Structured Hybrid Mechanistic Models for Robust Estimation of Time-Dependent Intervention Outcomes

TL;DR

The paper addresses robust estimation of time-dependent intervention outcomes in dynamical systems with incomplete mechanistic knowledge. It introduces a hybrid mechanistic-data-driven framework that decomposes the transition operator into parametric/mechanistic and nonparametric learned corrections, with a further split into intervention-dependent and intervention-independent components. A two-stage training procedure uses simulation-based encoder pretraining when mechanistic parameters are unknown, followed by learning residual corrections while freezing the mechanistic core. Experiments on pendulum dynamics and Propofol pharmacokinetics show that the hybrid approach outperforms purely mechanistic or purely data-driven models, particularly under out-of-distribution intervention or covariate shifts, highlighting its potential for robust, personalized intervention optimization in real-world dynamical systems.

Abstract

Estimating intervention effects in dynamical systems is crucial for outcome optimization. In medicine, such interventions arise in physiological regulation (e.g., cardiovascular system under fluid administration) and pharmacokinetics, among others. Propofol administration is an anesthetic intervention, where the challenge is to estimate the optimal dose required to achieve a target brain concentration for anesthesia, given patient characteristics, while avoiding under- or over-dosing. The pharmacokinetic state is characterized by drug concentrations across tissues, and its dynamics are governed by prior states, patient covariates, drug clearance, and drug administration. While data-driven models can capture complex dynamics, they often fail in out-of-distribution (OOD) regimes. Mechanistic models on the other hand are typically robust, but might be oversimplified. We propose a hybrid mechanistic-data-driven approach to estimate time-dependent intervention outcomes. Our approach decomposes the dynamical system's transition operator into parametric and nonparametric components, further distinguishing between intervention-related and unrelated dynamics. This structure leverages mechanistic anchors while learning residual patterns from data. For scenarios where mechanistic parameters are unknown, we introduce a two-stage procedure: first, pre-training an encoder on simulated data, and subsequently learning corrections from observed data. Two regimes with incomplete mechanistic knowledge are considered: periodic pendulum and Propofol bolus injections. Results demonstrate that our hybrid approach outperforms purely data-driven and mechanistic approaches, particularly OOD. This work highlights the potential of hybrid mechanistic-data-driven models for robust intervention optimization in complex, real-world dynamical systems.

Figures (9)

• Figure 1: A hybrid mechanistic-data-driven model with a two-step training process. In Step 1 (left), we generate synthetic training data from the known mechanistic model, which provides ground-truth parameter labels. This labeled data is used to train an encoder that maps the state trajectory and interventions to the parameter vector, using a mean squared error (MSE) loss between true and predicted parameters. In Step 2 (right), we train the correction networks using the original dataset while keeping the encoder network fixed, optimizing an MSE reconstruction loss between the observed and reconstructed signals.
• Figure 2: Cylindrical and point-mass pendulums
• Figure 3: Test Reconstruction Results on Pendulum: Box-plot across 20 replications of the mean reconstruction MSE (averaged over samples and time) for 50,000 test trajectories under in-distribution and out-of-distribution intervention types, on a logarithmic scale. Here, reconstruction refers to forecasting the system trajectory from randomly sampled initial conditions and parameters drawn from the training distribution, under given interventions (in-distribution or out-of-distribution), using the learned models, and comparing the resulting trajectories to those generated by the true underlying dynamics.
• Figure 4: Intervention Outcome Prediction Pendulum: Mean MSE and SEM across 5,000 test samples for different intervention values for all three models as a function of distance from training intervention set (logarithmic scale).
• Figure 5: PK Test Results: Selected-dose MAPE: mean and SEM over 20 replications for three test groups: In-distribution, OOD (age $>60$or BMI $>30$), and extreme OOD (age $>60$and BMI $>30$). OOD is defined with respect to the networks' training distribution only. The mechanistic model of schnider_influence_1998 was estimated using 24 patients aged 26-81.