Nicholas Geissler | Searcharxiv

arXiv2026

First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems

We introduce First-Order Trajectory Matching (FTM), a surrogate-modeling method that learns the first-order local transport of probability mass from trajectories of stochastic systems. By matching the symmetric first-order motion of trajectories, FTM learns the probability current velocity, whose flow preserves time marginals to match ensemble averages, while also capturing current-like trajectory quantities such as fluxes, circulations, and barrier-crossing currents. FTM learns the current velocity directly from trajectories, avoiding drift, diffusion, and score estimation. Our stability analysis separates discretization error from sampling variance and shows that the one-step simulation-free FTM loss is stable when temporal resolution and sample size are properly balanced. Across stochastic dynamical systems and PDE examples, we empirically demonstrate that FTM provides trajectory-aware ensemble predictions at low, deterministic-rollout cost.

cs.LG↗

arXiv2026

Hankel low-rank matrix approximation for gravitational-wave data analysis

Next-generation gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA), will observe vast numbers of overlapping signals. Disentangling these signals from instrumental noise and from one another constitutes a significant data analysis challenge. We explore a denoising technique based on embedding time series into Hankel matrices: a superposition of $n$ (damped) sinusoids corresponds to a matrix of rank $2n$. Thus, the problem of signal extraction is reduced to a structured low-rank approximation problem. Using synthetic data tailored to GW applications, we benchmark three Hankel-based algorithms: ESPRIT, Cadzow iterations, and iteratively reweighted least squares (IRLS). Our test scenarios include isolated and multi-component monochromatic signals, the resolution of sources with closely spaced frequencies, and the recovery of black hole quasinormal modes (QNM). All three algorithms achieve near-optimal performance consistent with Fisher matrix bounds, evidenced by an inverse-square scaling of the mismatch with the signal-to-noise ratio. Furthermore, a proof-of-concept application to numerical relativity waveforms validates the ability of these algorithms to extract QNM frequencies from ringdown signals. Hankel low-rank approximation therefore offers a transparent, computationally efficient avenue for preprocessing GW time series.

astro-ph.HE↗