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.

Offline reinforcement learning (RL) seeks to learn decision-making policies from historical datasets when online interaction is costly and risky. Static logs are common with suboptimal or noisy transitions and incomplete data coverage. Previous behavior-cloning methods regularize policies to shrink updates, yet they repeatedly sample low-quality transitions. Such uniform treatment propagates biases/errors in approximating Qfunction. Resampling strategies (e.g., PER and DisCor) attempt to identify the most valuable transitions but rely on online feedback or heuristic reward as utility estimates, inapplicable in purely offline contexts. We tackle this limitation with$S^{2} D C$, a selfsupervised distribution correction framework to reweight offline samples without any external supervision.$\mathbf{S}^{\mathbf{2}}$DC quantifies the information gain via how much each transition sharpens the current value estimate. It then adaptively reweights transitions to amplify high-utility transitions while downweighting redundant or suboptimal samples. Experiments on standard D4RL benchmarks and critical power system management show that$\mathbf{S}^{2}$DC significantly improves policy performance, convergence speed, and stability. This demonstrates that$\mathrm{S}^{2} \text{DC}$converts biased logs, which were previously intractable, into a learning asset to boost fully offline RL.

Invertible neural networks (INNs) have gained attention for solving inverse problems where learning a bijective mapping is essential. However, despite their popularity, little guidance exists on how to select, adapt, or deploy different INN architectures, such as i-ResNet, NICE, or DipDNN, across diverse application domains. In this paper, we provide a unified theoretical and empirical analysis of two major INN families: iterative-contraction networks (e.g., i-ResNet) and triangular coupling networks (e.g., NICE, DipDNN). We show that these models exhibit fundamental tradeoffs in invertibility, expressivity, and compatibility with domain constraints. For example, contractive models fail to recover mappings with large gains or sign flips, whereas triangular schemes inherit rigid channel splits that can restrict feature richness. Building on these insights, we introduce a general-purpose customization framework. It decouples physics-informed constraints from measurement-driven inversion through a parallel INN design. We benchmark representative INNs on cross-domain tasks: edge monitoring, PDE dynamics, and robotic control. Our findings offer first comprehensive design guideline for choosing and adapting INN architectures based on problem structure, shedding light on when and how invertibility-based bidirectional inferences can be reliably applied in practice.

Shapley value-based methods have become foundational in explainable artificial intelligence (XAI), offering theoretically grounded feature attributions through cooperative game theory. However, in practice, particularly in vision tasks, the assumption of feature independence breaks down, as features (i.e., pixels) often exhibit strong spatial and semantic dependencies. To address this, modern SHAP implementations now include the Owen value, a hierarchical generalization of the Shapley value that supports group attributions. While the Owen value preserves the foundations of Shapley values, its effectiveness critically depends on how feature groups are defined. We show that commonly used segmentations (e.g., axis-aligned or SLIC) violate key consistency properties, and propose a new segmentation approach that satisfies the$\mathcal{T}$-property to ensure semantic alignment across hierarchy levels. This hierarchy enables computational pruning while improving attribution accuracy and interpretability. Experiments on image and tabular datasets demonstrate that O-Shap outperforms baseline SHAP variants in attribution precision, semantic coherence, and runtime efficiency, especially when structure matters.

Consistent bi-directional inferences are the key for many machine learning applications. Without consistency, inverse learning-based inferences can cause fuzzy images, erroneous control signals, and cascading failure in SCADA systems. Since standard deep neural networks (DNNs) are not inherently invertible to offer consistency, some past methods reconstruct DNN architecture analytically for one-to-one correspondence but compromise key features such as universal approximation. Other work maintains the capability of universal approximation in DNNs via iterative numerical approximation. However, these methods limit their applications significantly due to Lipschitz conditions and issues of numerical convergence. The dilemma of the analytical and numerical methods is the incompatibility between nonlinear layer compositions and bijective function construction for inverse modeling. Based on the observation, we propose decomposed-invertible-pathway DNNs (DipDNN). It relaxes the redundant reconstruction of nested DNN in the former methods and eases the Lipschitz constraint. As a result, we strictly guarantee the consistency of global inverse modeling without harming DNN's capability for universal approximation. As numerical stability and generalizability are keys for controlling critical infrastructures, we integrate contractive property with a parallel structure for inductive biases, leading to stable performance. Numerical results show that DipDNN performs significantly better than past methods, thanks to its enforcement of inverse consistency, numerical stability, and physical regularization.

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.

In modern complex physical systems, advanced sensing technologies extend the sensor coverage but also increase the difficulties of improving system monitoring capabilities based on real-time data availability. Traditional model-based methods of sensor management are limited to specific systems/settings, which can be challenged when system knowledge is intractable. Fortunately, the large amount of data collected in real-time allows machine learning methods to be a complement. Especially, reinforcement learning-based control is recognized for its capability to dynamically interact with systems. However, the direct implementation of learning methods easily overfits and results in inaccurate physics modeling for sensor management. Although physical regularization is a popular direction to bridge the gap, learning-based sensor control still suffers from convergence failure under highly complex and uncertain scenarios. This paper develops physics-embedded and self-supervised reinforcement learning for sensor management using an intrinsic reward. Specifically, the intrinsic-motivated sensor management (IMSM) constructs the local surprise information from the physical latent features, which captures hidden states in observations, and thus intrinsically motivates the agent to speed-up exploration. We show that the designs can not only relieve the lack of consistency with underlying physics/physical dynamics, but also adapt the global objective of maximizing monitoring capabilities to local environment changes. We demonstrate its effectiveness by experiments on physical system sensor control. The proposed model is implemented for the sensor management of unmanned vehicles and sensor rescheduling in complex/settled power systems, with or without observability constraints. Numerical results show that our model provides consistently higher threat detection accuracy and better observability recovery, as compared to existing methods.

The large amount of data collected in complex physical systems allows machine learning models to solve a variety of prediction problems. However, the directly applied learning approaches, especially deep neural networks (DNN), are difficult to balance between universal approximation to minimize error and the interpretability to reveal underlying physical law. Their performance drops even faster with system unobservability (of measurements) issues due to limited measurements. In this paper, we construct the novel physics interpretable shallow-deep neural networks to integrate exact physical interpretation and universal approximation to address the concerns in previous methods. We show that not only the shallow layer of the structural DNN extracts interpretable physical features but also the designed physical-input convex property of the DNN guarantees the true physical function recovery. While input convexity conditions are strict, the proposed model retains the representation capability to universally approximate for the unobservable system regions. We demonstrate its effectiveness by experiments on physical systems. In particular, we implement the proposed model on the forward kinematics and complex power flow reproduction tasks, with or without observability issues. We show that, besides the physical interpretability, our model provides consistently smaller or similar prediction error for system identification, compared to the state-of-art learning methods.

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.