATION_KEY = 'gamma'
DYNAMIC_GENES_KEY = 'use_for_dynamics'

CELL_TYPE_ORDER = ['Meg', 'Ery', 'MEP-like', 'HSC', 'GMP-like', 'Mon', 'Bas', 'Neu']

# Network inference hyper-parameters
N_EPOCHS              = 1000
BATCH_SIZE            = 128
W_THRESHOLD           = 1e-12
SCAFFOLD_REGULARIZATION = 1e-2
DEVICE = 'cuda'   # or 'cpu'

/home/bernaljp/miniconda3/envs/SCH/lib/python3.11/site-packages/louvain/__init__.py:54: UserWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html. The pkg_resources package is slated for removal as early as 2025-11-30. Refrain from using this package or pin to Setuptools<81.
  from pkg_resources import get_distribution, DistributionNotFound

1.2 Data Loading

The hematopoiesis dataset can be loaded from two sources:

Option	Command	Notes
Local file	`sc.read_h5ad(DATA_PATH + DATASET_FILE)`	Fastest; requires the file on disk
dynamo	`dyn.sample_data.hematopoiesis()`	Downloads on first use; `pip install dynamo-release`

The cell below tries the local file first and falls back to dynamo automatically.

[2]:

from fileinput import filename
import os

print("Loading data...")
_local_path = DATA_PATH + DATASET_FILE

if os.path.exists(_local_path):
    print(f"  Source: local file ({_local_path})")
    adata = sc.read_h5ad(_local_path)
else:
    # Requires: pip install dynamo-release
    print("  Local file not found – downloading from dynamo (pip install dynamo-release)...")
    import dynamo as dyn
    adata = dyn.sample_data.hematopoiesis(filename=_local_path)
    # Optionally cache locally to skip the download next time:
    # os.makedirs(DATA_PATH, exist_ok=True)
    # adata.write_h5ad(_local_path)

print(f"  Loaded: {adata.n_obs} cells × {adata.n_vars} genes")
print(adata)

Loading data...
  Loaded: 1947 cells × 1956 genes
AnnData object with n_obs × n_vars = 1947 × 1956
    obs: 'batch', 'time', 'cell_type', 'nGenes', 'nCounts', 'pMito', 'pass_basic_filter', 'new_Size_Factor', 'initial_new_cell_size', 'total_Size_Factor', 'initial_total_cell_size', 'spliced_Size_Factor', 'initial_spliced_cell_size', 'unspliced_Size_Factor', 'initial_unspliced_cell_size', 'Size_Factor', 'initial_cell_size', 'ntr', 'cell_cycle_phase', 'leiden', 'control_point_pca', 'inlier_prob_pca', 'obs_vf_angle_pca', 'pca_ddhodge_div', 'pca_ddhodge_potential', 'acceleration_pca', 'curvature_pca', 'n_counts', 'mt_frac', 'jacobian_det_pca', 'manual_selection', 'divergence_pca', 'curv_leiden', 'curv_louvain', 'SPI1->GATA1_jacobian', 'jacobian', 'umap_ori_leiden', 'umap_ori_louvain', 'umap_ddhodge_div', 'umap_ddhodge_potential', 'curl_umap', 'divergence_umap', 'acceleration_umap', 'control_point_umap_ori', 'inlier_prob_umap_ori', 'obs_vf_angle_umap_ori', 'curvature_umap_ori'
    var: 'gene_name', 'gene_id', 'nCells', 'nCounts', 'pass_basic_filter', 'use_for_pca', 'frac', 'ntr', 'time_3_alpha', 'time_3_beta', 'time_3_gamma', 'time_3_half_life', 'time_3_alpha_b', 'time_3_alpha_r2', 'time_3_gamma_b', 'time_3_gamma_r2', 'time_3_gamma_logLL', 'time_3_delta_b', 'time_3_delta_r2', 'time_3_bs', 'time_3_bf', 'time_3_uu0', 'time_3_ul0', 'time_3_su0', 'time_3_sl0', 'time_3_U0', 'time_3_S0', 'time_3_total0', 'time_3_beta_k', 'time_3_gamma_k', 'time_5_alpha', 'time_5_beta', 'time_5_gamma', 'time_5_half_life', 'time_5_alpha_b', 'time_5_alpha_r2', 'time_5_gamma_b', 'time_5_gamma_r2', 'time_5_gamma_logLL', 'time_5_bs', 'time_5_bf', 'time_5_uu0', 'time_5_ul0', 'time_5_su0', 'time_5_sl0', 'time_5_U0', 'time_5_S0', 'time_5_total0', 'time_5_beta_k', 'time_5_gamma_k', 'use_for_dynamics', 'gamma', 'gamma_r2', 'use_for_transition', 'gamma_k', 'gamma_b'
    uns: 'PCs', 'VecFld_pca', 'VecFld_umap', 'X_umap_neighbors', 'cell_phase_genes', 'cell_type_colors', 'dynamics', 'explained_variance_ratio_', 'feature_selection', 'grid_velocity_pca', 'grid_velocity_umap', 'grid_velocity_umap_ori_perturbation', 'grid_velocity_umap_test', 'jacobian_pca', 'leiden', 'neighbors', 'pca_mean', 'pp', 'response'
    obsm: 'X', 'X_pca', 'X_pca_SparseVFC', 'X_umap', 'X_umap_SparseVFC', 'X_umap_ori_perturbation', 'X_umap_test', 'acceleration_pca', 'acceleration_umap', 'cell_cycle_scores', 'curvature_pca', 'curvature_umap', 'j_delta_x_perturbation', 'velocity_pca', 'velocity_pca_SparseVFC', 'velocity_umap', 'velocity_umap_SparseVFC', 'velocity_umap_ori_perturbation', 'velocity_umap_test'
    layers: 'M_n', 'M_nn', 'M_t', 'M_tn', 'M_tt', 'X_new', 'X_total', 'velocity_alpha_minus_gamma_s'
    obsp: 'X_umap_connectivities', 'X_umap_distances', 'connectivities', 'cosine_transition_matrix', 'distances', 'fp_transition_rate', 'moments_con', 'pca_ddhodge', 'perturbation_transition_matrix', 'umap_ddhodge'

1.3 Preprocessing

Remove genes with NaN velocities by subsetting adata, then identify the

dynamic genes that will be passed to the model.

