Open-source NLME modeling for pharmacometrics

ferx is an open-source nonlinear mixed-effects (NLME) modeling platform for population pharmacokinetic and pharmacodynamic (PopPK/PD) analysis. Its high-performance Rust engine supports established pharmacometric methods and NONMEM-compatible data through a command-line interface, Rust API, and R package.

Install ferx or run your first PopPK model.

Key Features

FOCE/FOCEI estimation – First-Order Conditional Estimation with optional interaction, the gold standard for PopPK
SAEM estimation – Stochastic Approximation EM for robust convergence on complex models
Gauss-Newton (BHHH) – Fast outer optimizer with Levenberg-Marquardt damping, plus a GN+FOCEI hybrid
Importance Sampling (IMP) and SIR – For exact likelihood estimation and posterior sampling
Analytical PK solutions – Built-in one-, two-, and three-compartment models (IV bolus, oral, infusion) with numerical stability guarantees
ODE solver – Dormand-Prince RK45 adaptive integrator for custom kinetic models (e.g. Michaelis-Menten), plus Rosenbrock (rodas4 / rodas5p / rosenbrock23) steppers for stiff systems
SDE / diffusion models – Extended Kalman Filter path for stochastic differential equations via the [diffusion] block
Analytic sensitivities – Hand-rolled Dual2 forward sensitivities for fast, exact FOCE/FOCEI and HMC gradients
Multiple error models – Additive, proportional, combined, and log-transform-both-sides (LTBS); per-CMT multi-endpoint models for joint PK/PD
Inter-occasion variability (IOV) – kappa random effects with FOCE/FOCEI and SAEM support
Lagtime / ALAG – Absorption lag for analytical and ODE paths
LOQ censoring – Beal M3 method for below-LLOQ and above-ULOQ observations
NCA-based starting values – inits_from_nca for automatic theta initialization from the data
Simple model DSL – Declarative .ferx model files that read like equations
NONMEM-compatible data – Reads standard NONMEM CSV datasets directly
Covariate support – Time-constant and time-varying covariates with automatic detection
Parallel estimation – Per-subject computations parallelized via Rayon
Neural network covariates – MLP-based covariate mapper behind the nn feature (experimental)

How It Compares

Feature	ferx-core	NONMEM	nlmixr2	Monolix	Pumas
Language	Rust	Fortran	R, C/C++ (rxode2)	C++	Julia
FOCE/FOCEI	Yes	Yes	Yes	No	Yes
SAEM	Yes	Yes	Yes	Yes	Yes
Analytical PK	Yes	Yes	Yes (`linCmt()`)	Yes	Yes
ODE models	Yes	Yes	Yes	Yes	Yes
Open source	Yes	No	Yes	No	No
License	MIT	Proprietary	GPL (≥ 3)	Proprietary¹	Proprietary²

Method coverage is broadly the same across these engines: NONMEM has offered SAEM, importance sampling and Bayesian estimation alongside FOCE since NONMEM 7, and Monolix estimates with SAEM rather than FOCE. The table compares method availability only, as documented by each tool (checked September 2026; sources below). It does not rank how each engine computes gradients, which differs by method and option; for ferx’s own approach see Gradient route (analytic vs FD).

Sources: NONMEM — Bauer, NONMEM Tutorial Part II: Estimation Methods and Advanced Examples, CPT:PSP 2019; nlmixr2 — CRAN package page and nlmixr2.org; Monolix — SAEM task documentation and licensing; Pumas — estimation documentation.

Architecture Overview

ferx-core uses a two-level optimization structure:

Outer loop: Optimizes population parameters (theta, omega, sigma) using NLopt L-BFGS, BOBYQA, SLSQP, MMA, built-in BFGS, Newton trust-region, or Gauss-Newton (BHHH). The default, optimizer = auto, picks L-BFGS when the exact analytic gradient is available and the derivative-free BOBYQA otherwise (see Outer Optimizers)
Inner loop: For each subject, finds empirical Bayes estimates (EBEs) of random effects by minimizing individual negative log-likelihood

Parameters are internally transformed for unconstrained optimization: theta and sigma are log-transformed, and omega uses Cholesky factorization to guarantee positive-definiteness.

Project Structure

src/                -- the ferx-core engine (one model, one dataset, one fit)
  types.rs          -- Core data structures
  api/              -- Public API (fit, simulate, predict)
  parser/           -- .ferx model file parser
  pk/               -- Analytical PK solutions
  ode/              -- ODE solver and predictions
  estimation/       -- FOCE/FOCEI, SAEM, Gauss-Newton, IMP, SIR, trust-region
  stats/            -- Likelihood and residual computations
  io/               -- Data reading and output writing
  sens/             -- Analytic Dual2 sensitivities (PkNum) for exact gradients
  nn/               -- Neural network components (DCM / NODE)
crates/
  ferx-tools/       -- Workflows that run many fits (bootstrap, model searches)
  ferx-cli/         -- The `ferx` command-line binary

License

ferx-core is released under the MIT License.

Footnotes

Free academic license for non-commercial use.↩︎
Free academic access for non-commercial research and education.↩︎