Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as conservation laws (linear and nonlinear) and physical consistencies, remains challenging. Existing methods often rely on soft penalties or architectural biases that fail to guarantee hard constraints. In this work, we propose Physics-Constrained Flow Matching (PCFM), a zero-shot inference framework that enforces arbitrary nonlinear constraints in pretrained flow-based generative models. PCFM continuously guides the sampling process through physics-based corrections applied to intermediate solution states, while remaining aligned with the learned flow and satisfying physical constraints. Empirically, PCFM outperforms both unconstrained and constrained baselines on a range of PDEs, including those with shocks, discontinuities, and sharp features, while ensuring exact constraint satisfaction at the final solution. Our method provides a flexible framework for enforcing hard constraints in both scientific and general-purpose generative models, especially in applications where constraint satisfaction is essential.

Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior knowledge in non-hybrid settings, overlooking the crucial integration of observational data, and are frequently limited to linear systems, unlike the prevalent nonlinear nature of many real-world applications. To address these limitations, we introduce a discrete weak form that unifies collocation and variational methods, enabling the incorporation of incomplete and complex physical constraints in hybrid learning settings. Within this formulation, we establish that the generalization performance of physics-informed regression in such hybrid settings is governed by the dimension of the affine variety associated with the physical constraint, rather than by the number of parameters. This enables a unified analysis that is applicable to both linear and nonlinear equations. We also present a method to approximate this dimension and provide experimental validation of our theoretical findings.

Fine-grained air pollution forecasting is crucial for urban management and the development of healthy buildings. Deploying portable sensors on mobile platforms such as cars and buses offers a low-cost, easy-to-maintain, and wide-coverage data collection solution. However, due to the random and uncontrollable movement patterns of these non-dedicated mobile platforms, the resulting sensor data are often incomplete and temporally inconsistent. By exploring potential training patterns in the reverse process of diffusion models, we propose Spatio-Temporal Physics-Informed Diffusion Models (STeP-Diff). STeP-Diff leverages DeepONet to model the spatial sequence of measurements along with a PDE-informed diffusion model to forecast the spatio-temporal field from incomplete and time-varying data. Through a PDE-constrained regularization framework, the denoising process asymptotically converges to the convection-diffusion dynamics, ensuring that predictions are both grounded in real-world measurements and aligned with the fundamental physics governing pollution dispersion. To assess the performance of the system, we deployed 59 self-designed portable sensing devices in two cities, operating for 14 days to collect air pollution data. Compared to the second-best performing algorithm, our model achieved improvements of up to 89.12% in MAE, 82.30% in RMSE, and 25.00% in MAPE, with extensive evaluations demonstrating that STeP-Diff effectively captures the spatio-temporal dependencies in air pollution fields.

Preprint accepted by IEEE Transactions on Industrial Cyber-Physical Systems. T o appear in TICPS on IEEE Explore. Abstract --This paper presents HERO (Hierarchical T esting with Rabbit Optimization), a novel black-box adversarial testing framework for evaluating the robustness of deep learning-based Prognostics and Health Management systems in Industrial Cyber-Physical Systems. Leveraging Artificial Rabbit Optimization, HERO generates physically constrained adversarial examples that align with real-world data distributions via global and local perspective. Its generalizability ensures applicability across diverse ICPS scenarios. This study specifically focuses on the Proton Exchange Membrane Fuel Cell system, chosen for its highly dynamic operational conditions, complex degradation mechanisms, and increasing integration into ICPS as a sustainable and efficient energy solution. Experimental results highlight HERO's ability to uncover vulnerabilities in even state-of-the-art PHM models, underscoring the critical need for enhanced robustness in real-world applications. By addressing these challenges, HERO demonstrates its potential to advance more resilient PHM systems across a wide range of ICPS domains. With the rapid development of net zero, there is a need for advanced predictive models and system integration plays a crucial role in the field of renewable energy technologies, particularly in the deployment and management of Proton Exchange Membrane Fuel Cells (PEMFC). Regarded as an integral part of future energy conversion technologies, PEMFC boast high energy conversion efficiency, low operating temperature, low emissions, and rapid startup capabilities [1].

Accurate prediction of vehicle collision dynamics is crucial for advanced safety systems and post-impact control applications, yet existing methods face inherent trade-offs among computational efficiency, prediction accuracy, and data requirements. This paper proposes a dual Physics-Informed Neural Network framework addressing these challenges through two complementary networks. The first network integrates Gaussian Mixture Models with PINN architecture to learn impact force distributions from finite element analysis data while enforcing momentum conservation and energy consistency constraints. The second network employs an adaptive PINN with dynamic constraint weighting to predict post-collision vehicle dynamics, featuring an adaptive physics guard layer that prevents unrealistic predictions whil e preserving data-driven learning capabilities. The framework incorporates uncertainty quantification through time-varying parameters and enables rapid adaptation via fine-tuning strategies. Validation demonstrates significant improvements: the impact force model achieves relative errors below 15.0% for force prediction on finite element analysis (FEA) datasets, while the vehicle dynamics model reduces average trajectory prediction error by 63.6% compared to traditional four-degree-of-freedom models in scaled vehicle experiments. The integrated system maintains millisecond-level computational efficiency suitable for real-time applications while providing probabilistic confidence bounds essential for safety-critical control. Comprehensive validation through FEA simulation, dynamic modeling, and scaled vehicle experiments confirms the framework's effectiveness for Precision Immobilization Technique scenarios and general collision dynamics prediction.