[3]:

# Remove genes that have any NaN velocity entry (hematopoiesis dataset)
print("Removing genes with NaN velocities...")
velocity_layer = adata.layers[VELOCITY_KEY]
if hasattr(velocity_layer, 'toarray'):
    velocity_layer = velocity_layer.toarray()
bad_gene_idx = np.unique(np.where(np.isnan(velocity_layer))[1])
keep_mask = np.ones(adata.n_vars, dtype=bool)
keep_mask[bad_gene_idx] = False
adata = adata[:, keep_mask].copy()
print(f"  After filtering: {adata.n_obs} cells × {adata.n_vars} genes")

# Boolean mask of dynamic genes used for modelling
genes_to_use = adata.var[DYNAMIC_GENES_KEY].values
n_genes = genes_to_use.sum()
print(f"  Dynamic genes for modelling: {n_genes}")

Removing genes with NaN velocities...
  After filtering: 1947 cells × 1728 genes
  Dynamic genes for modelling: 1728

1.4 Sigmoid Fitting

Fit a sigmoid function to each gene’s expression distribution.

\[\varphi_i(x_i) = \frac{x_i^{n_i}}{x_i^{n_i}+k_i^{n_i}}\]

The fitted parameters are stored in adata.var.

[4]:

sch.pp.fit_all_sigmoids(
    adata,
    spliced_key=SPLICED_KEY,
    genes=adata.var[DYNAMIC_GENES_KEY].values
)

sch.pp.compute_sigmoid(adata, spliced_key=SPLICED_KEY, copy=False)

print("Sigmoid fitting complete.")
print(adata)

/home/bernaljp/packages/scHopfield/scHopfield/_utils/math.py:93: RuntimeWarning: divide by zero encountered in divide
  ty = np.log(y / (1 - y))
/home/bernaljp/packages/scHopfield/scHopfield/_utils/math.py:93: RuntimeWarning: divide by zero encountered in log
  ty = np.log(y / (1 - y))

Sigmoid fitting complete.
AnnData object with n_obs × n_vars = 1947 × 1728
    obs: 'batch', 'time', 'cell_type', 'nGenes', 'nCounts', 'pMito', 'pass_basic_filter', 'new_Size_Factor', 'initial_new_cell_size', 'total_Size_Factor', 'initial_total_cell_size', 'spliced_Size_Factor', 'initial_spliced_cell_size', 'unspliced_Size_Factor', 'initial_unspliced_cell_size', 'Size_Factor', 'initial_cell_size', 'ntr', 'cell_cycle_phase', 'leiden', 'control_point_pca', 'inlier_prob_pca', 'obs_vf_angle_pca', 'pca_ddhodge_div', 'pca_ddhodge_potential', 'acceleration_pca', 'curvature_pca', 'n_counts', 'mt_frac', 'jacobian_det_pca', 'manual_selection', 'divergence_pca', 'curv_leiden', 'curv_louvain', 'SPI1->GATA1_jacobian', 'jacobian', 'umap_ori_leiden', 'umap_ori_louvain', 'umap_ddhodge_div', 'umap_ddhodge_potential', 'curl_umap', 'divergence_umap', 'acceleration_umap', 'control_point_umap_ori', 'inlier_prob_umap_ori', 'obs_vf_angle_umap_ori', 'curvature_umap_ori'
    var: 'gene_name', 'gene_id', 'nCells', 'nCounts', 'pass_basic_filter', 'use_for_pca', 'frac', 'ntr', 'time_3_alpha', 'time_3_beta', 'time_3_gamma', 'time_3_half_life', 'time_3_alpha_b', 'time_3_alpha_r2', 'time_3_gamma_b', 'time_3_gamma_r2', 'time_3_gamma_logLL', 'time_3_delta_b', 'time_3_delta_r2', 'time_3_bs', 'time_3_bf', 'time_3_uu0', 'time_3_ul0', 'time_3_su0', 'time_3_sl0', 'time_3_U0', 'time_3_S0', 'time_3_total0', 'time_3_beta_k', 'time_3_gamma_k', 'time_5_alpha', 'time_5_beta', 'time_5_gamma', 'time_5_half_life', 'time_5_alpha_b', 'time_5_alpha_r2', 'time_5_gamma_b', 'time_5_gamma_r2', 'time_5_gamma_logLL', 'time_5_bs', 'time_5_bf', 'time_5_uu0', 'time_5_ul0', 'time_5_su0', 'time_5_sl0', 'time_5_U0', 'time_5_S0', 'time_5_total0', 'time_5_beta_k', 'time_5_gamma_k', 'use_for_dynamics', 'gamma', 'gamma_r2', 'use_for_transition', 'gamma_k', 'gamma_b', 'scHopfield_used', 'sigmoid_threshold', 'sigmoid_exponent', 'sigmoid_offset', 'sigmoid_mse'
    uns: 'PCs', 'VecFld_pca', 'VecFld_umap', 'X_umap_neighbors', 'cell_phase_genes', 'cell_type_colors', 'dynamics', 'explained_variance_ratio_', 'feature_selection', 'grid_velocity_pca', 'grid_velocity_umap', 'grid_velocity_umap_ori_perturbation', 'grid_velocity_umap_test', 'jacobian_pca', 'leiden', 'neighbors', 'pca_mean', 'pp', 'response', 'scHopfield'
    obsm: 'X', 'X_pca', 'X_pca_SparseVFC', 'X_umap', 'X_umap_SparseVFC', 'X_umap_ori_perturbation', 'X_umap_test', 'acceleration_pca', 'acceleration_umap', 'cell_cycle_scores', 'curvature_pca', 'curvature_umap', 'j_delta_x_perturbation', 'velocity_pca', 'velocity_pca_SparseVFC', 'velocity_umap', 'velocity_umap_SparseVFC', 'velocity_umap_ori_perturbation', 'velocity_umap_test'
    layers: 'M_n', 'M_nn', 'M_t', 'M_tn', 'M_tt', 'X_new', 'X_total', 'velocity_alpha_minus_gamma_s', 'sigmoid'
    obsp: 'X_umap_connectivities', 'X_umap_distances', 'connectivities', 'cosine_transition_matrix', 'distances', 'fp_transition_rate', 'moments_con', 'pca_ddhodge', 'perturbation_transition_matrix', 'umap_ddhodge'

