Neural networks overview

ferx-core provides two complementary neural-network extensions. Both are gated behind the nn cargo feature and are being built incrementally.

Which extension do I need?

Known PK/PD structure? Known covariate model? Use
Yes (e.g. 2-cpt oral) Yes Classical analytical — no NN needed
Yes No / partial [covariate_nn] — Deep Compartment Model
No / partial Yes [dynamics_nn] — low-dim Neural ODE (Phase B, pending)
No No Both — they coexist in the same model

If you also need structural uncertainty — system noise that accumulates between observations — see [diffusion] (SDE / Extended Kalman Filter). It is orthogonal to either neural-network mechanism.

[covariate_nn] — Deep Compartment Models

A neural network replaces the typical-value covariate model. Instead of writing explicit power-law or linear covariate effects, a network maps subject covariates (WT, CRCL, …) to the typical PK parameters (CL, V, …), which then combine with ETAs in [individual_parameters] as usual.

The compartmental structure downstream is unchanged; inner FOCEI runs exactly as for a classical model.

Reference: Janssen et al. 2022 — Deep compartment models. CPT Pharmacometrics Syst Pharmacol 11:934–945. DOI 10.1002/psp4.12808.

→ See [covariate_nn] reference for full syntax and examples.

[dynamics_nn] — Low-dimensional Neural ODEs

Note

Phase B — pending. The [dynamics_nn] block is not yet available in released ferx builds. See the ferx-core roadmap for milestone status.

A small neural network appears on the right-hand side of an ODE, replacing mechanistic terms (Michaelis–Menten, linear elimination) when the dynamics are unknown. The compartmental topology and random effects structure are still specified by the modeler.

Reference: Bräm et al. 2025 — Low-dimensional neural ordinary differential equations. CPT Pharmacometrics Syst Pharmacol 14:5–16. DOI 10.1002/psp4.13265.

Status

Component Status
[covariate_nn] block — Deep Compartment Models Phase A (available in nn-feature builds)
[dynamics_nn] block — low-dim Neural ODEs Phase B (pending)
Covariance estimation for [covariate_nn] weights Enabled
Covariance estimation for [dynamics_nn] weights Disabled (auto-overridden)