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arXiv Machine Learning

Sparse Reconstruction by Direct Measurement-to-Field Generation in Function Space

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.

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arXiv Machine Learning
Aug 28

TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing

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
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arXiv AI
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DyPSI: Dynamic Physics Sensing via Joint Field and Sensor-Trajectory Generation

DyPSI is a dynamic physics sensing framework that jointly generates future spatiotemporal fields and sensor trajectories conditioned on past observations. It transforms discrete sensor positions into continuous Sensor Position Fields, encodes both fields and sensing configurations with a shared Functional Tucker representation, and trains a joint diffusion model in a latent space. Experiments on turbulent flow, sea‑surface temperature, and car aerodynamics demonstrate that DyPSI outperforms static and frame‑wise placement strategies, achieving substantial error reductions under tight sensor budgets.

By Yizhou Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Jianfeng Shi, Shikai Fang
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arXiv Machine Learning
Oct 16

Latent Annealed Posterior Sampling with a Variance-Preserving Bridge for Sparsely Observed Random Fields

The paper introduces Latent Annealed Posterior Sampling (LAPS), a method that maps sparsely observed random fields into a lower‑dimensional latent space and performs posterior sampling there. A variance‑preserving bridge controls local covariance inflation, while flow matching learns the latent prior. Experiments on Gaussian benchmarks, a bimodal posterior, and a Navier‑Stokes field show that LAPS accurately approximates posterior distributions, preserves multiple modes, and keeps conditional sampling costs nearly constant as spatial resolution increases.

By Jiankun Lei, Tian Qi
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arXiv Machine Learning
Aug 11

NeuralDMD: Interpretable Neural Representation of Dynamics from Sparse and Noisy Measurements

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
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arXiv Machine Learning
Sep 2

HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields

HarmoCore introduces a generative prior in a compact, continuous latent space for reconstructing oscillatory wave fields from extremely sparse sensor data. It models joint real–imaginary channels using Functional Tucker cores over shared spatial bases, learns a frequency‑conditioned diffusion prior, and performs diffusion posterior sampling directly in core space. Experiments on 2D and 3D Helmholtz problems demonstrate significant performance gains with only 1%–2% sensor coverage while remaining scalable to three dimensions.

By Lihao Chen, Xinyu Zhang, Panqi Chen, Lei Cheng, Ting Zhang, Jianlong Li, Shikai Fang
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