[5]:

# Visualize sigmoid fits for key genes
genes_to_plot = ['Gata1', 'Klf1', 'Gata2', 'Spi1', 'Cebpa', 'FLI1']
genes_to_plot = [g.upper() for g in genes_to_plot if g.upper() in adata.var_names]

if genes_to_plot:
    n_cols = min(3, len(genes_to_plot))
    n_rows = (len(genes_to_plot) + n_cols - 1) // n_cols
    fig, axes = plt.subplots(n_rows, n_cols, figsize=[5*n_cols, 4*n_rows])
    axes = np.atleast_2d(axes).flatten()

    for i, gene in enumerate(genes_to_plot):
        sch.pl.plot_sigmoid_fit(adata, gene=gene, ax=axes[i],
                                spliced_key='M_t', show_zeros=False)

    # Hide empty axes
    for j in range(i+1, len(axes)):
        axes[j].axis('off')

    plt.tight_layout()
    plt.show()

../_images/notebooks_01_getting_started_12_0.png

1.5 Network Inference (no scaffold)

Learn the interaction matrix W for each cell cluster by minimizing the

velocity reconstruction error.

[6]:

sch.inf.fit_interactions(
    adata,
    cluster_key=CLUSTER_KEY,
    spliced_key=SPLICED_KEY,
    velocity_key=VELOCITY_KEY,
    degradation_key=DEGRADATION_KEY,
    w_threshold=W_THRESHOLD,
    infer_I=True,
    refit_gamma=False,
    n_epochs=N_EPOCHS,
    criterion='MSE',
    batch_size=BATCH_SIZE,
    use_scheduler=True,
    get_plots=False,
    device=DEVICE,
)

print("Network inference complete (no scaffold).")

Inferring interaction matrix W and bias vector I for cluster Mon
Inferring interaction matrix W and bias vector I for cluster Meg
Inferring interaction matrix W and bias vector I for cluster MEP-like
Inferring interaction matrix W and bias vector I for cluster Ery
Inferring interaction matrix W and bias vector I for cluster Bas
Inferring interaction matrix W and bias vector I for cluster GMP-like
Inferring interaction matrix W and bias vector I for cluster HSC
Inferring interaction matrix W and bias vector I for cluster Neu
Inferring interaction matrix W and bias vector I for cluster all
Network inference complete (no scaffold).

1.6 Scaffold-Constrained Inference

Load a prior gene regulatory network (GRN) from CellOracle’s mouse scATAC-seq

atlas and use it as a scaffold to regularise the learned W matrix.

[7]:

import celloracle as co
import pandas as pd

print("Loading CellOracle scaffold...")
base_GRN = co.data.load_mouse_scATAC_atlas_base_GRN()
base_GRN.drop(['peak_id'], axis=1, inplace=True)

# Build scaffold matrix (genes × genes; 1 = edge allowed by prior)
scaffold = pd.DataFrame(
    0,
    index=adata.var.index[genes_to_use],
    columns=adata.var.index[genes_to_use]
)

tfs = list(set(base_GRN.columns.str.lower()) & set(scaffold.index.str.lower()))
target_genes = list(
    set(base_GRN['gene_short_name'].str.lower().values) & set(scaffold.columns.str.lower())
)

index_map = {gene.lower(): gene for gene in scaffold.index}
col_map   = {gene.lower(): gene for gene in scaffold.columns}

for tf in tfs:
    tf_original = index_map[tf]
    tf_col = [c for c in base_GRN.columns if c.lower() == tf][0]
    for target in base_GRN[base_GRN[tf_col] == 1]['gene_short_name']:
        if target.lower() in target_genes:
            scaffold.loc[tf_original, col_map[target.lower()]] = 1

print(f"  Scaffold: {scaffold.sum().sum()} potential connections")
print(f"  TFs: {len(tfs)}, Target genes: {len(target_genes)}")

which: no R in (/opt/slurm/puppet/bin:/opt/slurm/cluster/ibex/install-v2/RedHat-9/bin:/opt/slurm/scripts/bin:/usr/lpp/mmfs/bin:/home/bernaljp/miniconda3/envs/SCH/bin:/opt/slurm/puppet/bin:/opt/slurm/cluster/ibex/install-v2/RedHat-9/bin:/opt/slurm/scripts/bin:/usr/lpp/mmfs/bin:/home/bernaljp/miniconda3/condabin:/opt/slurm/puppet/bin:/usr/share/Modules/bin:/opt/slurm/cluster/ibex/install-v2/RedHat-9/bin:/opt/slurm/scripts/bin:/usr/lpp/mmfs/bin:/usr/local/bin:/usr/bin:/usr/local/sbin:/usr/sbin:/opt/slurm/scripts/bin:/opt/puppetlabs/bin:/home/bernaljp/.local/bin:/home/bernaljp/bin:/opt/slurm/scripts/bin:/home/bernaljp/.local/bin:/home/bernaljp/bin:/opt/slurm/scripts/bin:/home/bernaljp/.local/bin:/home/bernaljp/bin)

Loading CellOracle scaffold...
  Scaffold: 41693 potential connections
  TFs: 73, Target genes: 1148

[8]:

sch.inf.fit_interactions(
    adata,
    cluster_key=CLUSTER_KEY,
    spliced_key=SPLICED_KEY,
    velocity_key=VELOCITY_KEY,
    degradation_key=DEGRADATION_KEY,
    w_threshold=W_THRESHOLD,
    w_scaffold=scaffold.values.T,
    scaffold_regularization=SCAFFOLD_REGULARIZATION,
    only_TFs=True,
    infer_I=True,
    refit_gamma=False,
    n_epochs=N_EPOCHS,
    criterion='MSE',
    batch_size=BATCH_SIZE,
    use_scheduler=True,
    get_plots=False,
    device=DEVICE,
)

print("Scaffold-constrained network inference complete.")

