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OdeMHPlanner.jl

Welcome to the documentation for OdeMHPlanner.jl, a Julia package for uncertainty-aware learning and planning in dynamical systems with unknown parameters and infrequent output measurements.

OdeMHPlanner implements the method described in:

Learning Dynamics from Infrequent Output Measurements for Uncertainty-Aware Optimal Control Robert Lefringhausen, Theodor Springer, Sandra Hirche arXiv:2512.08013 (2025) https://arxiv.org/abs/2512.08013

Overview

The package targets control problems in which the system dynamics are partially unknown and the state is only indirectly observed through infrequent and noisy output measurements. Rather than identifying a single nominal model, OdeMHPlanner explicitly represents uncertainty over both the model parameters and the latent state trajectory, and propagates this uncertainty into the control design.

The approach follows a Bayesian workflow:

  1. Learning: A Metropolis–Hastings (MH) sampler, equipped with a numerical ODE solver, draws samples from the posterior distribution over unknown parameters and latent state trajectories, conditioned on infrequent input–output measurements.
  2. Planning: The posterior samples are used to formulate a scenario-based optimal control problem (OCP), yielding control inputs that explicitly account for the inferred uncertainty.

This enables principled uncertainty quantification and safer decision-making compared to point-estimate-based approaches.

Installation

This package is not registered in the General registry. Clone the repository and instantiate the environment locally:

git clone https://github.com/TUM-ITR/ode-mh-planner.git
cd ode-mh-planner
julia --project=. -e 'using Pkg; Pkg.instantiate()'

Getting Started

The Experiments section provides a structured entry point into the package. The framework is demonstrated on a glucose regulation task for Type 1 diabetes patients, and the section is organized as follows:

  • Experiments Overview: Simulation setup, model description, prior distributions, cost functional, and baseline definitions.
  • Inference and Sampler Tuning: How to infer unknown dynamics and latent state trajectories from infrequent input–output data using the MH sampler, including tuning and diagnostics for reliable posterior exploration.
  • Optimal Control: How to formulate and solve a scenario-based OCP using the inferred posterior samples.
  • Monte Carlo Study: Statistical evaluation of the method across 100 independent runs.

Each subpage combines a scientific explanation with practical code examples and guidance.