Uncertainty-Aware Digital Twins: Robust Model Predictive Control using Time-Series Deep Quantile Learning

TL;DR

This work addresses the challenge of real-time, uncertainty-aware decision-making in Digital Twins by marrying a simultaneous multi-step robust MPC framework with Time-Series Dense Encoder (TiDE) and deep quantile learning. TiDE provides one-shot multi-step predictions along with learned quantiles, enabling a trajectory-level uncertainty bound that informs a constraint-tightened MPC formulated as a deterministic optimization via quantiles. The approach is validated through illustrative simulations and a Directed Energy Deposition (DED) additive manufacturing case, demonstrating improved constraint satisfaction with less conservatism and acceptable computation times for real-time deployment. By integrating data-driven surrogates with quantile-based UQ and optimization acceleration (auto-diff, augmented Lagrangian, warm starts), the framework offers a practical tool for proactive, uncertainty-aware Digital Twin control in complex engineering systems.

Abstract

Digital Twins, virtual replicas of physical systems that enable real-time monitoring, model updates, predictions, and decision-making, present novel avenues for proactive control strategies for autonomous systems. However, achieving real-time decision-making in Digital Twins considering uncertainty necessitates an efficient uncertainty quantification (UQ) approach and optimization driven by accurate predictions of system behaviors, which remains a challenge for learning-based methods. This paper presents a simultaneous multi-step robust model predictive control (MPC) framework that incorporates real-time decision-making with uncertainty awareness for Digital Twin systems. Leveraging a multistep ahead predictor named Time-Series Dense Encoder (TiDE) as the surrogate model, this framework differs from conventional MPC models that provide only one-step ahead predictions. In contrast, TiDE can predict future states within the prediction horizon in a one-shot, significantly accelerating MPC. Furthermore, quantile regression is employed with the training of TiDE to perform flexible while computationally efficient UQ on data uncertainty. Consequently, with the deep learning quantiles, the robust MPC problem is formulated into a deterministic optimization problem and provides a safety buffer that accommodates disturbances to enhance constraint satisfaction rate. As a result, the proposed method outperforms existing robust MPC methods by providing less-conservative UQ and has demonstrated efficacy in an engineering case study involving Directed Energy Deposition (DED) additive manufacturing. This proactive while uncertainty-aware control capability positions the proposed method as a potent tool for future Digital Twin applications and real-time process control in engineering systems.

Figures (12)

• Figure 1: Proposed multi-step robust MPC framework.
• Figure 2: Illustration of MPC and robust MPC. (a) Illustration of MPC at time = $k$. (b) Illustration of MPC at time $k+1$. (c) Illustration of robust MPC. The green line are the optimal control input sequences, and the blue dash lines are the state prediction from the model given the optimal control inputs. The gray tube in (c) represents the quantified uncertainty.
• Figure 3: Network structure of TiDE, modified from das2023long.
• Figure 4: Data structure of the input and output of TiDE.
• Figure 5: Illustration of gradient-based optimization using auto-differentiation.