Inferring interaction matrix W and bias vector I for cluster Mon

/home/bernaljp/packages/scHopfield/scHopfield/inference/optimizer.py:18: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.detach().clone() or sourceTensor.detach().clone().requires_grad_(True), rather than torch.tensor(sourceTensor).
  self.register_buffer('mask', torch.tensor(mask, dtype=torch.float32, device=device))
Training Epochs:   1%|▏         | 13/1000 [00:00<00:17, 57.61it/s]

[Epoch 1/1000] Total Loss: 64.630268, Reconstruction Loss: 0.509252, LR: 1.00e-01, Batch size: 128

Training Epochs:  11%|█▏        | 114/1000 [00:01<00:07, 117.88it/s]

[Epoch 101/1000] Total Loss: 10.317851, Reconstruction Loss: 0.008718, LR: 4.00e-02, Batch size: 128

Training Epochs:  22%|██▏       | 218/1000 [00:01<00:06, 121.09it/s]

[Epoch 201/1000] Total Loss: 3.396171, Reconstruction Loss: 0.001726, LR: 1.60e-02, Batch size: 128

Training Epochs:  32%|███▏      | 322/1000 [00:02<00:05, 121.19it/s]

[Epoch 301/1000] Total Loss: 1.288166, Reconstruction Loss: 0.000778, LR: 6.40e-03, Batch size: 128

Training Epochs:  41%|████▏     | 413/1000 [00:03<00:04, 120.04it/s]

[Epoch 401/1000] Total Loss: 0.448385, Reconstruction Loss: 0.000669, LR: 2.56e-03, Batch size: 128

Training Epochs:  52%|█████▏    | 517/1000 [00:04<00:04, 120.24it/s]

[Epoch 501/1000] Total Loss: 0.181946, Reconstruction Loss: 0.000663, LR: 1.02e-03, Batch size: 128

Training Epochs:  62%|██████▏   | 621/1000 [00:05<00:03, 121.60it/s]

[Epoch 601/1000] Total Loss: 0.082942, Reconstruction Loss: 0.000658, LR: 4.10e-04, Batch size: 128

Training Epochs:  72%|███████▎  | 725/1000 [00:06<00:02, 121.45it/s]

[Epoch 701/1000] Total Loss: 0.030161, Reconstruction Loss: 0.000653, LR: 1.64e-04, Batch size: 128

Training Epochs:  82%|████████▏ | 816/1000 [00:06<00:01, 121.36it/s]

[Epoch 801/1000] Total Loss: 0.011939, Reconstruction Loss: 0.000655, LR: 6.55e-05, Batch size: 128

Training Epochs:  92%|█████████▏| 920/1000 [00:07<00:00, 121.64it/s]

[Epoch 901/1000] Total Loss: 0.005090, Reconstruction Loss: 0.000657, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:08<00:00, 118.75it/s]
/home/bernaljp/packages/scHopfield/scHopfield/inference/optimizer.py:18: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.detach().clone() or sourceTensor.detach().clone().requires_grad_(True), rather than torch.tensor(sourceTensor).
  self.register_buffer('mask', torch.tensor(mask, dtype=torch.float32, device=device))

[Epoch 1000/1000] Total Loss: 0.002839, Reconstruction Loss: 0.000648, LR: 1.05e-05, Batch size: 128
Inferring interaction matrix W and bias vector I for cluster Meg

Training Epochs:   4%|▎         | 35/1000 [00:00<00:02, 341.73it/s]

[Epoch 1/1000] Total Loss: 73.839462, Reconstruction Loss: 0.418692, LR: 1.00e-01, Batch size: 128

Training Epochs:  14%|█▍        | 142/1000 [00:00<00:02, 350.40it/s]

[Epoch 101/1000] Total Loss: 12.315012, Reconstruction Loss: 0.022208, LR: 4.00e-02, Batch size: 128

Training Epochs:  25%|██▌       | 250/1000 [00:00<00:02, 351.62it/s]

[Epoch 201/1000] Total Loss: 3.871475, Reconstruction Loss: 0.002862, LR: 1.60e-02, Batch size: 128

Training Epochs:  36%|███▌      | 358/1000 [00:01<00:01, 350.26it/s]

[Epoch 301/1000] Total Loss: 1.582910, Reconstruction Loss: 0.001613, LR: 6.40e-03, Batch size: 128

Training Epochs:  47%|████▋     | 466/1000 [00:01<00:01, 350.94it/s]

[Epoch 401/1000] Total Loss: 0.629308, Reconstruction Loss: 0.001433, LR: 2.56e-03, Batch size: 128

Training Epochs:  54%|█████▍    | 538/1000 [00:01<00:01, 349.74it/s]

[Epoch 501/1000] Total Loss: 0.266602, Reconstruction Loss: 0.001431, LR: 1.02e-03, Batch size: 128

Training Epochs:  64%|██████▍   | 644/1000 [00:01<00:01, 350.63it/s]

[Epoch 601/1000] Total Loss: 0.107586, Reconstruction Loss: 0.001420, LR: 4.10e-04, Batch size: 128

Training Epochs:  75%|███████▌  | 751/1000 [00:02<00:00, 349.75it/s]

[Epoch 701/1000] Total Loss: 0.044884, Reconstruction Loss: 0.001442, LR: 1.64e-04, Batch size: 128

Training Epochs:  86%|████████▌ | 859/1000 [00:02<00:00, 349.57it/s]

[Epoch 801/1000] Total Loss: 0.019176, Reconstruction Loss: 0.001432, LR: 6.55e-05, Batch size: 128

Training Epochs:  96%|█████████▋| 965/1000 [00:02<00:00, 349.67it/s]

[Epoch 901/1000] Total Loss: 0.008195, Reconstruction Loss: 0.001432, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:02<00:00, 349.73it/s]

[Epoch 1000/1000] Total Loss: 0.004075, Reconstruction Loss: 0.001431, LR: 1.05e-05, Batch size: 128
Inferring interaction matrix W and bias vector I for cluster MEP-like

Training Epochs:   1%|          | 12/1000 [00:00<00:08, 115.12it/s]

