César Ali Ojeda Marin 1, Ramsés J. Sanchéz 3,5, Niklas Hartung 1, Wilhelm Huisinga 1,6, Piyush Kumar 1, Marian Klose 4,6, Tim Jahn 7, Darius A. Faroughy 2
1 University Of Potsdam (Potsdam, Germany), 2 Rutgers Univesity (New Jersey, United States of America), 3 University of Bonn (Bonn, Germany), 4 Freie Universität Berlin (Berlin, Germany), 5 Lamarr Institute (, Germany), 6 Graduate Research Training Program PharMetrX (Berlin/Potsdam, Germany), 7 Technische Universität Berlin (Berlin, Germany)
Objectives
Nonlinear mixed-effects (NLME) modelling [1] is the established population approach for pharmacokinetics (PK) and has been highly successful in practice, but it typically involves per-compound model specification and estimation workflows that are difficult to scale across many compounds and sparse, irregular sampling designs. Neural models have been used to model specific trials, yet a single pre-trained model that generalizes out-of-the-box to new compounds and studies remains limited. We present Amortized Generative Models for Pharmacokinetics (AGM-PK), a prior-fitted and in-context framework that amortizes inference across studies and compounds. AGM-PK targets two capabilities: (i) calibrated individual forecasting from a few early concentration measurements while leveraging the collective context of previously profiled individuals in the same (as e.g., relevant in model informed precision dosing), and (ii) conditional generation of coherent virtual individuals for population-level simulation and evaluation.
Methods
AGM-PK represents each study as a set of individuals with irregular observation tokens (sampling time, concentration) together with dosing tokens (amount, route, schedule; optional infusion duration). A permutation-invariant context encoder aggregates the entire study into a latent representation capturing shared structure and between-individual variability. Conditioning is mixed-effects-like but implicit: the model is conditioned on population context without requiring an explicit fixed/random-effects parameterization, covariate model, or per-study optimization at inference.
The generative component is transport-based [5,6]: it learns a conditional mapping from a simple base distribution to full concentration–time trajectories, with population context entering only as conditioning input. In practice, we instantiate this mapping either as (i) a learned velocity field (flow matching) or (ii) a score function inducing a reverse-time drift (diffusion); both are treated as implementations of the same conditional transport principle.
To endow strong inductive biases (“prior fitting”)[4], we pre-train on large-scale synthetic PK trajectories simulated from compartmental ODE models [2], where log-parameters evolve under Ornstein–Uhlenbeck SDE priors to encode realistic variability across individuals and compounds. To calibrate prior ranges and validate physiological plausibility in the absence of subject-level raw data, we construct a reference dataset of real-world PK parameters by mining summary statistics from open-access bioequivalence (BE) studies using an LLM-assisted extraction pipeline; BE studies follow standardized protocols and report consistent PK summaries under controlled dosing conditions. To disentangle architectural choices from the training regime, we re-trained external Neural ODE and Transformer architectures [3] using our prior-fitted amortized pretraining pipeline; improvements therefore reflect the proposed model design rather than differences in supervision or data availability.
Results
We evaluated AGM-PK on a public benchmark comprising 20 compounds (including parent drugs and metabolites) with heterogeneous dosing and sampling. Using log-RMSE as the primary forecasting metric, the AGM-PK family (two instantiations: an earlier amortized latent-variable/neural-process-style model and a transport-based generator) achieved the best performance on 12/20 compounds (60%), compared with NLME on 4/20 (20%), a transformer baseline on 3/20 (15%), and a NODE baseline on 1/20 (5%). On the subset where an NLME reference was available (12/20 compounds), the best AGM-PK variant improved log-RMSE over NLME in 7/12 cases (58%). Representative gains include mean log-RMSE reductions from 0.732→0.184 (theophylline), 1.300→0.593 (omeprazole), 0.582→0.245 (indometacin), 0.723→0.421 (tolbutamide), and 0.294→0.174 (caffeine). Performance improvements relative to both NLME and amortized neural baselines indicate that the combination of prior-fitted simulator pretraining and population-context conditioning provides benefits beyond amortization alone, while also enabling conditional virtual-cohort generation in the same modelling framework.
Conclusions
AGM-PK provides a foundation-style alternative/complement to bespoke per-compound PK workflows: by combining compartmental simulator priors (with SDE-regularized parameter variability) and in-context conditioning on study populations, AGM-PK supports calibrated forecasting under sparse sampling and coherent generation of virtual individuals without per-study optimization. The BE-literature-derived reference dataset enables realism checks and prior calibration, strengthening physiological plausibility of generated concentration–time profiles for training and supporting scalable population-aware PK modelling.
References:
[1] Lavielle, Marc. Mixed effects models for the population approach: models, tasks, methods and tools. CRC press, 2014.
[2] Lu, James, Brendan Bender, Jin Y. Jin, and Yuanfang Guan. “Deep learning prediction of patient response time course from early data via neural-pharmacokinetic/pharmacodynamic modelling.” Nature machine intelligence 3, no. 8 (2021): 696-704.
[3] Vaswani, Ashish, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. “Attention is all you need.” Advances in neural information processing systems 30 (2017).
[4 ]Müller, Samuel, Noah Hollmann, Sebastian Pineda Arango, Josif Grabocka, and Frank Hutter. “Transformers Can Do Bayesian Inference.” In International Conference on Learning Representations.
[5] Lipman, Yaron, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matthew Le. “Flow Matching for Generative Modeling.” In The Eleventh International Conference on Learning Representations.
[6] Song, Yang, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. “Score-Based Generative Modeling through Stochastic Differential Equations.” In International Conference on Learning Representations.
Reference: PAGE 34 (2026) Abstr 12101 [www.page-meeting.org/?abstract=12101]
Poster: Methodology – AI/Machine Learning