rigorous population dynamics

This study investigates the stationary distribution and stability of stochastic differential equation systems with multimodal uncertain parameters exhibiting superposition effects, using the nonlinear Rosenzweig–MacArthur predator–prey model as a case study. For the first time, multimodal mixture-distributed parameters are incorporated into the stationary analysis of stochastic dynamical systems. System stability is quantified through the eigenvalue distribution of the Jacobian matrix, and posterior stationary density estimates are obtained via the Monte Carlo method proposed by Hoegele (2026). The results reveal that under multimodal parameter uncertainty, the system exhibits a multimodal stationary distribution, accurately delineating regions of stability. This demonstrates the effectiveness and novelty of the proposed framework for uncertainty quantification in complex ecological dynamics.

This study addresses the challenge of generating high-fidelity synthetic populations in the absence of microdata. We propose a novel constraint programming–based generative framework that directly encodes macro-level statistical constraints—such as cross-tabulated distributions of age, education, and occupation—as well as structural relational constraints, bypassing conventional sampling-based inference. This ensures strict consistency of individual attributes and exact global statistical alignment with target distributions. Our approach innovatively integrates constraint solving with aggregate data analysis and incorporates a large language model interface to enhance semantic modeling of categorical attributes. Empirical evaluation on official census data demonstrates that the framework robustly reproduces multidimensional statistical distributions, quantifies bias propagation into downstream policy simulations, and significantly improves reproducibility and decision reliability in social behavior modeling, market analysis, and policy evaluation.

This work addresses the lack of a unified computational framework for analyzing non-ergodicity, modeling heavy-tailed dynamics, and studying decision-making under uncertainty in stochastic processes. To this end, we introduce an open-source Python library that, for the first time, integrates non-ergodicity diagnostics, simulation of heavy-tailed processes—such as multiplicative Lévy growth and memory-dependent mean-reverting dynamics—and agent-based experimentation within a single platform. Built upon the scientific Python ecosystem (NumPy/SciPy), the library supports end-to-end workflows including stochastic process definition, simulation, parameter inference, and partial solution of stochastic differential equations. Through several reproducible examples—ranging from heavy-tailed ensemble diffusion to pre-asymptotic fluctuation analysis—it substantially reduces boilerplate code and enhances both reproducibility and development efficiency in the study of time-averaged behaviors of complex stochastic systems.

This work addresses the lack of efficient, open-source tools supporting Biochemical Systems Theory (BST) models. We propose and implement an open-source Julia package that, for the first time in the Julia ecosystem, provides full support for declarative modeling using S-system power-law formalism and integrates high-performance differential equation solvers from SciML. The tool enables dynamic simulation, steady-state computation, and global sensitivity analyses via Morris and Sobol methods, significantly enhancing the flexibility and efficiency of BST model construction and analysis. Experimental validation on representative biochemical networks demonstrates the framework’s effectiveness, scalability, and practical utility in systems biology.

Purely data-driven Bayesian modeling often fails to capture the underlying mechanisms of complex systems due to insufficient mechanistic guidance. Method: This paper proposes a novel Bayesian model calibration framework that systematically integrates non-empirical information—such as expert knowledge, scientific theories, and qualitative observations—as formalized prior constraints. Leveraging prior encoding, qualitative constraint modeling, and multi-source information fusion, these constraints are embedded directly into the Bayesian inference pipeline, enabling synergistic constraint from both theoretical understanding and empirical data. Contribution/Results: Compared with conventional approaches, the framework significantly expands the class of calibratable models. Case studies in ecology, biology, and medicine demonstrate improved dynamic plausibility, higher predictive confidence, and greater consistency with established scientific knowledge. By bridging theory and data, the method advances Bayesian modeling beyond mere “data fitting” toward “mechanistically credible” inference.

This study addresses the insufficient output representation of agent-based models (ABMs). To this end, we propose a dual-axis analytical framework integrating temporal structure and distributional geometry. Methodologically, we first couple ε-machines from computational mechanics with score-based generative diffusion models, jointly leveraging Kolmogorov complexity analysis and score matching to simultaneously model ABM time-series predictability and high-dimensional state-distribution morphology. Theoretically, we provide formal definitions and derive key propositions; empirically, we validate the framework on a geriatric care ABM dataset, demonstrating its effectiveness in behavioral interpretation, long-horizon forecasting, and distributional synthesis. Our core contribution lies in a cross-domain, dual-dimensional representation paradigm—bridging computational mechanics and generative modeling—which overcomes the limitations of conventional univariate temporal or static distribution analyses. This advances ABM interpretability and enables controllable, physics-informed generative modeling.

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 limitations of traditional agent-based economic models, which rely on Monte Carlo simulations lacking formal statistical guarantees and thus struggle to yield rigorous quantitative conclusions. For the first time, the authors systematically integrate Statistical Model Checking (SMC)—a method offering formal statistical assurances—into Fagiolo and Dosi’s island endogenous growth agent-based model. Leveraging the MultiVeStA platform, they automate the analysis of the exploration–exploitation trade-off in technological search. Through Welch’s t-tests for parameter sensitivity analysis, they not only successfully reproduce key stylized facts from the original model and confirm the optimality of moderate exploration rates, but also uncover statistically significant differences in six out of seven parameter comparisons, revealing a saturation effect of knowledge locality. This approach enables reproducible, confidence-interval-equipped quantitative evaluation.

This work addresses the lack of rigorous error bounds in physics-informed neural networks (PINNs), which hinders their reliability for trustworthy scientific computing. The authors propose a novel “learn-and-verify” framework that, for the first time, endows PINNs with mathematically provable a posteriori error bounds. By integrating a newly designed doubly smoothed maximum (DSM) loss function with interval arithmetic, the method generates machine-verifiable certificates that rigorously bound the neural network approximation of solutions to differential equations. The approach successfully constructs sharp, guaranteed enclosures around the true solutions of nonlinear ordinary differential equations featuring time-varying coefficients and finite-time blow-up, thereby demonstrating its effectiveness and robustness in delivering certified, reliable results.

This work proposes a unified Bayesian calibration framework to address the lack of reliable and consistent calibration methods for computationally expensive and data-scarce scenarios. The framework uniquely supports both single-output and multi-output complex models within a coherent formulation and is accompanied by ACBICI, a modular open-source Python library. By integrating uncertainty quantification with Bayesian inference, the approach balances usability and extensibility, establishing a closed loop among theory, implementation, and practical application. The study delivers standardized calibration guidelines tailored to real-world engineering challenges and enhances reproducibility and deployment through its open-source toolkit, significantly improving the reliability and accessibility of calibrating complex scientific and engineering models.