[Epoch 1/1000] Total Loss: 64.425922, Reconstruction Loss: 0.457732, LR: 1.00e-01, Batch size: 128

Training Epochs:  12%|█▏        | 115/1000 [00:00<00:07, 121.61it/s]

[Epoch 101/1000] Total Loss: 10.250659, Reconstruction Loss: 0.006966, LR: 4.00e-02, Batch size: 128

Training Epochs:  22%|██▏       | 219/1000 [00:01<00:06, 120.06it/s]

[Epoch 201/1000] Total Loss: 3.441626, Reconstruction Loss: 0.001272, LR: 1.60e-02, Batch size: 128

Training Epochs:  32%|███▏      | 323/1000 [00:02<00:05, 120.57it/s]

[Epoch 301/1000] Total Loss: 1.277202, Reconstruction Loss: 0.000542, LR: 6.40e-03, Batch size: 128

Training Epochs:  41%|████▏     | 414/1000 [00:03<00:04, 121.17it/s]

[Epoch 401/1000] Total Loss: 0.453951, Reconstruction Loss: 0.000449, LR: 2.56e-03, Batch size: 128

Training Epochs:  52%|█████▏    | 518/1000 [00:04<00:04, 120.23it/s]

[Epoch 501/1000] Total Loss: 0.179148, Reconstruction Loss: 0.000451, LR: 1.02e-03, Batch size: 128

Training Epochs:  62%|██████▏   | 622/1000 [00:05<00:03, 120.11it/s]

[Epoch 601/1000] Total Loss: 0.082500, Reconstruction Loss: 0.000452, LR: 4.10e-04, Batch size: 128

Training Epochs:  72%|███████▏  | 721/1000 [00:05<00:02, 119.60it/s]

[Epoch 701/1000] Total Loss: 0.030633, Reconstruction Loss: 0.000443, LR: 1.64e-04, Batch size: 128

Training Epochs:  82%|████████▏ | 824/1000 [00:06<00:01, 119.85it/s]

[Epoch 801/1000] Total Loss: 0.011891, Reconstruction Loss: 0.000443, LR: 6.55e-05, Batch size: 128

Training Epochs:  92%|█████████▏| 920/1000 [00:07<00:00, 118.74it/s]

[Epoch 901/1000] Total Loss: 0.004998, Reconstruction Loss: 0.000449, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:08<00:00, 120.02it/s]

[Epoch 1000/1000] Total Loss: 0.002539, Reconstruction Loss: 0.000437, LR: 1.05e-05, Batch size: 128
Inferring interaction matrix W and bias vector I for cluster Ery

Training Epochs:   3%|▎         | 34/1000 [00:00<00:02, 332.50it/s]

[Epoch 1/1000] Total Loss: 73.817230, Reconstruction Loss: 0.397020, LR: 1.00e-01, Batch size: 128

Training Epochs:  14%|█▍        | 139/1000 [00:00<00:02, 343.05it/s]

[Epoch 101/1000] Total Loss: 12.342674, Reconstruction Loss: 0.016045, LR: 4.00e-02, Batch size: 128

Training Epochs:  24%|██▍       | 244/1000 [00:00<00:02, 342.50it/s]

[Epoch 201/1000] Total Loss: 3.884972, Reconstruction Loss: 0.001988, LR: 1.60e-02, Batch size: 128

Training Epochs:  35%|███▍      | 349/1000 [00:01<00:01, 344.04it/s]

[Epoch 301/1000] Total Loss: 1.576656, Reconstruction Loss: 0.001246, LR: 6.40e-03, Batch size: 128

Training Epochs:  45%|████▌     | 454/1000 [00:01<00:01, 344.45it/s]

[Epoch 401/1000] Total Loss: 0.628460, Reconstruction Loss: 0.001144, LR: 2.56e-03, Batch size: 128

Training Epochs:  56%|█████▌    | 559/1000 [00:01<00:01, 345.28it/s]

[Epoch 501/1000] Total Loss: 0.265586, Reconstruction Loss: 0.001133, LR: 1.02e-03, Batch size: 128

Training Epochs:  66%|██████▋   | 664/1000 [00:01<00:00, 345.31it/s]

[Epoch 601/1000] Total Loss: 0.106788, Reconstruction Loss: 0.001082, LR: 4.10e-04, Batch size: 128

Training Epochs:  77%|███████▋  | 769/1000 [00:02<00:00, 345.70it/s]

[Epoch 701/1000] Total Loss: 0.043843, Reconstruction Loss: 0.001136, LR: 1.64e-04, Batch size: 128

Training Epochs:  84%|████████▍ | 839/1000 [00:02<00:00, 344.89it/s]

[Epoch 801/1000] Total Loss: 0.018806, Reconstruction Loss: 0.001135, LR: 6.55e-05, Batch size: 128

Training Epochs:  94%|█████████▍| 944/1000 [00:02<00:00, 345.13it/s]

[Epoch 901/1000] Total Loss: 0.007990, Reconstruction Loss: 0.001082, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:02<00:00, 344.10it/s]

[Epoch 1000/1000] Total Loss: 0.003727, Reconstruction Loss: 0.001065, LR: 1.05e-05, Batch size: 128
Inferring interaction matrix W and bias vector I for cluster Bas

Training Epochs:   3%|▎         | 34/1000 [00:00<00:02, 338.89it/s]

[Epoch 1/1000] Total Loss: 74.011673, Reconstruction Loss: 0.420055, LR: 1.00e-01, Batch size: 128

Training Epochs:  14%|█▍        | 140/1000 [00:00<00:02, 347.34it/s]

[Epoch 101/1000] Total Loss: 12.369323, Reconstruction Loss: 0.018950, LR: 4.00e-02, Batch size: 128

Training Epochs:  25%|██▍       | 246/1000 [00:00<00:02, 348.14it/s]

[Epoch 201/1000] Total Loss: 3.888886, Reconstruction Loss: 0.002169, LR: 1.60e-02, Batch size: 128

Training Epochs:  35%|███▌      | 351/1000 [00:01<00:01, 346.70it/s]

[Epoch 301/1000] Total Loss: 1.600862, Reconstruction Loss: 0.001095, LR: 6.40e-03, Batch size: 128

