Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918524398600192 |
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| author | Yi, Letian Zhang, Tingpeng Zhou, Mingyuan Wang, Guannan Su, Quanke Lai, Zhilu |
| author_facet | Yi, Letian Zhang, Tingpeng Zhou, Mingyuan Wang, Guannan Su, Quanke Lai, Zhilu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade Yi, Letian Zhang, Tingpeng Zhou, Mingyuan Wang, Guannan Su, Quanke Lai, Zhilu Machine Learning Artificial Intelligence Applied Physics 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. |
| title | Reconstructing Multi-Scale Physical Fields from Extremely Sparse Measurements with an Autoencoder-Diffusion Cascade |
| topic | Machine Learning Artificial Intelligence Applied Physics |
| url | https://arxiv.org/abs/2512.01572 |