arXiv subjects

Christine Thomas

Publications and source records attributed to Christine Thomas.

4 recordsLinked to original sources

arXiv2026

When Do Autoregressive Sequence Models Forecast Physical Wavefields? A Controlled Study on Synthetic Seismograms

Long-horizon autoregressive forecasting of oscillatory physical signals, such as seismograms, gravitational-wave strain, and similar wavefields is limited by error accumulation: as a causal model is fed its own outputs over hundreds of steps, small per-step errors compound into phase drift that pointwise metrics fail to detect. We ask when such rollout stays stable, using synthetic three-component seismograms as a physically structured testbed and the \textsc{SeismoGPT} autoregressive forecaster as the model under study. Through controlled architecture ablations evaluated on free rollout with paired significance tests, we isolate the contribution of each design choice. Multi-token prediction is the dominant stabilizer, accounting for almost the entire improvement over a single-token baseline ($+0.042$ median NCC); a horizon-embedding hybrid prediction head and a cross-horizon STFT-magnitude coherence loss each add a small but consistent further gain. Performance depends sharply on a context-ratio threshold near one, roughly the full P-S interval of observed signal, below which rollout generalization collapses. The dominant residual failure is a polarity inversion: a magnitude-based spectral loss reduces its incidence but, by construction, cannot penalize an inverted segment once it occurs, identifying phase-aware objectives as the natural next step. We frame this as a controlled study of rollout stability on oscillatory wavefields, not a benchmark of forecasting architectures.

cs.LG↗

arXiv2026

Data-Driven Forecasting of three-Component Seismograms Using Transformer Architectures

Forecasting seismic waveforms beyond observed data remains challenging due to the nonlinear, dispersive, and multi-scale nature of seismic wave propagation. In this work, we introduce \textsc{SeismoGPT}, a transformer-based autoregressive model designed to forecast three-component seismic waveforms directly in the time domain. Forecasting is formulated as a physically constrained continuation problem in which the model receives waveform context beginning at the P-wave arrival and extending a defined time beyond the S-wave arrival, after which future motion is generated recursively without access to ground-truth samples. Evaluation is performed on synthetic seismograms spanning source depths of 5--100\,km, epicentral distances of 10--90$^\circ$, and magnitudes $3 \leq M_w \leq 7$. To disentangle the effects of context length and prediction horizon, we define three evaluation configurations using a distance-normalized context ratio and fixed prediction horizons of 120 and 240\,s. Across all configurations, the model achieves a median normalized cross correlation of 0.93 or higher. Analysis of representative forecasts shows that successful predictions preserve both phase coherence and spectral energy distribution. Where failure cases arise, this is primarily due to gradual phase drift during autoregressive rollout rather than unphysical signal generation. These results demonstrate that transformer-based sequence models can learn stable dynamical continuation of seismic wavefields, highlighting the potential of foundation-model approaches for physics-driven time-series forecasting. There are potential applications of this methodology in seismic warning and hazard mitigation, particularly for next-generation gravitational-wave observatories, such as the Einstein Telescope.

astro-ph.IM↗

arXiv2025

The Complex-Step Integral Transform

Building on the well-established connection between the Hilbert transform and derivative operators, and motivated by recent developments in complex-step differentiation, we introduce the Complex-Step Integral Transform (CSIT): a generalized integral transform that combines analytic continuation, derivative approximation, and multi-scale smoothing within a unified framework. A spectral analysis shows that the CSIT preserves phase while suppressing high-wavenumber noise, offering advantages over conventional Fourier derivatives. We discuss the roles of the real and imaginary step parameters, compare FFT-based and interpolation-based implementations, and demonstrate the method on the advection equation and instantaneous-frequency computation. Results show that the CSIT yields smoother, more robust attributes than Hilbert-based methods and provides built-in stabilization for PDE solvers. The CSIT thus represents a flexible alternative for numerical differentiation, spectral analysis, and seismic signal processing. The method opens several avenues for future work, including non-periodic implementations, adaptive parameter selection, and integration with local interpolation frameworks such as high-order Finite-Element methods.

math.NA↗

arXiv2025

Forecasting Seismic Waveforms: A Deep Learning Approach for Einstein Telescope

We introduce \textit{SeismoGPT}, a transformer-based model for forecasting three-component seismic waveforms in the context of future gravitational wave detectors like the Einstein Telescope. The model is trained in an autoregressive setting and can operate on both single-station and array-based inputs. By learning temporal and spatial dependencies directly from waveform data, SeismoGPT captures realistic ground motion patterns and provides accurate short-term forecasts. Our results show that the model performs well within the immediate prediction window and gradually degrades further ahead, as expected in autoregressive systems. This approach lays the groundwork for data-driven seismic forecasting that could support Newtonian noise mitigation and real-time observatory control.

cs.LG↗