Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning (ME-EQL)

Agent-based modeling (ABM) is a powerful tool for understanding self-organizing biological systems, but it is computationally intensive and often not analytically tractable. Equation learning (EQL) methods can derive continuum models from ABM data, but they typically require extensive simulations for each parameter set, raising concerns about generalizability. In this work, we extend EQL to Multi-experiment equation learning (ME-EQL) by introducing two methods: one-at-a-time ME-EQL (OAT ME-EQL), which learns individual models for each parameter set and connects them via interpolation, and embedded structure ME-EQL (ES ME-EQL), which builds a unified model library across parameters. We demonstrate these methods using a birth--death mean-field model and an on-lattice agent-based model of birth, death, and migration with spatial structure. Our results show that both methods significantly reduce the relative error in recovering parameters from agent-based simulations, with OAT ME-EQL offering better generalizability across parameter space. Our findings highlight the potential of equation learning from multiple experiments to enhance the generalizability and interpretability of learned models for complex biological systems.

Statistical and Topological Summaries Aid Disease Detection for Segmented Retinal Vascular Images

Disease complications can alter vascular network morphology and disrupt tissue functioning. Diabetic retinopathy, for example, is a complication of type 1 and 2 diabetus mellitus that can cause blindness. Microvascular diseases are assessed by visual inspection of retinal images, but this can be challenging when diseases exhibit silent symptoms or patients cannot attend in-person meetings. We examine the performance of machine learning algorithms in detecting microvascular disease when trained on either statistical or topological summaries of segmented retinal vascular images. We apply our methods to four publicly-available datasets and find that the fractal dimension performs best for high resolution images. By contrast, we find that topological descriptor vectors quantifying the number of loops in the data achieve the highest accuracy for low resolution images. Further analysis, using the topological approach, reveals that microvascular disease may alter morphology by reducing the number of loops in the retinal vasculature. Our work provides preliminary guidelines on which methods are most appropriate for assessing disease in high and low resolution images. In the longer term, these methods could be incorporated into automated disease assessment tools.