HIPNO: Symmetry-Aware Physics-Informed Neural Operators for Noninvasive Hemodynamic Inference

Continuous hemodynamic monitoring guides treatment decisions in surgery and intensive care. However, gold-standard signals are only measured in severe cases due to risks associated with invasive measurement. In this work, we introduce HIPNO (Hemodynamic Inference via Physics-informed Neural Operators) to recover hemodynamic state from ubiquitous, non-invasive signals and expand access to advanced monitoring. HIPNO addresses a problem of scale symmetry in physics-informed hemodynamic inference, where different combinations of flow, resistance, and compliance can generate the same observed pressure. We identify the symmetry group of the observation model and parameterize the network in its quotient space. For the 3-element Windkessel model, the quotient coordinates are the compliance-normalized flow $U=Q/C$, the decay time constant $τ_{WK}=R_2 C$, and the characteristic-impedance coordinate $κ=R_1 C$. Across 945499 intraoperative windows from 2562 patients, HIPNO predicts $τ_{wave}$, a proxy for vascular decay derived from pressure, with 32% lower error on the log scale than a population baseline while preserving mean arterial pressure accuracy. Because vascular decay and flow drive occupy separate coordinates, counterfactual perturbations produce the expected directional responses in at least 90% of windows in almost all prespecified scenarios, a separation unavailable to pressure-only baselines. The coordinates are also used as inputs to a calibration model for monitored cardiac output. Finally, the formulation identifies the external compliance or flow reference required to recover absolute physical scale.

Water Reflection Detection Using Symmetric Attention

Reflections of water pose a significant challenge for computer vision systems, as standard deep learning models frequently confuse objects with their mirror images, producing spurious false positives and negatives in tasks such as object detection and semantic segmentation. As a result, detecting reflection axes in natural-water scenes is pivotal for reliable object detection and scene understanding. To mitigate this issue, we leverage the intrinsic imperfect reflective symmetry of water and introduce a Symmetry-Aware Water Reflection Detection Network, namely, SAWRD-Net, that couples dihedral group-equivariant convolutions with a matrix-decomposition decoder in an end-to-end framework. First, dihedral group convolutional layers extract geometry-consistent feature maps that explicitly encode both rotational and mirror symmetries. A Multi-scale Reflection Equivariant block then aggregates features across scales and employs a symmetric-attention mechanism to highlight reflection-relevant regions. The proposed matrix-decomposition decoder factorizes high-dimensional features into compact low-rank parameter and confidence spaces, after which the network directly regresses keypoints on the reflection axis. Then a robust principal component analysis fits the final axis. Evaluated on the largest available water reflection scene data set, SAWRD-Net achieves a true-positive rate of 0.890 against human annotations, outperforming all existing water reflection detectors.

DDSNet: Dual-domain Symmetry-aware Network for PCSEL Property Prediction

Efficient exploration of the photonic crystal (PhC) lattice design space is essential for developing photonic crystal surface-emitting lasers. While coupled-wave theory (CWT) provides an effective physical framework, its computational cost remains prohibitive for large-scale exploration, driving the demand for neural surrogates. However, existing AI models underexploit two key factors of PhC unit-cell dielectric patterns indicated by CWT: spectral components and asymmetric structures, which largely govern devices' physical properties. This mismatch weakens surrogate accuracy and screening reliability, especially in structure-sensitive regions. To address this, we propose the Dual-Domain Symmetry-Aware Network (DDSNet). It integrates translation-equivariant spectral filtering with a symmetry-induced structural prior. The spectral filtering injects a spectral inductive bias into vision model while preserving translation equivariance on lattices. Meanwhile, the structural prior decomposes lattice features into irreducible representation-associated, symmetry-resolved components and processes them in separate branches. Experiments demonstrate that DDSNet significantly outperforms existing AI baselines in property prediction and high-throughput screening, exhibiting superior reliability in structure-sensitive regions. Crucially, component masking analyses reveal that the network successfully learns property-specific dependencies aligned with physical priors. These results indicate that DDSNet effectively captures physically meaningful structure-property relationships, establishing a highly reliable neural surrogate for PhC design space exploration.

Symmetry-Aware 9D Pose Estimation with Sim(3)-Consistent Feature and Spherical Inception Convolution

Object pose estimation is a fundamental problem for an agent system to perceive or manipulate objects in images or videos. However, current instance-level methods struggle with generalization to unseen objects. Category-level methods seek to address this, but remain constrained by the complexities of learning in the non-linear Sim(3) space and intra-class variations. To address these challenges, We propose an effective method for category-level object pose estimation with two key innovations: (1) A translation/size estimator, featuring a semantic-guided symmetry-aware module that leverages robust generalization capabilities of a large vision model (LVM) to infer symmetry points, resulting in accurate translation and size without shape priors. This result serves as a precomputed cue for rotation estimation, thereby reducing the difficulty of learning in the non-linear Sim(3) space and laying a robust foundation for tackling the inherently more challenging rotation estimation. (2) A feature fusion module, based on our proposed spherical large-kernel inception convolution, fuses semantic features from the LVM with systematically computed geometric features to extract essential pose features from intra-class variations by modeling long-range dependencies without excessive computational cost. Built on these innovations, we achieve SOTA on benchmarks and real-world scenes, while developing a robust robotic picking system capable of handling diverse objects. Our code will be available at the project page: {\hypersetup{urlcolor=blue}https://panfei-cheng.github.io/SSH-Pose}.