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Discovering intrinsic multi-compartment pharmacometric models using Physics Informed Neural Networks

Imran Nasim, Adam Nasim

TL;DR

Pharmacometric models rely on PK-PD models described by ODEs, but deriving these equations is labor-intensive. This paper introduces PKINNs, a data-driven framework that couples physics-informed neural networks with symbolic regression to discover intrinsic multi-compartment pharmacometric models from noisy data and estimate unknown parameters. PKINNs accurately predict derivatives and state trajectories, are robust to noise, and enable extrapolation; symbolic regression via PySR and SINDy yields interpretable approximate ODEs, with SINDy aligning more closely to the ground-truth PK model. The framework offers a scalable path to automatic model discovery in pharmacometrics, reducing manual derivation and enabling parsimonious, interpretable models suitable for large datasets.

Abstract

Pharmacometric models are pivotal across drug discovery and development, playing a decisive role in determining the progression of candidate molecules. However, the derivation of mathematical equations governing the system is a labor-intensive trial-and-error process, often constrained by tight timelines. In this study, we introduce PKINNs, a novel purely data-driven pharmacokinetic-informed neural network model. PKINNs efficiently discovers and models intrinsic multi-compartment-based pharmacometric structures, reliably forecasting their derivatives. The resulting models are both interpretable and explainable through Symbolic Regression methods. Our computational framework demonstrates the potential for closed-form model discovery in pharmacometric applications, addressing the labor-intensive nature of traditional model derivation. With the increasing availability of large datasets, this framework holds the potential to significantly enhance model-informed drug discovery.

Discovering intrinsic multi-compartment pharmacometric models using Physics Informed Neural Networks

TL;DR

Pharmacometric models rely on PK-PD models described by ODEs, but deriving these equations is labor-intensive. This paper introduces PKINNs, a data-driven framework that couples physics-informed neural networks with symbolic regression to discover intrinsic multi-compartment pharmacometric models from noisy data and estimate unknown parameters. PKINNs accurately predict derivatives and state trajectories, are robust to noise, and enable extrapolation; symbolic regression via PySR and SINDy yields interpretable approximate ODEs, with SINDy aligning more closely to the ground-truth PK model. The framework offers a scalable path to automatic model discovery in pharmacometrics, reducing manual derivation and enabling parsimonious, interpretable models suitable for large datasets.

Abstract

Pharmacometric models are pivotal across drug discovery and development, playing a decisive role in determining the progression of candidate molecules. However, the derivation of mathematical equations governing the system is a labor-intensive trial-and-error process, often constrained by tight timelines. In this study, we introduce PKINNs, a novel purely data-driven pharmacokinetic-informed neural network model. PKINNs efficiently discovers and models intrinsic multi-compartment-based pharmacometric structures, reliably forecasting their derivatives. The resulting models are both interpretable and explainable through Symbolic Regression methods. Our computational framework demonstrates the potential for closed-form model discovery in pharmacometric applications, addressing the labor-intensive nature of traditional model derivation. With the increasing availability of large datasets, this framework holds the potential to significantly enhance model-informed drug discovery.
Paper Structure (10 sections, 6 equations, 3 figures, 2 tables)

This paper contains 10 sections, 6 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology and Experiments
  3. Results
  4. Impact statement
  5. PKINNs details
  6. Loss function
  7. Model training details
  8. Extrapolation Error
  9. Pharmacology model details
  10. Parameters

Figures (3)

  • Figure 1: Schematic of the PKINNs architecture.
  • Figure 2: Drug concentration curves for the datasets. Raw data is represented as filled circles and the PKINNs model are solid lines, where the extrapolated region of the model is shown by dashed lines in the shaded region. Line colours: $X_1$ (black), $X_2$ (green), $X_3$ (red).
  • Figure 3: Comparison between the calculated derivatives and predicted derivatives of PKINNs. Low noise (upper panels), medium noise (middle panels) and high noise (upper panels).