Mathematical modeling of celiac disease

Q: What does this research mean for the field?

Imputation techniques, recurrent neural networks, and Sparse-Regression Physics-Informed Neural Networks (SR-PINNs) exhibit significant limitations and struggle to accurately model biological processes when applied to the small, sparse, and stiff longitudinal data typical of celiac disease. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Kailey Reese Walker

doi:10.25365/thesis.81085

January 1, 2026Open Access

Mathematical modeling of celiac disease

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Key Points

The aim is to develop personalized mathematical models for celiac disease based on patient data to improve treatment strategies.
Utilized multiple imputation and recurrent neural networks to address missing data and irregular sampling.
Developed an ordinary differential equations (ODE) model to describe patient responses to gluten exposure and gluten-free diet.
Assessed Sparse-Regression Physics-Informed Neural Networks (SR-PINNs) for recovering underlying equations from synthetic biological time series data.
Imputation and neural network techniques showed significant limitations with small longitudinal data.
SR-PINNs performed well on benchmark problems but struggled with realistic stiff equations for modeling biological processes.
The findings highlight challenges of applying advanced methods to data-sparse biological issues.

Implication

Investigates mathematical models for personalized celiac disease treatment, suggesting new insights into data challenges.

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Cite This Study

Kailey Reese Walker (2026) studied this question.

synapsesocial.com/papers/6a1fc56bdee9eb8c0dce6cd6 https://doi.org/10.25365/thesis.81085

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Mathematical modeling of celiac disease

Key Points

Implication

Abstract

Discussion

Cite This Study

Mathematical modeling of celiac disease

Key Points

Implication

Abstract

Discussion

Cite This Study

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