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.

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.

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.