Neural Dynamic Modes: Computational Imaging of Dynamical Systems from Sparse Observations

TL;DR

NeuralDMD is a novel, model-free framework combining neural implicit representations with Dynamic Mode Decomposition to reconstruct and forecast complex spatio-temporal dynamical systems from sparse, noisy measurements.

Contribution

It introduces NeuralDMD, a new approach that leverages neural representations and DMD for stable, low-dimensional modeling of complex dynamics from limited data.

Findings

Outperforms existing methods in reconstructing wind-speed fields from sparse data.

Successfully recovers plasma evolution near the Galactic-center black hole.

Demonstrates broad applicability across geoscience and astronomy.

Abstract

Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts never-before-seen dynamics observed through indirect, noisy, and highly sparse measurements. We present NeuralDMD, a model-free framework that combines neural implicit representations with Dynamic Mode Decomposition (DMD) to reconstruct continuous spatio-temporal dynamics from such measurements. The expressiveness of neural representations enables capturing complex spatial structures, while the linear dynamical modes of DMD introduce an inductive bias that guides training and supports stable, low-dimensional representations and forecasting. We validate NeuralDMD on two real-world problems: reconstructing near-surface wind-speed fields over North America from sparse station observations, and recovering the evolution of plasma near the Galactic-center black hole, Sgr A*. In both cases, NeuralDMD outperforms established baselines, demonstrating its potential as a general tool for imaging dynamical systems across geoscience, astronomy, and beyond.