Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins

Digital twins of natural systems must remain aligned with physical systems that evolve over time, are only partially observed, and are typically modeled by mechanistic simulators whose parameters cannot be measured directly. In such settings, model adaptation is naturally posed as a simulation-based inference problem. However, sparse and indirect observations often fail to identify a unique and optimal calibration, leaving several simulator parameterizations compatible with the available evidence. This article presents a GFlowNet-based approach to model adaptation for digital twins of natural systems. We formulate adaptation as a generative modeling problem over complete simulator configurations, so that plausible parameterizations can be sampled with probability proportional to a reward derived from agreement between simulated and observed behavior. Using a controlled environment agriculture case study based on a mechanistic tomato model, we show that the learned policy recovers dominant regions of the adaptation landscape, retrieves strong calibration hypotheses, and preserves multiple plausible configurations under uncertainty.

Digital twins provide a powerful paradigm for diagnostic and prognostic tasks in the monitoring and control of engineered systems; however, their deployment for complex structures remains challenged by model-form uncertainty, arising from unknown nonlinear dynamics, and by sparse sensing. These limitations hinder reliable online state estimation using either purely physics-based or purely data-driven approaches. This work introduces the Physics-Guided Graph Neural ODE (PiGGO) framework, a physics-informed, graph-based Bayesian state estimation approach in which a learned graph neural ordinary differential equation (GNODE) serves as the continuous-time state-transition model within an extended Kalman filter. The graph representation explicitly defines the system state-space, while physics-guided inductive biases encode known structural relationships and constrain the learning of nonlinear dynamics. By integrating graph-native learned dynamics with recursive Bayesian filtering, the proposed PiGGO framework enables online virtual sensing and uncertainty-aware state estimation for nonlinear systems with unknown model form, while maintaining generalisation across topologically similar structures. Numerical case studies demonstrate improved robustness to model uncertainty and measurement noise, outperforming both open-loop graph neural models and conventional filtering approaches in online prediction tasks.

Digital Twins rely on surrogate models to mirror physical systems in real time, yet these models can degrade as operating conditions evolve, a phenomenon known as concept drift. Maintaining surrogate fidelity under drift, particularly when models must also capture aleatoric uncertainty, remains an open challenge. Existing adaptive frameworks lack principled mechanisms for detecting when updates are needed, for efficiently adapting models from limited streaming data, and for certifying that updates genuinely improve predictive performance. Here we present an adaptive Digital Twin framework that integrates a Fisher score--based multivariate drift detector, Low-Rank Adaptation (LoRA) for parameter-efficient continual learning, and a Mann--Whitney $U$ test for online statistical validation. The framework monitors surrogate-model confidence via Fisher score vectors, triggers targeted fine-tuning of fewer than 1% of model parameters upon drift detection, and statistically certifies predictive improvement before deploying the updated surrogate. Applied to a stochastic linear system and a directed energy deposition additive manufacturing process as case studies, the framework successfully detects distributional shifts with short delays and restores both predictive accuracy and uncertainty quantification under abrupt and incremental drift. These results establish a statistically rigorous and computationally tractable pathway for sustaining the trustworthiness of neural-network--based Digital Twins throughout their operational life cycle.