ArticlePhysical review letters2014
Model reduction by manifold boundaries.
Article in Physical review letters, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 34 papers.
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Who cites it
34 citing papers in PubMed.
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- Unifying theories in high-dimensional biophysics: approaches, challenges and opportunities.NPJ systems biology and applications · 2026Article
- Format-Preserving Reduction of Canonical Nonlinear Models.Bulletin of mathematical biology · 2026Article
- Towards practical radiopharmaceutical treatment planning: a review of dosimetry simplification techniques.Theranostics · 2026Review
- Scarce data, noisy inferences and overfitting: the hidden flaws in ecological dynamics modelling.Journal of the Royal Society, Interface · 2025Article
- Exploring Emergent Properties in Enzymatic Reaction Networks: Design and Control of Dynamic Functional Systems.Chemical reviews · 2024Review
- Mathematical Modeling of Photo- and Thermomorphogenesis in Plants.Methods in molecular biology (Clifton, N.J.) · 2024Article
- Predictive power of non-identifiable models.Scientific reports · 2023Article
- Mechanobiology as a tool for addressing the genotype-to-phenotype problem in microbiology.Biophysics reviews · 2023Review
- Minimal frustration underlies the usefulness of incomplete regulatory network models in biology.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Information geometry for multiparameter models: new perspectives on the origin of simplicity.Reports on progress in physics. Physical Society (Great Britain) · 2022Review
- On the parameter combinations that matter and on those that do not: data-driven studies of parameter (non)identifiability.PNAS nexus · 2022Article
- Human inference reflects a normative balance of complexity and accuracy.Nature human behaviour · 2022Article
- Ion channel model reduction using manifold boundaries.Journal of the Royal Society, Interface · 2022Article
- Discovering sparse control strategies in neural activity.PLoS computational biology · 2022Article
- Parameter estimation and uncertainty quantification using information geometry.Journal of the Royal Society, Interface · 2022Review
- GAMES: A Dynamic Model Development Workflow for Rigorous Characterization of Synthetic Genetic Systems.ACS synthetic biology · 2022Article
- Boolean modelling in plant biology.Quantitative plant biology · 2022Review
- Causal Geometry.Entropy (Basel, Switzerland) · 2020Article
Corrections and comments
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Authors and funding
2 authors.
Funding
Abstract
Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce "black boxes" disconnected from the microscopic physics. We propose a new approach by translating the model reduction problem for an arbitrary statistical model into a geometric problem of constructing a low-dimensional, submanifold approximation to a high-dimensional manifold. When models are overly complex, we use the observation that the model manifold is bounded with a hierarchy of widths and propose using the boundaries as submanifold approximations. We refer to this approach as the manifold boundary approximation method. We apply this method to several models, including a sum of exponentials, a dynamical systems model of protein signaling, and a generalized Ising model. By focusing on parameters rather than physical degrees of freedom, the approach unifies many other model reduction techniques, such as singular limits, equilibrium approximations, and the renormalization group, while expanding the domain of tractable models. The method produces a series of approximations that decrease the complexity of the model and reveal how microscopic parameters are systematically "compressed" into a few macroscopic degrees of freedom, effectively building a bridge between the microscopic and the macroscopic descriptions.
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