Modern power systems are becoming increasingly dynamic, with changing topologies and time-varying loads driven by renewable energy variability, electric vehicle adoption, and active grid reconfiguration. Despite these changes, publicly available test cases remain scarce, due to security concerns and the significant effort required to anonymize real systems. Such limitations call for generative tools that can jointly synthesize grid structure and nodal dynamics. However, modeling the joint distribution of network topology, branch attributes, bus properties, and dynamic load profiles remains a major challenge, while preserving physical feasibility and avoiding prohibitive computational costs. We present PowerGrow, a co-generative framework that significantly reduces computational overhead while maintaining operational validity. The core idea is dependence decomposition: the complex joint distribution is factorized into a chain of conditional distributions over feasible grid topologies, time-series bus loads, and other system attributes, leveraging their mutual dependencies. By constraining the generation process at each stage, we implement a hierarchical graph beta-diffusion process for structural synthesis, paired with a temporal autoencoder that embeds time-series data into a compact latent space, improving both training stability and sample fidelity. Experiments across benchmark settings show that PowerGrow not only outperforms prior diffusion models in fidelity and diversity but also achieves a 98.9% power flow convergence rate and improved N-1 contingency resilience. This demonstrates its ability to generate operationally valid and realistic power grid scenarios.

Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time formulations such as the family of Neural Ordinary Differential Equations (Neural ODEs). Generally, they have shown that capturing the underlying dynamics is beneficial for generic tasks like interpolation, extrapolation, and classification. However, existing methods approximate the dynamics using unconstrained neural networks, which struggle to adapt reliably under distributional shifts. In this paper, we recast time-series problems as the continuous ODE-based optimal control problem. Rather than learning dynamics solely from data, we optimize control actions that steer ODE trajectories toward task objectives, bringing control-theoretical performance guarantees. To achieve this goal, we need to (1) design the appropriate control actions and (2) apply effective optimal control algorithms. As the actions should contain rich context information, we propose to employ the discrete-time model to process past sequences and generate actions, leading to a coordinate model to extract long-term temporal features to modulate short-term continuous dynamics. During training, we apply model predictive control to plan multi-step future trajectories, minimize a task-specific cost, and greedily select the optimal current action. We show that, under mild assumptions, this multi-horizon optimization leads to exponential convergence to infinite-horizon solutions, indicating that the coordinate model can gain robust and generalizable performance. Extensive experiments on diverse time-series datasets validate our method's superior generalization and adaptability compared to state-of-the-art baselines.

Worldwide urbanization requires control systems to accommodate uncertain sources, e.g., wind and solar generations in the energy sector. This uncertainty poses significant challenges to optimal system operations. One solution is the data-driven approach, requiring great data qualities. To produce high-fidelity data, recent studies combine Generative Adversarial Networks (GANs) with physics to explore the stochastic physical data generation. Such an idea belongs to Physics-Informed Neural Networks (PINNs). However, PINN is not implementable when the parameters of system equations are unknown. While parameters of equations can be estimated via measurements, the estimation is inaccurate due to insufficient and/or missing data (e.g., derivatives of system states). We tackle the problem with an intuitive design: enhance the estimation by leveraging highfidelity fake data from GANs. Therefore, we propose to Enhance Physics-Informed Estimation via GAN (PIX-GAN). Specifically, PIX-GAN is based on the stochastic State Space Model (SSM) of physical systems. Then, we design a stochastic PINN to generate fake data. For example, the generator of PIX-GAN contains a probabilistic boundary-condition loss, quantified via a distribution difference. To measure the difference, a discriminator is utilized. Additionally, we design a parameter estimator to estimate the parameters of the SSM, bringing a function-form loss to PIX-GAN to better fit the underlying physics. Finally, we propose an iterative algorithm to train PIX-GAN efficiently. Extensive experiments demonstrate the high performance of PIXGAN using diversified physical systems.

Physical systems are extending their monitoring capacities to edge areas with low-cost, low-power sensors and advanced data mining and machine learning techniques. However, new systems often have limited data for training the model, calling for effective knowledge transfer from other relevant grids. Specifically, Domain Adaptation (DA) seeks domain-invariant features to boost the model performance in the target domain. Nonetheless, existing DA techniques face significant challenges due to the unique characteristics of physical datasets: (1) complex spatial-temporal correlations, (2) diverse data sources including node/edge measurements and labels, and (3) large-scale data sizes. In this paper, we propose a novel cross-graph DA based on two core designs of graph kernels and graph coarsening. The former design handles spatial-temporal correlations and can incorporate networked measurements and labels conveniently. The spatial structures, temporal trends, measurement similarity, and label information together determine the similarity of two graphs, guiding the DA to find domain-invariant features. Mathematically, we construct a Graph kerNel-based distribution Adaptation (GNA) with a specifically-designed graph kernel. Then, we prove the proposed kernel is positive definite and universal, which strictly guarantees the feasibility of the used DA measure. However, the computation cost of the kernel is prohibitive for large systems. In response, we propose a novel coarsening process to obtain much smaller graphs for GNA. Finally, we report the superiority of GNA in diversified systems, including power systems, mass-damper systems, and human-activity sensing systems.

Deep neural networks (DNNs) have been extensively applied to various fields, including physical-system monitoring and control. However, the requirement of a high confidence level in physical systems made system operators hard to trust black-box type DNNs. For example, while DNN can perform well at both training data and testing data, but when the physical system changes its operation points at a completely different range, never appeared in the history records, DNN can fail. To open the black box as much as possible, we propose a Physics-Consistent Neural Network (PCNN) for physical systems with the following properties: (1) PCNN can be shrunk to physical equations for sub-areas with full observability, (2) PCNN reduces unobservable areas into some virtual nodes, leading to a reduced network. Thus, for such a network, PCNN can also represent its underlying physical equation via a specifically designed deep-shallow hierarchy, and (3) PCNN is theoretically proved that the shallow NN in the PCNN is convex with respect to physical variables, leading to a set of convex optimizations to seek for the physics-consistent initial guess for the PCNN. We also develop a physical rule-based approach for initial guesses, significantly shortening the searching time for large systems. Comprehensive experiments on diversified systems are implemented to illustrate the outstanding performance of our PCNN.

Machine Learning (ML) is gaining increasing popularity to tackle uncertainty in physical systems, such as modern power systems. However, ML models can be hardly trained for newly-built power grids with limited data, especially when different power grids have different dimensionalities and distributions for measurement data. To tackle this problem, we propose a novel Heterogeneous Transfer Learning (HTL)-based method to boost the data volume of the target grid. Specifically, we propose a Merged Multi-Modal Gaussian Graphical Model ( M3G2M) with a physical data merging process for knowledge transfer. To solve the maximum likelihood estimation of M3G2M with imbalanced data from two grids, we propose a novel Expectation-Maximization algorithm. Finally, we quantify the negative transfer via the KL-Divergence to measure the distribution similarity between the source grid and the target grid for the transferring confidence. We demonstrate the advantages and the generalizability of our proposed models in diversified data sets for power systems and human action-sensing systems.