arXiv:2512.01572v3 Announce Type: replace 
Abstract: Extreme sensor sparsity makes full-field reconstruction a fundamentally ill-posed problem in scientific sensing,where the goal is to infer physical fields from sparse measurements.In this regime,the posterior is severely underconstrained and inherently multimodal,making its approximation highly ill-conditioned.Specifically,deterministic mappings collapse uncertainty,direct conditional learning cannot cover the space of possible observation-conditioned solutions,and likelihood-guided sampling becomes highly sensitive to noise and sensor configurations.These limitations result in unstable posterior estimates and highlight the need for modeling uncertainty in a structural manner.To this end,we propose Cascaded Sensing,a hierarchical framework that restructures posterior inference across scales.Rather than modeling the full-field posterior directly,Cas-Sensing first resolves global structural ambiguity through a deterministic coarse-stage estimator.A neural-operator-based functional autoencoder,trained with masked inputs,maps sparse observations to a coarse-scale structural field,acting analogously to a maximum a posteriori estimator that selects the dominant global configuration.This structural anchor fixes the principal degrees of freedom of the posterior and transforms the problem into a better-conditioned residual inference task.A conditional diffusion model then learns only the refined-scale residual distribution,confining sampling to a stable neighborhood of plausible solutions and suppressing competition among observation-consistent modes.To enhance robustness under varying sensing conditions,we introduce mask-cascade training,which exposes the model to diverse sparse observation patterns through intermediate coarse reconstructions.During inference,manifold-constrained guidance enforces observation consistency as a refinement mechanism rather than a global mode-selection process.

قدمت دراسة حديثة نهجًا جديدًا يسمى Cascaded Sensing، والذي يهدف إلى إعادة بناء المجالات الفيزيائية متعددة المقاييس من قياسات نادرة للغاية باستخدام سلسلة من نماذج التشفير والتفريق. تتناول هذه الطريقة التحديات التي تطرحها ندرة أجهزة الاستشعار، حيث تكافح تقنيات إعادة البناء التقليدية بسبب عدم كفاية القيود والاحتمالات المتعددة.

Un estudio reciente ha presentado un nuevo enfoque llamado Cascaded Sensing, que tiene como objetivo reconstruir campos físicos multiescalares a partir de mediciones extremadamente escasas utilizando una cascada de autoencoders-difusión. Este método aborda los desafíos que plantea la escasez extrema de sensores, donde las técnicas de reconstrucción tradicionales luchan debido a posteriore subcondicionados y multimodales.

Une étude récente a introduit une nouvelle approche appelée Cascaded Sensing, qui vise à reconstruire des champs physiques multi-échelles à partir de mesures extrêmement rares en utilisant une cascade d'autoencodeurs-diffusion. Cette méthode aborde les défis posés par l'extrême rareté des capteurs, où les techniques de reconstruction traditionnelles peinent en raison de postérieurs sous-contraints et multimodaux.

A recent study has introduced a novel approach called Cascaded Sensing, which aims to reconstruct multi-scale physical fields from extremely sparse measurements using an autoencoder-diffusion cascade. This method addresses the challenges posed by extreme sensor sparsity, where traditional reconstruction techniques struggle due to underconstrained and multimodal posteriors.