#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.NI
RAMA: Retrieval-Augmented Multi-Agent Routing with Episodic Memory for LEO Satellite Networks
Xin Ming Li, Peng Hu
Low-Earth orbit (LEO) satellite networks present a challenging routing environment due to rapidly changing topology, traffic, and link conditions. Existing deep reinforcement learning (DRL) routing methods typically rely on current observations and information encoded in network weights, limiting their ability to exploit successful past experiences. We propose RAMA, a retrieval-augmented multi-agent DRL framework with Approximate Information State (AIS), in which each satellite combines its local observation, recent routing history, neighboring state information, and retrieved entries from a per-satellite episodic memory. Retrieved experiences are integrated through a Transformer-based decision network trained with AIS-based auxiliary objectives. With weights frozen in a 140-satellite Kepler constellation, RAMA reduces mean end-to-end latency by 13.4% and 99th-percentile latency by 66.7% relative to the state-of-theart double deep Q-network (DDQN) routing method, mainly by avoiding long detours. Updated online, RAMA remains stable while DDQN degrades. On the 1,584-satellite Starlink shell 1, the reduction in mean latency grows to 93.2%, and updating RAMA online lowers its mean latency by a further 25.5%. These results demonstrate the effectiveness of retrieval-augmented memory for scalable decentralized routing in LEO satellite networks.
#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.CV
Learning Clean Generative Processes from Noisy Measurements
Fabian Kruse, Lorenzo Baldassari, Ivan Dokmanić
We study how to learn a generative model of clean images using only noisy observations. Diffusion processes and their generalizations to non-Gaussian noise require posterior predictions at every noise level. We first show that it is possible to learn these predictions from independent noisy views using Noise2Noise regression, but only at or above the noise level of the training data. To learn the predictions below that level, needed to generate clean images, we impose consistency: a prediction should equal its expectation after continuing the sampling process. We derive conditions under which consistency uniquely determines the continuation to the clean image distribution and verify them for Poisson, binomial, Gamma, and negative-binomial measurements. Experiments on CIFAR-10, photon-counting microscopy, and synthetic aperture radar show that the required posterior predictions can be learned from noisy views alone and that the consistency relation repairs the continuation beyond the noise level of the data, which severely deteriorates without consistency.