Training Epochs:  46%|████▌     | 457/1000 [00:01<00:01, 347.96it/s]

[Epoch 401/1000] Total Loss: 0.632268, Reconstruction Loss: 0.000978, LR: 2.56e-03, Batch size: 128

Training Epochs:  56%|█████▌    | 562/1000 [00:01<00:01, 347.75it/s]

[Epoch 501/1000] Total Loss: 0.264172, Reconstruction Loss: 0.000935, LR: 1.02e-03, Batch size: 128

Training Epochs:  67%|██████▋   | 669/1000 [00:01<00:00, 348.48it/s]

[Epoch 601/1000] Total Loss: 0.106983, Reconstruction Loss: 0.000956, LR: 4.10e-04, Batch size: 128

Training Epochs:  74%|███████▍  | 740/1000 [00:02<00:00, 348.17it/s]

[Epoch 701/1000] Total Loss: 0.044257, Reconstruction Loss: 0.000955, LR: 1.64e-04, Batch size: 128

Training Epochs:  85%|████████▍ | 846/1000 [00:02<00:00, 348.44it/s]

[Epoch 801/1000] Total Loss: 0.018226, Reconstruction Loss: 0.000959, LR: 6.55e-05, Batch size: 128

Training Epochs:  95%|█████████▌| 953/1000 [00:02<00:00, 348.59it/s]

[Epoch 901/1000] Total Loss: 0.007662, Reconstruction Loss: 0.000973, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:02<00:00, 347.40it/s]

[Epoch 1000/1000] Total Loss: 0.003573, Reconstruction Loss: 0.000967, LR: 1.05e-05, Batch size: 128
Inferring interaction matrix W and bias vector I for cluster GMP-like

Training Epochs:   4%|▎         | 35/1000 [00:00<00:02, 341.57it/s]

[Epoch 1/1000] Total Loss: 73.960991, Reconstruction Loss: 0.378584, LR: 1.00e-01, Batch size: 128

Training Epochs:  14%|█▍        | 142/1000 [00:00<00:02, 349.31it/s]

[Epoch 101/1000] Total Loss: 12.395257, Reconstruction Loss: 0.011156, LR: 4.00e-02, Batch size: 128

Training Epochs:  25%|██▌       | 250/1000 [00:00<00:02, 349.98it/s]

[Epoch 201/1000] Total Loss: 3.846868, Reconstruction Loss: 0.001018, LR: 1.60e-02, Batch size: 128

Training Epochs:  36%|███▌      | 358/1000 [00:01<00:01, 349.96it/s]

[Epoch 301/1000] Total Loss: 1.566379, Reconstruction Loss: 0.000362, LR: 6.40e-03, Batch size: 128

Training Epochs:  47%|████▋     | 466/1000 [00:01<00:01, 350.61it/s]

[Epoch 401/1000] Total Loss: 0.630207, Reconstruction Loss: 0.000301, LR: 2.56e-03, Batch size: 128

Training Epochs:  54%|█████▍    | 538/1000 [00:01<00:01, 350.82it/s]

[Epoch 501/1000] Total Loss: 0.263469, Reconstruction Loss: 0.000286, LR: 1.02e-03, Batch size: 128

Training Epochs:  65%|██████▍   | 646/1000 [00:01<00:01, 350.29it/s]

[Epoch 601/1000] Total Loss: 0.106407, Reconstruction Loss: 0.000286, LR: 4.10e-04, Batch size: 128

Training Epochs:  75%|███████▌  | 754/1000 [00:02<00:00, 350.60it/s]

[Epoch 701/1000] Total Loss: 0.043902, Reconstruction Loss: 0.000291, LR: 1.64e-04, Batch size: 128

Training Epochs:  86%|████████▌ | 862/1000 [00:02<00:00, 350.23it/s]

[Epoch 801/1000] Total Loss: 0.017809, Reconstruction Loss: 0.000289, LR: 6.55e-05, Batch size: 128

Training Epochs:  97%|█████████▋| 970/1000 [00:02<00:00, 350.66it/s]

[Epoch 901/1000] Total Loss: 0.007113, Reconstruction Loss: 0.000297, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:02<00:00, 349.80it/s]

[Epoch 1000/1000] Total Loss: 0.002894, Reconstruction Loss: 0.000289, LR: 1.05e-05, Batch size: 128
Inferring interaction matrix W and bias vector I for cluster HSC

Training Epochs:   2%|▏         | 18/1000 [00:00<00:05, 173.32it/s]

[Epoch 1/1000] Total Loss: 66.329967, Reconstruction Loss: 0.507938, LR: 1.00e-01, Batch size: 128

Training Epochs:  13%|█▎        | 126/1000 [00:00<00:04, 177.87it/s]

[Epoch 101/1000] Total Loss: 10.176931, Reconstruction Loss: 0.009899, LR: 4.00e-02, Batch size: 128

Training Epochs:  23%|██▎       | 234/1000 [00:01<00:04, 177.97it/s]

[Epoch 201/1000] Total Loss: 4.540389, Reconstruction Loss: 0.001357, LR: 1.60e-02, Batch size: 128

Training Epochs:  32%|███▏      | 324/1000 [00:01<00:03, 178.25it/s]

[Epoch 301/1000] Total Loss: 1.749087, Reconstruction Loss: 0.000375, LR: 6.40e-03, Batch size: 128

Training Epochs:  43%|████▎     | 432/1000 [00:02<00:03, 178.21it/s]

[Epoch 401/1000] Total Loss: 0.573783, Reconstruction Loss: 0.000285, LR: 2.56e-03, Batch size: 128

Training Epochs:  52%|█████▏    | 522/1000 [00:02<00:02, 178.20it/s]

[Epoch 501/1000] Total Loss: 0.243815, Reconstruction Loss: 0.000278, LR: 1.02e-03, Batch size: 128

Training Epochs:  63%|██████▎   | 630/1000 [00:03<00:02, 177.69it/s]

[Epoch 601/1000] Total Loss: 0.095035, Reconstruction Loss: 0.000280, LR: 4.10e-04, Batch size: 128

Training Epochs:  72%|███████▏  | 720/1000 [00:04<00:01, 177.78it/s]

