{"ID":2834466,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.01572","arxiv_id":"2512.01572","title":"Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade","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.","short_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.Specific...","url_abs":"https://arxiv.org/abs/2512.01572","url_pdf":"https://arxiv.org/pdf/2512.01572v3","authors":"[\"Letian Yi\",\"Tingpeng Zhang\",\"Mingyuan Zhou\",\"Guannan Wang\",\"Quanke Su\",\"Zhilu Lai\"]","published":"2025-12-01T11:46:14Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"physics.app-ph\"]","methods":"[\"Diffusion Model\"]","has_code":false}