ArXiv

NoLimits.jl: Flexible and Composable Nonlinear Mixed-Effects Modeling in Julia

2026-06-23 · 11:04 UTC ·Manuel Huth, Jonas Arruda, Nina Schmid... ·1 min read
Authors
Manuel Huth, Jonas Arruda, Nina Schmid...
Categories
stat.CO, stat.ML
arXiv
https://arxiv.org/abs/2606.24427v1
PDF
https://arxiv.org/pdf/2606.24427v1

Brief

NoLimits.jl delivers a composable DSL for nonlinear mixed-effects modeling that composes ODEs, Markov models, and neural networks, and allows covariate-dependent observation and random-effects distributions. It provides a unified interface to Laplace approximation, stochastic EM, and Bayesian MCMC, and demonstrates three case studies — including differentiable ML and normalizing-flow random-effects — to extend capabilities beyond existing open-source tools.

Why it matters

NoLimits.jl (Manuel Huth et al., arXiv 2026-06-23) is an open-source Julia package that provides a macro-based modeling language to build nonlinear mixed-effects models from ODEs, Markov models, and neural networks (paper: 74 pages, 9 figures).

Key details

  • The package supports flexible, covariate-dependent observation and random-effects distributions and unifies frequentist and Bayesian inference via Laplace approximation, stochastic expectation-maximization, and Markov chain Monte Carlo, with support for automatic differentiation and differentiable ML components.
  • The authors demonstrate three case studies, including integration of neural-network components and data-driven estimation of random-effects distributions using normalizing flows, expanding the set of models estimable within a single open-source framework.
Source evidence

Abstract

Nonlinear mixed-effects models are widely used to analyze longitudinal data, but existing open-source software often supports only a limited subset of the model structures, inference methods, machine-learning components, automatic differentiation techniques, and random-effects distributions required in modern applications. We introduce NoLimits.jl, an open-source Julia package for flexible and composable nonlinear mixed-effects modeling. Its macro-based modeling language enables observation and latent-state models to be constructed from diverse building blocks, including ordinary differential equations, Markov models, and neural networks. NoLimits.jl supports flexible, covariate-dependent observation and random-effects distributions and provides a unified interface to frequentist inference through Laplace approximation, stochastic expectation maximization, and Bayesian Markov chain Monte Carlo methods. We demonstrate the package on three case studies showcasing its workflows, integration of differentiable machine-learning components, and data-driven estimation of random-effects distributions using normalizing flows. Together, these capabilities substantially expand the range of nonlinear mixed-effects models that can be specified, estimated, and compared within a single open-source framework.

Comment: 74 pages (52 main), 9 Figures (6 main)