NoLimits.jl: Julia package expands nonlinear mixed-effects modeling with ML and flexible inference

NoLimits.jl, introduced by Manuel Huth, Jonas Arruda, and colleagues, is an open-source Julia package that addresses a critical gap in nonlinear mixed-effects (NLME) modeling. Existing open-source tools often restrict users to a narrow set of model structures, inference methods, or machine-learning integrations. NoLimits.jl breaks these limits with a macro-based modeling language that allows researchers to compose observation and latent‑state models from diverse building blocks: ordinary differential equations, Markov models, and neural networks. It supports flexible, covariate‑dependent observation and random‑effects distributions, and provides a unified interface for frequentist inference through Laplace approximation and stochastic expectation maximization, as well as Bayesian inference via Markov chain Monte Carlo. This design lets data scientists and statisticians seamlessly combine traditional statistical modeling with modern differentiable machine learning.

The package’s true strength lies in its composability and extensibility. Three case studies demonstrate its workflows, including the integration of differentiable ML components and the data‑driven estimation of random‑effects distributions using normalizing flows. By enabling normalizing flows within an NLME framework, NoLimits.jl allows complex, non‑Gaussian random effects to be learned from data rather than assumed. This capability, combined with support for ODE‑based dynamical systems and neural‑network submodels, makes the package suitable for pharmacokinetics, disease progression modeling, and any domain requiring longitudinal data analysis with hierarchical structure. At 74 pages (52 main), the preprint provides thorough technical documentation. NoLimits.jl is positioned to become a foundational tool for researchers who need both flexibility and rigor in mixed‑effects modeling.