Abstract--Developing a dynamic model for a high-performance vehicle is a complex problem that requires extensive structural information about the system under analysis. This information is often unavailable to those who did not design the vehicle and represents a typical issue in autonomous driving applications, which are frequently developed on top of existing vehicles; therefore, vehicle models are developed under conditions of information scarcity. This paper proposes a lightweight encoder-decoder model based on Gate Recurrent Unit layers to correlate the vehicle's future state with its past states, measured onboard, and control actions the driver performs. The results demonstrate that the model achieves a maximum mean relative error below 2.6% in extreme dynamic conditions. It also shows good robustness when subject to noisy input data across the interested frequency components. Furthermore, being entirely data-driven and free from physical constraints, the model exhibits physical consistency in the output signals, such as longitudinal and lateral accelerations, yaw rate, and the vehicle's longitudinal velocity. N the automotive sector developing a representative vehicle dynamics model is a complex and multifaceted challenge [1]-[3]. Numerous nonlinear factors influence vehicle dynamics, including tire characteristics, suspension geometry, aerodynamics, drivetrain effects, and external environmental factors, such as road surface grip conditions and climatic effects (e.g., wind). Accurately capturing these effects in a computational model requires high-fidelity multibody simulation software and a profound understanding of the vehicle system.

Arterial aneurysm (Fig.1) is a bulb-shape local expansion of human arteries, the rupture of which is a leading cause of morbidity and mortality in US. Therefore, the prediction of arterial aneurysm rupture is of great significance for aneurysm management and treatment selection. The prediction of aneurysm rupture depends on the analysis of the time series of aneurysm growth history. However, due to the long time scale of aneurysm growth, the time series of aneurysm growth is not always accessible. We here proposed a method to reconstruct the aneurysm growth time series directly from patient parameters. The prediction is based on data pairs of [patient parameters, patient aneurysm growth time history]. To obtain the mapping from patient parameters to patient aneurysm growth time history, we first apply autoencoder to obtain a compact representation of the time series for each patient. Then a mapping is learned from patient parameters to the corresponding compact representation of time series via a five-layer neural network. Moving average and convolutional output layer are implemented to explicitly taking account the time dependency of the time series. Apart from that, we also propose to use prior knowledge about the mechanism of aneurysm growth to improve the time series reconstruction results. The prior physics-based knowledge is incorporated as constraints for the optimization problem associated with autoencoder. The model can handle both algebraic and differential constraints. Our results show that including physical model information about the data will not significantly improve the time series reconstruction results if the training data is error-free. However, in the case of training data with noise and bias error, incorporating physical model constraints can significantly improve the predicted time series.

Bayesian physics-informed neural networks (B-PINNs) merge data with governing equations to solve differential equations under uncertainty. However, interpreting uncertainty and overconfidence in B-PINNs requires care due to the poorly understood effects the physical constraints have on the network; overconfidence could reflect warranted precision, enforced by the constraints, rather than miscalibration. Motivated by the need to further clarify how individual physical constraints shape these networks, we introduce a scalable, matrix-free Laplace framework that decomposes the posterior Hessian into contributions from each constraint and provides metrics to quantify their relative influence on the loss landscape. Applied to the Van der Pol equation, our method tracks how constraints sculpt the network's geometry and shows, directly through the Hessian, how changing a single loss weight non-trivially redistributes curvature and effective dominance across the others.

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints.

The ability to adapt to physical actions and constraints in an environment is crucial for embodied agents (e.g., robots) to effectively collaborate with humans. Such physically grounded human-AI collaboration must account for the increased complexity of the continuous state-action space and constrained dynamics caused by physical constraints. In this paper, we introduce Moving Out, a new human-AI collaboration benchmark that resembles a wide range of collaboration modes affected by physical attributes and constraints, such as moving heavy items together and maintaining consistent actions to move a big item around a corner. Using Moving Out, we designed two tasks and collected human-human interaction data to evaluate models' abilities to adapt to diverse human behaviors and unseen physical attributes. To address the challenges in physical environments, we propose a novel method, BASS (Behavior Augmentation, Simulation, and Selection), to enhance the diversity of agents and their understanding of the outcome of actions. Our experiments show that BASS outperforms state-of-the-art models in AI-AI and human-AI collaboration. The project page is available at https://live-robotics-uva.github.io/movingout_ai/.