[Epoch 701/1000] Total Loss: 0.042646, Reconstruction Loss: 0.000282, LR: 1.64e-04, Batch size: 128

Training Epochs:  83%|████████▎ | 828/1000 [00:04<00:00, 178.19it/s]

[Epoch 801/1000] Total Loss: 0.015770, Reconstruction Loss: 0.000280, LR: 6.55e-05, Batch size: 128

Training Epochs:  94%|█████████▎| 936/1000 [00:05<00:00, 178.32it/s]

[Epoch 901/1000] Total Loss: 0.006564, Reconstruction Loss: 0.000278, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:05<00:00, 178.11it/s]

[Epoch 1000/1000] Total Loss: 0.002728, Reconstruction Loss: 0.000277, LR: 1.05e-05, Batch size: 128
Inferring interaction matrix W and bias vector I for cluster Neu

Training Epochs:   4%|▍         | 43/1000 [00:00<00:02, 428.66it/s]

[Epoch 1/1000] Total Loss: 74.491829, Reconstruction Loss: 0.433057, LR: 1.00e-01, Batch size: 32

Training Epochs:  19%|█▊        | 186/1000 [00:00<00:01, 466.45it/s]

[Epoch 101/1000] Total Loss: 12.266115, Reconstruction Loss: 0.028103, LR: 4.00e-02, Batch size: 32

Training Epochs:  28%|██▊       | 281/1000 [00:00<00:01, 470.28it/s]

[Epoch 201/1000] Total Loss: 3.847661, Reconstruction Loss: 0.003100, LR: 1.60e-02, Batch size: 32

Training Epochs:  38%|███▊      | 377/1000 [00:00<00:01, 471.26it/s]

[Epoch 301/1000] Total Loss: 1.536790, Reconstruction Loss: 0.001474, LR: 6.40e-03, Batch size: 32

Training Epochs:  47%|████▋     | 473/1000 [00:01<00:01, 472.79it/s]

[Epoch 401/1000] Total Loss: 0.621251, Reconstruction Loss: 0.001264, LR: 2.56e-03, Batch size: 32

Training Epochs:  57%|█████▋    | 569/1000 [00:01<00:00, 473.19it/s]

[Epoch 501/1000] Total Loss: 0.274787, Reconstruction Loss: 0.001268, LR: 1.02e-03, Batch size: 32

Training Epochs:  66%|██████▋   | 665/1000 [00:01<00:00, 472.87it/s]

[Epoch 601/1000] Total Loss: 0.107496, Reconstruction Loss: 0.001261, LR: 4.10e-04, Batch size: 32

Training Epochs:  76%|███████▌  | 761/1000 [00:01<00:00, 472.61it/s]

[Epoch 701/1000] Total Loss: 0.045860, Reconstruction Loss: 0.001261, LR: 1.64e-04, Batch size: 32

Training Epochs:  86%|████████▌ | 857/1000 [00:01<00:00, 472.97it/s]

[Epoch 801/1000] Total Loss: 0.019908, Reconstruction Loss: 0.001261, LR: 6.55e-05, Batch size: 32

Training Epochs:  95%|█████████▌| 953/1000 [00:02<00:00, 472.33it/s]

[Epoch 901/1000] Total Loss: 0.007731, Reconstruction Loss: 0.001261, LR: 2.62e-05, Batch size: 32

Training Epochs: 100%|██████████| 1000/1000 [00:02<00:00, 470.02it/s]

[Epoch 1000/1000] Total Loss: 0.003867, Reconstruction Loss: 0.001261, LR: 1.05e-05, Batch size: 32
Inferring interaction matrix W and bias vector I for cluster all

Training Epochs:   0%|          | 3/1000 [00:00<00:42, 23.74it/s]

[Epoch 1/1000] Total Loss: 37.163322, Reconstruction Loss: 0.238663, LR: 1.00e-01, Batch size: 128

Training Epochs:  10%|█         | 105/1000 [00:04<00:36, 24.37it/s]

[Epoch 101/1000] Total Loss: 7.501845, Reconstruction Loss: 0.004914, LR: 4.00e-02, Batch size: 128

Training Epochs:  20%|██        | 204/1000 [00:08<00:32, 24.33it/s]

[Epoch 201/1000] Total Loss: 2.499651, Reconstruction Loss: 0.001558, LR: 1.60e-02, Batch size: 128

Training Epochs:  30%|███       | 303/1000 [00:12<00:28, 24.32it/s]

[Epoch 301/1000] Total Loss: 0.952395, Reconstruction Loss: 0.000967, LR: 6.40e-03, Batch size: 128

Training Epochs:  40%|████      | 405/1000 [00:16<00:24, 24.48it/s]

[Epoch 401/1000] Total Loss: 0.367137, Reconstruction Loss: 0.000861, LR: 2.56e-03, Batch size: 128

Training Epochs:  50%|█████     | 504/1000 [00:20<00:20, 24.46it/s]

[Epoch 501/1000] Total Loss: 0.145286, Reconstruction Loss: 0.000847, LR: 1.02e-03, Batch size: 128

Training Epochs:  60%|██████    | 603/1000 [00:24<00:16, 24.39it/s]

[Epoch 601/1000] Total Loss: 0.060421, Reconstruction Loss: 0.000840, LR: 4.10e-04, Batch size: 128

Training Epochs:  70%|███████   | 705/1000 [00:28<00:12, 24.45it/s]

[Epoch 701/1000] Total Loss: 0.025516, Reconstruction Loss: 0.000842, LR: 1.64e-04, Batch size: 128

Training Epochs:  80%|████████  | 804/1000 [00:32<00:08, 24.48it/s]

[Epoch 801/1000] Total Loss: 0.010301, Reconstruction Loss: 0.000835, LR: 6.55e-05, Batch size: 128

Training Epochs:  90%|█████████ | 903/1000 [00:36<00:03, 24.44it/s]

[Epoch 901/1000] Total Loss: 0.004753, Reconstruction Loss: 0.000836, LR: 2.62e-05, Batch size: 128

Training Epochs: 100%|██████████| 1000/1000 [00:40<00:00, 24.49it/s]

[Epoch 1000/1000] Total Loss: 0.003123, Reconstruction Loss: 0.000836, LR: 1.05e-05, Batch size: 128
Scaffold-constrained network inference complete.

