#01Oct 30, 2026
physics.flu-dyn
Hard Constraint Projection in a Physics Informed Neural Network (Burgers)
Miranda J S Horne, Peter K Jimack, Amirul Khan and 1 more
Physics informed machine learning provides a framework to study and simulate fluid dynamics, potentially at a fraction of the computational cost of traditional numerical methods, with the goal of improving the explainability, accuracy and robustness of purely data driven machine learning methods. In this work, we extend the hard constraint projection (HCP) method developed by Chen et al. [Journal of Computational Physics, 445, 110624, 2021] from a linear partial differential equation (PDE) to a nonlinear PDE: the 1D Burgers' equation. To strictly impose a discrete approximation of the governing equation, the Burgers' equation is first locally discretised (using a finite difference stencil) then decomposed into a constraint matrix and a prediction matrix. Using tools from linear algebra, the constraint matrix is used to construct a projection matrix. A physics informed neural network (PINN) [Raissi et al. Journal of Computational Physics, 378, 686, 2019] is used to predict the velocity, and a final unlearnable layer projects the velocity prediction to the hyperplane of exact solutions to a discretised form of the Burgers' equation. Our initial results indicate that the HCP-PINN initially trains similarly to an equivalent PINN, and as the PINN loss plateaus, the HCP-PINN loss continues to decline. When tested on a previously unseen uniform grid of points covering the domain, the HCP-PINN exhibits higher accuracy, converging to a data error approximately an order of magnitude lower than the comparable PINN. We also observe that the inclusion of the HCP layer results in better observance of the governing PDE. Our findings suggest that the HCP-PINN can be more robust to the selection of physics collocation points, and less dependent on collocation point quantity.
#02Oct 30, 2026
cs.CV
Latent Reasoning in Continuous Space for Unified Multimodal Models
Byungwoo Jeon, Yoonwoo Jeong, Hyunseok Lee and 2 more
Unified Multimodal Models (UMMs) achieve remarkable success on diverse multimodal understanding and generation tasks, yet they still struggle to effectively leverage language-based chain-of-thought reasoning for image generation. As a result, existing reasoning-augmented UMMs often fail to inherit the test-time scaling and fine-grained controllability observed in large language models. We attribute this failure to a fundamental modality mismatch: reasoning is performed in a discrete token space, whereas image generation operates in a continuous space. To bridge this gap, we introduce a Latent Reasoning framework in Continuous space (LARC), which alleviates the token-level bottleneck by reasoning over continuous hidden states. Specifically, the training framework consists of two stages: (i) curriculum supervised fine-tuning (SFT), and (ii) information-gain reinforcement learning (RL). First, the curriculum SFT stage gradually converts token-level reasoning into latent reasoning. Subsequently, the information-gain RL stage self-evolves latent reasoning without ground truth supervision. Experiments across diverse text-to-image generation benchmarks show that LARC consistently improves generation quality, prompt following, and compositional fidelity. Notably, LARC achieves state-of-the-art performance on GenEval with a 7%p gain over BAGEL and demonstrates clear test-time scaling behavior, outperforming token-based generation under both parallel and sequential test-time scaling strategies.
#03Oct 30, 2026
math.ST
On Statistical-Computational Gaps in Graph Combinatorial Testing Problems
Ikjun Choi, Pratik Patil, Alessandro Rinaldo
We study high-dimensional graph combinatorial hypothesis testing problems in which a signal is supported on the edge set of an unknown subgraph drawn from a class invariant under vertex relabeling. For Gaussian observations, we characterize sharp statistical and computational thresholds (at polynomial order) for the signal magnitude required for strong detection across various combinatorial graph alternatives. Our analysis is based on bounding the second moments of the full and low-degree likelihood ratios in terms of the overlap of two independent latent structures and comparing the resulting lower bounds with scan, average, and coordinatewise maximum tests. Under an appropriate low-degree conjecture for computational hardness, we obtain planted-clique thresholds matching those known for Gaussian submatrix detection and identify new statistical-computational gaps for multiple planted cliques and hypercliques, thick cycles and thick paths. We also establish a novel transfer principle across natural exponential family observation models: matching the one-coordinate chi-square divergence preserves full likelihood-ratio second moments exactly and makes low-degree second moments equivalent up to constant factors under a degree condition. Under local regularity, we obtain corresponding testing upper bounds in terms of an effective signal strength. When these upper and lower bounds match, they yield universal threshold scales in the local alternative regime. As a consequence, statistical-computational gaps for planted-clique detection in Erdős--Rényi settings can be deduced from the Gaussian model.
#04Oct 30, 2026
physics.ao-ph
SATFRONT: Detecting Atmospheric Fronts with Satellite Data using Machine Learning
Ioannis Dravilas, Miruna Stoicescu, Roope Tervo and 5 more
Atmospheric fronts are associated with much of the high-impact weather in the mid-latitudes, yet their identification and classification remain largely manual and subjective. Existing deep learning approaches rely primarily on gridded reanalysis or forecast data, limiting their applicability to satellite observations available for time-critical applications. We introduce SATFRONT, a machine learning framework for detecting cold, warm, and occluded fronts over Europe from geostationary satellite observations, with reanalysis data as an optional additional input. The model is trained on frontal analyses from five European national meteorological services and evaluated against UK Met Office analyses for 2024. Using satellite observations alone, SATFRONT achieves a Critical Success Index (CSI) of 0.428 at a 150 km tolerance, within the range of agreement between analyses from different meteorological services (0.277-0.501) and higher than that of an operational rule-based front detector that uses satellite data (0.133). Adding ERA5 reanalysis increases the CSI to 0.591. ERA5 substantially improves the placement of individual fronts, although its effect on their annual spatial distribution varies by front type. These results demonstrate that cold, warm, and occluded fronts can be detected directly from geostationary satellite observations, providing a basis for automated frontal analyses at the high temporal frequency required for time-critical applications.
#05Oct 30, 2026
cs.LG
Hyperbolic Inverse Reinforcement Learning
Iulia Rusu, Anoop Praturu, Sergei Gepshtein and 1 more
Inverse reinforcement learning (IRL) seeks to infer the reward function underlying observed behavior, but its predictive accuracy and interpretability depend on how that reward is computed from the underlying features. While prior IRL reward functions have been implemented through a variety of techniques including linear weights, neural networks, or other function approximators, none make assumptions about the geometry of the underlying feature space. Inspired by geometric organization observed in neural circuits, we introduce Hyperbolic inverse reinforcement learning (Hyperbolic IRL), which parameterizes reward as a function of Hyperbolic distance between the feature vector and a learned parameter vector, as well as its Euclidean distance variant. We tested our methods against a range of linear and nonlinear IRL baselines under both deterministic and stochastic policies. Our Hyperbolic approach achieved comparable performance to state-of-the-art models on established benchmarks and excelled in the low data limit and across dense environments. Applied to human navigation among multiple exhibits in a museum room, Hyperbolic IRL reveals reward structure that depends not only on individual exhibit-distance features, but also on non-separable conjunctions between them. Together, these results demonstrate that a Hyperbolic reward parameterization can improve both the predictive accuracy and interpretability of IRL, providing a framework for studying how non-separable, conjunctive structure can begin to explain behavior.