Sparse Reconstruction by Direct Measurement-to-Field Generation in Function Space introduces a functional rectified flow framework called Direct Measurement-to-Field Generation (DMF) that learns to generate physical fields directly from sparse measurements. Unlike traditional grid-based methods, DMF jointly learns a sensor–global–sensor representation and a generative transport mechanism, enabling dynamic fusion of local grounding with global context to evaluate fields at arbitrary query coordinates. Benchmarks demonstrate that DMF outperforms baselines in scenarios with unknown boundaries, missing high-resolution training data, and unmeasured quantities, while its stochastic ensemble generation provides reliable uncertainty quantification and improved continuous ranked probability scores.
By Linzheng Wang, Jason Chen, Nicolas Tricard, Zituo Chen, Xingsen Guo, Sili Deng
arXiv:2610.16645v1 Announce Type: cross
Abstract: Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representatio...
By Ramzi Idoughi, Radouan Boukharfane, Peter Wonka
TRACE is a retrospective streaming generative reconstruction framework designed to recover continuous physical fields from sparse, structured sensing streams. It performs approximate Bayesian inference in a continuous-coordinate latent space, fuses sparse off‑grid measurements with a state‑space temporal prior via Kalman‑style filtering, and refines past frames through retrospective smoothing. Experiments on active matter, ocean sound‑speed fields, and supernova simulations demonstrate that TRACE matches or surpasses existing frame‑wise generative reconstructors, offline spatiotemporal methods, and streaming data‑assimilation baselines in reconstruction quality under temporally sparse and spatially localized sensing protocols.
By Xinyu Zhang, Lihao Chen, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang
arXiv:2507. 03094v2 Announce Type: replace-cross Abstract: Many challenges in scientific imaging involve solving ill-posed inverse problems, where the goal is to recover spatio-temporal fields from indirect, noisy, and highly sparse measurements - often without access to ground truth data or reliable simulators.
By Ali SaraerToosi, Renbo Tu, Esther Y. H. Lin, Kamyar Azizzadenesheli, Aviad Levis
The paper introduces Observation‑Aligned Two‑Stage Domain Decomposition Physics‑Informed Neural Networks (TSDD‑PINN) for reconstructing traffic speed fields from sparse fixed sensors. It first trains a global PINN, then uses its residuals to partition the domain and warm‑start child networks, allowing spatial, temporal, or space‑time refinement. Experiments on the I‑24 MOTION dataset show that TSDD‑PINN achieves lower relative L2 error in most configurations and trains faster than the XPINN baseline, with performance depending on sensing density.
By Eunhan Ka, Ludovic Leclercq, Satish V. Ukkusuri
arXiv:2602.23188v2 Announce Type: replace
Abstract: We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while...
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
The paper presents a lightweight retraining strategy for a parameterized Reduced Order Model (ROM) that achieves full‑model accuracy using only a fraction of the computational effort and sparse observations. The ROM architecture combines a Variational Autoencoder for dimensionality reduction with a transformer network that evolves latent states while accounting for the Reynolds number as an external control variable. By leveraging the probabilistic VAE, the method generates trajectory ensembles and uncertainty estimates, and adapts to out‑of‑sample parameters through sparse data assimilation with an ensemble Kalman filter, focusing retraining on the autoencoder to correct latent manifold distortions.
By Isma\"el Zighed, Andrea N\'ovoa, Luca Magri, Taraneh Sayadi
arXiv:2611.06711v1 Announce Type: new
Abstract: Deep generative models, particularly Flow Matching frameworks, have emerged as powerful tools for synthesizing complex physical systems. However, stand...
By Giuliano Galadini, Aurelio Uncini, Danilo Comminiello
arXiv:2607. 03349v1 Announce Type: cross Abstract: The accuracy of consumer-grade inertial navigation is bottlenecked by the stochastic noise of Micro-Electro-Mechanical Systems (MEMS).
By I-Hao Lu, Dongsoo Han
arXiv:2610.01759v1 Announce Type: new
Abstract: Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a di...
By Zhenyu Liang, Yining Huang, Yubo Zhao, Jack C. P. Cheng
PMosFM introduces a preconditioned manifold matching framework that enables one‑step physics‑constrained generation by encoding constraints in a manifold decoder. The method learns transport in intrinsic coordinates, eliminating the need for residual losses or trajectory unrolling, and employs a geometric preconditioner and covariance transform to improve conditioning. Experiments demonstrate reduced training and sampling time compared to multi‑step baselines while maintaining comparable physical and distributional fidelity.
By Zhangyong Liang, Haibin Ling
PR‑Smoother is an amortized smoothing method that preserves the explicit use of a prescribed simulator in both the evidence lower bound and the variational family. It learns only future‑conditioned corrections to the simulator’s rollout, yielding a non‑Gaussian smoothing distribution that can jointly infer state, parameters, and sensor bias from observations alone. The approach recovers the exact smoother in deterministic and linear‑Gaussian limits and has been shown to capture multimodal posteriors in Lorenz‑96 and scale to 16,384‑dimensional Kolmogorov flow.
By Yuta Tarumi