1.7 Save / Load Model

Models can be serialised to an HDF5 file for later use. This is especially

useful for large datasets where re-inference is expensive.

[9]:

# Save the fitted model
MODEL_FILE = 'model.h5sch'
sch.tl.save_model(adata, MODEL_FILE, overwrite=True)
print(f"Model saved to '{MODEL_FILE}'")

Model saved to 'model.h5sch'  |  clusters=['Bas', 'Ery', 'GMP-like', 'HSC', 'MEP-like', 'Meg', 'Mon', 'Neu', 'all']  |  genes=1728
Model saved to 'model.h5sch'

[10]:

# Load the model back into a fresh AnnData object.
# If adata_loaded has more genes than the saved model (e.g. the full dataset
# before NaN filtering), load_model subsets it in-place to the model gene set.
adata_loaded = sc.read_h5ad(DATA_PATH + DATASET_FILE)
adata_loaded = sch.tl.load_model(adata_loaded, MODEL_FILE)
print("Model loaded successfully.")
print(adata_loaded)

Model loaded from 'model.h5sch'  |  clusters=['Bas', 'Ery', 'GMP-like', 'HSC', 'MEP-like', 'Meg', 'Mon', 'Neu', 'all']  |  genes=1728
Model loaded successfully.
AnnData object with n_obs × n_vars = 1947 × 1728
    obs: 'batch', 'time', 'cell_type', 'nGenes', 'nCounts', 'pMito', 'pass_basic_filter', 'new_Size_Factor', 'initial_new_cell_size', 'total_Size_Factor', 'initial_total_cell_size', 'spliced_Size_Factor', 'initial_spliced_cell_size', 'unspliced_Size_Factor', 'initial_unspliced_cell_size', 'Size_Factor', 'initial_cell_size', 'ntr', 'cell_cycle_phase', 'leiden', 'control_point_pca', 'inlier_prob_pca', 'obs_vf_angle_pca', 'pca_ddhodge_div', 'pca_ddhodge_potential', 'acceleration_pca', 'curvature_pca', 'n_counts', 'mt_frac', 'jacobian_det_pca', 'manual_selection', 'divergence_pca', 'curv_leiden', 'curv_louvain', 'SPI1->GATA1_jacobian', 'jacobian', 'umap_ori_leiden', 'umap_ori_louvain', 'umap_ddhodge_div', 'umap_ddhodge_potential', 'curl_umap', 'divergence_umap', 'acceleration_umap', 'control_point_umap_ori', 'inlier_prob_umap_ori', 'obs_vf_angle_umap_ori', 'curvature_umap_ori'
    var: 'gene_name', 'gene_id', 'nCells', 'nCounts', 'pass_basic_filter', 'use_for_pca', 'frac', 'ntr', 'time_3_alpha', 'time_3_beta', 'time_3_gamma', 'time_3_half_life', 'time_3_alpha_b', 'time_3_alpha_r2', 'time_3_gamma_b', 'time_3_gamma_r2', 'time_3_gamma_logLL', 'time_3_delta_b', 'time_3_delta_r2', 'time_3_bs', 'time_3_bf', 'time_3_uu0', 'time_3_ul0', 'time_3_su0', 'time_3_sl0', 'time_3_U0', 'time_3_S0', 'time_3_total0', 'time_3_beta_k', 'time_3_gamma_k', 'time_5_alpha', 'time_5_beta', 'time_5_gamma', 'time_5_half_life', 'time_5_alpha_b', 'time_5_alpha_r2', 'time_5_gamma_b', 'time_5_gamma_r2', 'time_5_gamma_logLL', 'time_5_bs', 'time_5_bf', 'time_5_uu0', 'time_5_ul0', 'time_5_su0', 'time_5_sl0', 'time_5_U0', 'time_5_S0', 'time_5_total0', 'time_5_beta_k', 'time_5_gamma_k', 'use_for_dynamics', 'gamma', 'gamma_r2', 'use_for_transition', 'gamma_k', 'gamma_b', 'I_Bas', 'I_Ery', 'I_GMP-like', 'I_HSC', 'I_MEP-like', 'I_Meg', 'I_Mon', 'I_Neu', 'I_all', 'scHopfield_used', 'sigmoid_exponent', 'sigmoid_mse', 'sigmoid_offset', 'sigmoid_threshold'
    uns: 'PCs', 'VecFld_pca', 'VecFld_umap', 'X_umap_neighbors', 'cell_phase_genes', 'cell_type_colors', 'dynamics', 'explained_variance_ratio_', 'feature_selection', 'grid_velocity_pca', 'grid_velocity_umap', 'grid_velocity_umap_ori_perturbation', 'grid_velocity_umap_test', 'jacobian_pca', 'leiden', 'neighbors', 'pca_mean', 'pp', 'response', 'scHopfield'
    obsm: 'X', 'X_pca', 'X_pca_SparseVFC', 'X_umap', 'X_umap_SparseVFC', 'X_umap_ori_perturbation', 'X_umap_test', 'acceleration_pca', 'acceleration_umap', 'cell_cycle_scores', 'curvature_pca', 'curvature_umap', 'j_delta_x_perturbation', 'velocity_pca', 'velocity_pca_SparseVFC', 'velocity_umap', 'velocity_umap_SparseVFC', 'velocity_umap_ori_perturbation', 'velocity_umap_test'
    layers: 'M_n', 'M_nn', 'M_t', 'M_tn', 'M_tt', 'X_new', 'X_total', 'velocity_alpha_minus_gamma_s'
    obsp: 'X_umap_connectivities', 'X_umap_distances', 'connectivities', 'cosine_transition_matrix', 'distances', 'fp_transition_rate', 'moments_con', 'pca_ddhodge', 'perturbation_transition_matrix', 'umap_ddhodge'
    varp: 'W_Bas', 'W_Ery', 'W_GMP-like', 'W_HSC', 'W_MEP-like', 'W_Meg', 'W_Mon', 'W_Neu', 'W_all'