Hybridizing Data Science and Mechanistic Models for Biological Systems

Biological systems exhibit complex, multiscale dynamics driven by heterogeneity, stochasticity, and partial observability, thereby posing fundamental challenges for both mechanistic modeling and purely data-driven approaches. In this talk, I present several frameworks for hybrid modeling of biological data that integrate topological data analysis, equation learning, and distributional inverse problems for parameter estimation in dynamical systems. Topological summaries distill complex spatiotemporal structure into geometry-aware features that make agent-based model comparison, parameter estimation, and uncertainty quantification feasible through likelihood-free methods such as Approximate Bayesian Computation. Equation learning methods enable discovery of governing ODE and PDE models from noisy data and stochastic simulations, and I will introduce the concept of multi-experiment equation learning to enforce structural invariance and improve generalization across parameter space. To rigorously quantify biological heterogeneity and uncertainty, I highlight distributional inverse problem formulations based on the Prohorov metric framework, which shifts inference from point estimates to parameter distributions consistent with aggregate data. I will illustrate these different approaches for hybridizing data science into model discovery, selection, and uncertainty quantification through applications to collective cell motion, angiogenesis, reaction-diffusion systems, tumor growth and infectious disease modeling. For more information see: 1) Ciocanel, Maria-Veronica, et al. "Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning for biological systems." PLOS Computational Biology 22.4 (2026): e1014161. https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1014161&type=printable 2) Lagergren, John H., et al. "Biologically-informed neural networks guide mechanistic modeling from sparse experimental data." PLoS computational biology 16.12 (2020): e1008462. https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1008462&type=printable 3) Nardini, John T., et al. "Learning differential equation models from stochastic agent-based model simulations." Journal of the Royal Society Interface 18.176 (2021). https://royalsocietypublishing.org/rsif/article/18/176/20200987/89891 4) Hamilton, Franz, Alun L. Lloyd, and Kevin B. Flores. "Hybrid modeling and prediction of dynamical systems." PLoS computational biology 13.7 (2017): e1005655. https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1005655&type=printable *Contents* 00:00 - Introduction 06:04 - Hybridizing Data Science and Mechanistic Models for Biological Systems 35:00 - Discussion and Questions For a copy of the slides for this video visit: https://drive.google.com/file/d/1NIQryaM_0sZyzuSK2gzrDDLTrmYVPRWS/view?usp=sharing Moderated by: James A. Glazier If you found this video useful, please check out our other videos on computational modeling, infection and immunology: https://youtube.com/playlist?list=PLiEtieOeWbMKh9VcQoinSwODcSZKMTGat Please consider joining our IMAG/MSM WG on Multiscale Modeling and Viral Pandemics: https://www.imagwiki.nibib.nih.gov/content/msm-viral-pandemics-meetings Please also consider joining the Global Alliance for Immune Prediction and Intervention: http://glimprint.org/