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

arXiv: https://arxiv.org/abs/2606.24427 · HTML: https://mlsanity.com/paper/2606.24427/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 99 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 3 of 3)

- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Extending the saemix package for R to fit non Gaussian outcomes](https://mlsanity.com/paper/2603.03154/) (2026)
- [Fitting Large Nonlinear Mixed Effects Models Using Variational Expectation Maximization](https://mlsanity.com/paper/2604.26160/) (2026)

## Abstract (arXiv)

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.