aiqbench analysis
NeuralDMD advances scientific imaging by integrating neural implicit representations with Dynamic Mode Decomposition to solve ill-posed inverse problems from sparse, noisy data. The framework successfully reconstructs continuous spatio-temporal dynamics for applications ranging from weather assimilation to black hole interferometry without requiring ground truth or simulators. While primarily a machine learning method for physics-informed reconstruction, its core contribution lies in leveraging AI to interpret complex dynamical systems rather than general-purpose computer vision tasks.
NeuralDMD: Interpretable Neural Representation of Dynamics from Sparse and Noisy Measurements
arXiv:2507.03094v3 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. To address this challenging scenario, we present NeuralDMD, an interpretable, untrained (per-instance) reconstruction framework that combines neural implicit representations with Dynamic Mode Decomposition (DMD) to reconstruct continuous spatio-temporal dynamics directly from measurements. NeuralDMD parameterizes DMD modes as continuous neural fields, and imposes a low-rank linear dynamics prior with spectral time evolution to enforce temporal continuity. This formulation enables both forecasting under sparsity, and yields interpretable modes and spectra. We find that NeuralDMD outperforms baselines on a wide variety of tasks: from weather data assimilation from sparse station observations to interferometric (Fourier domain) observations of Sagittarius A, the black hole at the center of our galaxy. Moreover, NeuralDMD remains stable when extrapolating into the future. While this framework is most naturally suited to linear dynamics, we show that it can be applied to nonlinear regimes, though with extrapolation performance that degrades with increasing nonlinearity. Together, these results show that NeuralDMD enables interpretable reconstruction and forecasting of spatio-temporal dynamics directly from sparse and indirect measurements without relying on numerical simulators or training data.
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. To address this challenging scenario, we present NeuralDMD, an interpretable, untrained (per-instance) reconstruction framework that combines neural implicit representations with Dynamic Mode Decomposition (DMD) to reconstruct continuous spatio-temporal dynamics directly from measurements. NeuralDMD parameterizes DMD modes as continuous neural fields, and imposes a low-rank linear dynamics prior with spectral time evolution to enforce temporal continuity. This formulation enables both forecasting under sparsity, and yields interpretable modes and spectra. We find that NeuralDMD outperforms baselines on a wide variety of tasks: from weather data assimilation from sparse station observations to interferometric (Fourier domain) observations of Sagittarius A, the black hole at the center of our galaxy. Moreover, NeuralDMD remains stable when extrapolating into the future. While this framework is most naturally suited to linear dynamics, we show that it can be applied to nonlinear regimes, though with extrapolation performance that degrades with increasing nonlinearity. Together, these results show that NeuralDMD enables interpretable reconstruction and forecasting of spatio-temporal dynamics directly from sparse and indirect measurements without relying on numerical simulators or training data.
Computer Vision and Pattern Recognition (cs.CV); Instrumentation and Methods for Astrophysics (astro-ph.IM); Machine Learning (cs.LG); Atmospheric and Oceanic Physics (physics.ao-ph)
arXiv:2507.03094 [cs.CV]
(or arXiv:2507.03094v3 [cs.CV] for this version)
Computer Vision - ECCV 2026, Lecture Notes in Computer Science, vol. 17038, pp. 1-20 (2026)
https://doi.org/10.1007/978-3-032-37447-9_1 DOI(s) linking to related resources
Full text under the publisher's open licence · 256 words
Related coverage
PIRAMID: Progress and Plans
LessWrong · Jul 27, 2026
MURAL: Multimodal Uncertainty-aware Recommendation via Adaptive edge Learning
arXiv · Sep 7, 2026
J++ Lens: Jacobian Filtering Enables More Faithful Workspace Lenses
LessWrong · Oct 8, 2026
Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling
arXiv · Jul 23, 2026