identifiability analysis

This study addresses the structural identifiability of model parameters in partially observed stochastic processes, focusing on parameter uniqueness from two data modalities: single-particle trajectories and population density measurements. For spatiotemporal stochastic dynamics, the authors employ individual-based stochastic models to analyze trajectory data and partial differential equation (PDE)-based density evolution models for population-level observations. They innovatively extend differential algebraic methods to PDE models of stochastic processes and introduce a novel framework based on characteristic equations to construct Taylor expansions that explicitly account for the influence of initial conditions on identifiability. Their results demonstrate that parameters are globally identifiable from trajectory data, whereas only local identifiability can be achieved using density data alone, thereby highlighting the critical role of initial condition information in structural identifiability analysis.

This study addresses the structural identifiability determination problem for compartmental models—such as those used in epidemiology and tumor dynamics—where existing methods rely heavily on numerical simulation and lack generality. We propose a novel theoretical framework integrating differential algebra and graph theory to directly infer structural identifiability from model topology alone. For linear compartmental models, we develop an automated reparameterization algorithm that systematically resolves unidentifiability. Our work unifies identifiability criteria across diverse application domains and establishes the first end-to-end structural identifiability analysis paradigm—spanning model formulation, identifiability assessment, and structural reconstruction. This significantly enhances the reliability and interpretability of complex dynamical system modeling. Moreover, the framework lays the theoretical foundation for extending identifiability analysis to nonlinear systems and for joint data–model identifiability approaches.

This study addresses parameter identifiability—a critical challenge in systems biology modeling—encompassing structural and practical identifiability, parameter interdependence, and reliability of extrapolative predictions. We propose embedding identifiability analysis throughout the entire modeling workflow, integrating global sensitivity analysis, simulation-based computational assessments (e.g., profile likelihood, Monte Carlo sampling), and output observability diagnostics to systematically quantify parameter uncertainty. A key innovation lies in emphasizing the synergistic roles of optimal experimental design, incorporation of prior knowledge, and model reduction in enhancing identifiability. Results demonstrate that weakly identifiable parameters severely compromise extrapolative predictive performance; our framework effectively pinpoints bottleneck parameters and informs targeted data acquisition strategies, thereby enabling the construction of biologically predictive models with robust uncertainty quantification.

Structural identifiability analysis lacks rigorous theoretical foundations and computational tools for partially observable, near-linear stochastic differential equation (SDE) models. Method: This paper introduces the first formal definition of structural identifiability for SDEs and establishes a moment-based analytical framework grounded in the dynamics of statistical moments. It derives observable moment constraints to assess exact identifiability of parameter combinations, characterizes the fundamental role of initial conditions, and extends the differential algebra approach to stochastic systems—enabling analysis of two- and higher-dimensional linear and near-linear SDEs. Symbolic computation and algebraic elimination are employed to verify identifiability. Contribution/Results: The work fills a critical theoretical gap in stochastic system identifiability, providing the first general, computationally tractable framework for structural identifiability analysis of SDEs. It yields explicit characterizations of identifiable parameter subsets across multiple model classes, thereby enabling principled stochastic modeling and parameter inference in domains such as systems biology.

This work addresses the structural identifiability of parameters in stochastic differential equation (SDE) models under multiple interventions—i.e., whether SDE parameters can be uniquely recovered from samples of post-intervention stationary distributions. Theoretically, we establish the first uniqueness guarantee for SDE parameter recovery under multi-intervention settings; for linear SDEs, we derive a tight lower bound on the minimum number of required interventions; for weak-noise nonlinear SDEs, we obtain an upper bound on identifiability. Methodologically, we propose a parametric framework featuring learnable activation functions, integrating intervention modeling, stationary distribution analysis, and weak-noise asymptotic theory. Experiments on synthetic data demonstrate that our approach accurately recovers ground-truth parameters, and the theory-guided learnable architecture significantly improves both estimation accuracy and robustness.

This work addresses the structural identifiability of ordinary differential equation (ODE)-based mechanistic models—specifically, whether model parameters can be uniquely determined from ideal observational data—and proposes a unified symbolic analysis framework implemented in Julia. Built upon the StructuralIdentifiability.jl package, the framework integrates symbolic computation with parameter-output mapping analysis to support assessments of local and global identifiability, observability, and extraction of identifiable parameter combinations. As the first fully reproducible tutorial within the SciML ecosystem, it not only enables model reparameterization and informs experimental design but also demonstrates its efficacy across seven representative case studies spanning epidemiology, pharmacokinetics, and other domains, thereby offering both a practical workflow and theoretical foundation for modeling complex dynamical systems.

This study addresses the long-standing reliance of Boolean factor model identifiability on the pure node assumption, which severely restricts the applicability of interpretable models. By leveraging Hasse diagrams to reformulate the identifiability problem as a graph isomorphism task and integrating Boolean satisfiability (SAT) algorithms, this work establishes necessary and sufficient conditions for identifiability without requiring pure nodes, further extending these results to probabilistic settings. The proposed framework transcends traditional pure node constraints by introducing novel graphical and algebraic identifiability theories alongside efficient verification tools. Ultimately, this research substantially broadens the class of interpretable Boolean factor models and equips practitioners with concrete methodologies for assessing identifiability in practice.

This work addresses the lack of a clear definition of representation stability in existing representation learning methods, particularly the conflation of statistical consistency and structural alignment. It formally introduces, for the first time, the notions of statistical identifiability and structural identifiability, and proposes a model-agnostic ε-approximate identifiability framework that accommodates nonlinear decoders—such as those in masked autoencoders (MAE) and supervised models. The framework extends identifiability theory to intermediate-layer representations and integrates ICA-based post-processing to achieve effective disentanglement. Experiments demonstrate state-of-the-art disentanglement performance on synthetic data and successful separation of biological variation from batch effects in foundation models for cellular microscopy, substantially improving downstream generalization.

This study addresses the problem of global parameter identifiability for linear ordinary differential equation models in which parameters depend linearly on state variables and rationally on other parameters. By reformulating identifiability as the injectivity of the corresponding input–output map and leveraging tools from algebraic geometry and differential algebra, the authors establish—for the first time—that this identifiability problem is NP-hard. This result resolves a longstanding gap in the computational complexity theory of identifiability for this important class of models, providing a rigorous lower bound on its intrinsic computational difficulty. Consequently, it offers a solid theoretical foundation for the design and performance evaluation of future algorithms aimed at tackling parameter identifiability in such systems.

This study addresses the challenge of parameter inference in ordinary differential equation models arising from structural non-identifiability. It introduces, for the first time, an explicit integration of structural identifiability analysis into the design of Markov chain Monte Carlo (MCMC) algorithms, proposing two novel sampling strategies: one constructs efficient proposals both within and orthogonal to the non-identifiable manifold, while the other performs inference in a low-dimensional space of identifiable parameter combinations and subsequently reconstructs the full parameter vector. By combining geometric MCMC with pseudo-marginal MCMC techniques, the method establishes a Bayesian inference framework tailored to equivalence solution manifolds. This approach significantly enhances sampling efficiency and convergence speed compared to standard MCMC methods, while preserving posterior correctness and chain ergodicity.