NoLimits.jl provides a unified, open-source framework for specifying, estimating, and diagnosing hierarchical models of longitudinal data. It is designed for life-science applications — from pharmacokinetics and systems biology to ecology and neuroscience — where population variability, mechanistic dynamics, and complex outcome structures must be modeled jointly.

NoLimits.jl is developed and maintained by the Hasenauer Lab at the University of Bonn, with Manuel Huth as the main developer and maintainer.

Nonlinear mixed-effects (NLME) models are the standard tool for longitudinal analysis in the biomedical sciences, but existing software enforces trade-offs between expressiveness, estimation flexibility, and modern machine-learning integration. NoLimits.jl addresses these gaps through a single, composable modeling language in which mechanistic structure, learned components, flexible random-effect distributions, and diverse outcome types coexist within one coherent specification — and can be estimated with multiple inference strategies without rewriting the model.

All components are freely composable: a single model can simultaneously use ODE dynamics, neural-network subterms, multiple RE grouping levels with flow-based distributions, and mixed outcome types.

All methods share a single fit_model interface, enabling direct comparison across inference paradigms on the same model and dataset.

• Wald intervals (Hessian or sandwich covariance)
• Profile-likelihood intervals (LikelihoodProfiler.jl)
• Posterior intervals from MCMC chains or VI variational posteriors
• All accessible through a unified compute_uq interface

Visual predictive checks (VPCs), residual diagnostics (QQ, PIT, ACF), random-effects distribution diagnostics, observation-level predictive distribution plots, multistart waterfall plots, and UQ parameter distribution plots.

The example below fits a one-compartment pharmacokinetic model with subject-level random effects on clearance and volume using a Laplace approximation.

using NoLimits, DataFrames, Distributions, OrdinaryDiffEq

# --- 1. Define the model ---
model = @Model begin
    @fixedEffects begin
        log_cl   = RealNumber(log(5.0))          # log-clearance (population)
        log_v    = RealNumber(log(30.0))          # log-volume (population)
        omega_cl = RealNumber(0.3, scale=:log)    # RE SD for clearance
        omega_v  = RealNumber(0.3, scale=:log)    # RE SD for volume
        sigma    = RealNumber(0.2, scale=:log)    # residual SD
    end

    @covariates begin
        t = Covariate()                           # observation time column
    end

    @randomEffects begin
        eta_cl = RandomEffect(Normal(0.0, omega_cl); column=:ID)
        eta_v  = RandomEffect(Normal(0.0, omega_v);  column=:ID)
    end

    @preDifferentialEquation begin
        cl = exp(log_cl + eta_cl)
        v  = exp(log_v  + eta_v)
    end

    @DifferentialEquation begin
        D(A) ~ -(cl / v) * A                     # one-compartment elimination
    end

    @initialDE begin
        A = 100.0                                 # bolus dose at t = 0
    end

    @formulas begin
        conc = A(t) / v
        y ~ Normal(conc, sigma)
    end
end

# --- 2. Bind to data ---
dm = DataModel(model, df; primary_id=:ID, time_col=:t)

# --- 3. Fit ---
res = fit_model(dm, Laplace())

# --- 4. Inspect results ---
get_params(res; scale=:untransformed)
re  = get_random_effects(res)
uq  = compute_uq(res; method=:wald)

# --- 5. Diagnostics ---
plot_fits(res)
plot_vpc(res; n_simulations=200)
plot_residuals(res)

More examples — including neural-ODE models, HMM outcomes, normalizing-flow random effects, and multi-method comparison — are available in the Tutorials.

NoLimits.jl is built on and integrates directly with established Julia packages. Users familiar with any of these libraries will find the interfaces immediately familiar.

NoLimits.jl requires Julia 1.12 or later. Install directly from GitHub:

using Pkg
Pkg.add(url="https://github.com/manuhuth/NoLimits.jl")

Registry-based installation (Pkg.add("NoLimits")) will be available once the package is registered in the Julia General Registry.

Full documentation, including tutorials, method descriptions, and API reference:

A manuscript describing NoLimits.jl is in preparation. In the meantime, if you use this package in published work, please cite this repository:

@software{NoLimits_jl_2026,
  title  = {{NoLimits.jl}},
  author = {Huth, Manuel and Arruda, Jonas and Peiter, Clemens and Schmid, Nina and Hasenauer, Jan},
  year   = {2026},
  url    = {https://github.com/manuhuth/NoLimits.jl}
}

NoLimits.jl is released under the MIT License. See LICENSE for details.