Neural-ESO’s dual-pathway architecture (predictive + disturbance-rejection) will synchronize with persistent Brownian motions in confluent tissues under junctional tension fluctuations, with cross-correlation > 0.7 in the 0.1–1 Hz band when trained on active foam model trajectories.

A Neural Extended State Observer (Neural-ESO) with dual-pathway architecture — one subnetwork trained to predict tissue displacement fields from junctional tension time-series, the other trained as a disturbance-rejection/residual estimator — when trained exclusively on simulated active foam model (AFM) trajectories (vertex-model or Voronoi-based confluent tissue simulations with stochastic junctional tension), will produce output velocity/displacement predictions whose cross-correlation with held-out real (or independently simulated) confluent epithelial tissue motion trajectories exceeds r = 0.7 in the 0.1–1 Hz frequency band, computed via band-limited cross-correlation or coherence analysis on cell-centroid velocity time-series, across ≥5 independent tissue samples/simulation replicates with 95% CI lower bound > 0.7. The claim is falsifiable: if mean cross-correlation in-band is ≤0.7, or if the effect is fully attributable to a single-pathway (predictive-only or disturbance-only) ablation achieving statistically indistinguishable performance, the hypothesis is disproven.

Minimum viable test: (1) Generate/obtain 20 active foam model simulation trajectories (vertex model, ~500 cells, 20 min duration, dt=0.05s) for training; (2) Train Neural-ESO dual-pathway model on 15 trajectories, validate on 5 held-out simulation trajectories; (3) Obtain 5 independent real epithelial monolayer imaging datasets (or 5 independently-parameterized simulations if real data unavailable) as generalization test set; (4) Run trained model on real/held-out data without fine-tuning; (5) Compute band-limited (0.1–1 Hz) cross-correlation between model output and ground-truth centroid velocity fields; (6) Run ablations (predictive-only, disturbance-only, random-architecture baseline); (7) Statistical test (paired bootstrap, n=1000) comparing full model vs. ablations and vs. threshold 0.7.

# Dual-pathway Neural-ESO
class NeuralESO(nn.Module):
    def __init__(self):
        self.predictive_pathway = TransformerSeq2Seq(input=tension_series, output=displacement_pred)
        self.disturbance_pathway = GRUResidualEstimator(input=[tension_series, prediction_error_history])

    def forward(self, tension_seq, past_error=None):
        pred = self.predictive_pathway(tension_seq)
        disturbance_est = self.disturbance_pathway(tension_seq, past_error)
        return pred + disturbance_est  # combined state estimate

# Training loop
for traj in simulation_trajectories:
    tension, true_velocity = extract_features(traj)
    pred_velocity = model(tension)
    loss = mse(pred_velocity, true_velocity) + reg_term
    backprop_and_update()

# Evaluation
for test_traj in held_out_or_real_data:
    pred = model(test_traj.tension)
    coherence = welch_coherence(pred, test_traj.true_velocity, band=(0.1,1.0))
    record(coherence)

# Ablation
model_pred_only = disable(disturbance_pathway)
model_dist_only = disable(predictive_pathway)
compare_statistically([full_model, model_pred_only, model_dist_only])