Introduction

ferx-core is a high-performance Nonlinear Mixed Effects (NLME) modeling engine written in Rust. It is designed for population pharmacokinetic (PopPK) analysis, implementing the same statistical methodology as established tools like NONMEM, Monolix, and Pumas.

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)
  • 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 Monolix Pumas
Language Rust Fortran C++ Julia
FOCE/FOCEI Yes Yes No Yes
SAEM Yes No Yes Yes
Analytical PK Yes Yes Yes Yes
ODE models Yes Yes Yes Yes
Exact gradients Yes (analytic sensitivities) No No Yes (ForwardDiff)
Open source Yes No No No

Architecture Overview

ferx-core uses a two-level optimization structure:

  • Outer loop: Optimizes population parameters (theta, omega, sigma) using NLopt BOBYQA (default), SLSQP, L-BFGS, MMA, built-in BFGS, Newton trust-region, or Gauss-Newton (BHHH)
  • 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/
  types.rs          -- Core data structures
  api.rs            -- 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)
  bin/run_model.rs  -- CLI binary

License

ferx-core is released under the MIT License.