Operator learning for models of tear film breakup

TL;DR

This work tackles the computational burden of inferring tear film thickness $h(t)$ and osmolarity $c(t)$ from fluorescence time series $I(t)$ by training neural operators on simulated TF dynamics. It compares three operator-learning architectures—FFN, Dense-PCA, and Dense-PCAX—across two mathematical models (a 1D PDE and a reduced ODE) and evaluates them on synthetic and experimental data. Findings indicate that all approaches achieve roughly 1–2 digit accuracy on synthetic data, with model-specific differences observed on experimental data, underscoring identifiability limits and the influence of the chosen physical model. The study highlights the potential of fast, data-driven, real-time inference for tear film dynamics and points to physics-informed extensions to further improve generalization and robustness.

Abstract

Tear film (TF) breakup is a key driver of understanding dry eye disease, yet estimating TF thickness and osmolarity from fluorescence (FL) imaging typically requires solving computationally expensive inverse problems. We propose an operator learning framework that replaces traditional inverse solvers with neural operators trained on simulated TF dynamics. This approach offers a scalable path toward rapid, data-driven analysis of tear film dynamics.

Figures (9)

• Figure 1: Mechanisms in the tear film at a later time $t>0$. Evaporation occurs at the top, osmosis at the bottom; $\Gamma$ represents the surfactant concentration, and $h$ represents the tear film thickness.
• Figure 2: Relative RMSE for synthetic testing of ML models trained by ODE data. Top to bottom: FFN, Dense-PCA, Dense-PCAX.
• Figure 3: Two-dimensional histograms showing counts of predictions by ODE-trained learners on the synthetic ODE testing data. First row: predictions of final thickness. Second row: predictions of final osmolarity.
• Figure 4: Relative RMSE for synthetic self-consistency testing of ML models trained by PDE data. Top to bottom: FFN, Dense-PCA, Dense-PCAX.
• Figure 5: Two-dimensional histograms showing counts of predictions by PDE-trained learners on the synthetic PDE testing data. First row: Predictions of final thickness. Second row: Predictions of final osmolarity.