Digital Twins: McKean-Pontryagin Control for Partially Observed Physical Twins
On the map: Deep reinforcement learning methods → RL theory and sample complexity
Abstract (arXiv)
Optimal control for fully observed diffusion processes is well established and has led to numerous numerical implementations based on, for example, Bellman's principle, model free reinforcement learning, Pontryagin's maximum principle, and model predictive control. In contrast, much fewer algorithms are available for optimal control of partially observed processes. However, this scenario is central to the digital twin paradigm, where a physical twin is partially observed and control laws are derived based on a digital twin. In this paper, we contribute to this challenge by combining data assimilation in the form of the ensemble Kalman filter with the recently proposed McKean-Pontryagin approach to stochastic optimal control. We derive forward evolving mean-field evolution equations for states and co-states which simultaneously allow for an online assimilation of data as well as an online computation of control laws. The proposed methodology is therefore perfectly suited for real time applications of digital twins. We present numerical results for controlled Lorenz-63 and Lorenz-96 systems as well as an inverted pendulum.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 9 of its 53 references that are in the map. First posted on arXiv 1 Oct 2025.
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References · 9
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- 2014Online Planning Algorithms for POMDPscited by 45
- 2020Spectral convergence of diffusion maps: improved error bounds and an alternative normalisationcited by 26
- 2017Manifold learning with bi-stochastic kernelscited by 20
- 2021Belief Space Planning: A Covariance Steering Approachcited by 5
- 2025Sequential Monte Carlo for Policy Optimization in Continuous POMDPscited by 4
- 2024Localized Schr"odinger Bridge Samplercited by 3
- 2025Ensemble Kalman-Bucy filtering for nonlinear model predictive controlcited by 1
- 2025On a mean-field Pontryagin minimum principle for stochastic optimal controlcited by 1
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- 2024Data Assimilation in Chaotic Systems Using Deep Reinforcement Learning
- 2026Trajectory Design and Budgeted Querying for Digital Twin Calibration
- 2026Digital Twin AI: Opportunities and Challenges from Large Language Models to World Models
- 2026State-space models through the lens of ensemble control
- 2024State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics