A multimodal Transformer for InSAR-based ground deformation forecasting with cross-site generalization across Europe

TL;DR

This work tackles the challenge of predicting near-term InSAR-based ground deformation over large European regions. It introduces a multimodal patch-based Transformer that fuses recent displacement maps with static deformation indicators and harmonic day-of-year encodings to perform single-step nowcasting on a $64\times64$ grid. Across experiments on six European tiles representing diverse deformation regimes, the multimodal Transformer achieves superior accuracy (e.g., RMSE ≈ $0.90$ mm, $R^2 ≈ 0.97$ on the eastern Ireland tile) and demonstrates strong cross-site generalization, including zero-shot transfer to unseen regions. The results highlight the practical potential for continental-scale, transfer-ready deformation monitoring and point to future directions in multi-step forecasting, uncertainty quantification, and domain adaptation.

Abstract

Near-real-time regional-scale monitoring of ground deformation is increasingly required to support urban planning, critical infrastructure management, and natural hazard mitigation. While Interferometric Synthetic Aperture Radar (InSAR) and continental-scale services such as the European Ground Motion Service (EGMS) provide dense observations of past motion, predicting the next observation remains challenging due to the superposition of long-term trends, seasonal cycles, and occasional abrupt discontinuities (e.g., co-seismic steps), together with strong spatial heterogeneity. In this study we propose a multimodal patch-based Transformer for single-step, fixed-interval next-epoch nowcasting of displacement maps from EGMS time series (resampled to a 64x64 grid over 100 km x 100 km tiles). The model ingests recent displacement snapshots together with (i) static kinematic indicators (mean velocity, acceleration, seasonal amplitude) computed in a leakage-safe manner from the training window only, and (ii) harmonic day-of-year encodings. On the eastern Ireland tile (E32N34), the STGCN is strongest in the displacement-only setting, whereas the multimodal Transformer clearly outperforms CNN-LSTM, CNN-LSTM+Attn, and multimodal STGCN when all models receive the same multimodal inputs, achieving RMSE = 0.90 mm and $R^2$ = 0.97 on the test set with the best threshold accuracies.

Figures (7)

• Figure 1: Overall workflow of the proposed EGMS-based multimodal deformation nowcasting framework, from EGMS L3 data acquisition through pre-processing and sample construction to model training and single-tile / cross-site evaluation.
• Figure 2: Conceptual architecture of the multimodal patch-based Transformer for EGMS ground-motion forecasting. For each tile and acquisition epoch, the vertical displacement history, static deformation indicators, and harmonic day-of-year encodings are stacked into a multi-channel grid. The grid is partitioned into fixed-size patches and linearly projected into patch embeddings, which are combined with spatial positional encodings. Together with temporal query tokens representing the forecast horizon ($t{+}1$), these embeddings are processed by a Transformer encoder with multi-head self-attention. The output query tokens are mapped back to patch-level residuals, assembled into a grid-based displacement map, and added to the last observed displacement. After de-normalisation, this yields the final single-step forecast in millimetres.
• Figure 3: Single–step predicted displacement map comparison for the displacement–only setting on tile E32N34.
• Figure 4: Single–step predicted displacement map comparison for the multimodal setting on tile E32N34.
• Figure 5: Comparison between unimodal and multimodal performance analyses on tile E32N34.