MIAI Cluster Chair · 2026 — 2029

Geometry for multivariate time series analysis

Riemannian geometry meets machine learning to read satellite image time series — frugal models, little labelled data, robust results.

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Why geometry?

Σ ∈ SPD(p)
U ∈ St(p, k)
θ ∈ 𝕋ⁿ

Satellites such as Sentinel-1 and Sentinel-2 photograph the same places again and again. Each pixel becomes a multivariate time series — radar echoes, spectral bands, interferometric phases — recording how glaciers flow, cities subside and volcanoes deform. These measurements do not live in flat space: their natural home is curved — spheres, tori, spaces of covariance matrices.

GEOMETRY takes this curvature seriously. By computing directly on these manifolds, we aim for algorithms that learn from far fewer labelled examples, run lighter — an environmental concern as much as a practical one — and stay robust to the noise and variability inherent to remote sensing.

Formally: invariant features on Grassmann and Stiefel manifolds for InSAR and PolInSAR, transformer and federated extensions of SPDNet for temporal and multimodal data, and Riemannian flow-matching models for denoising, interpolation and prediction — all evaluated on public remote-sensing datasets and released as an open toolbox.

high-dimensional time seriesRiemannian geometrySAR · InSARmultispectral imagingfrugal machine learning

Three work packages

Overview →

WP 1 Geometric invariant features for InSAR & PolInSAR Geometric phases as low-dimensional, gauge-invariant signatures of ground displacement — glaciers, volcanoes, subsidence. WP 2 New geometric machine learning models Extending SPDNet to transformer architectures for the temporal dimension, and to federated learning for multimodal data. WP 3 Flow matching on manifolds Riemannian generative models for denoising SAR imagery, and interpolating or predicting images between acquisition dates.

In collaboration with

DataIA · Univ. Paris-SaclayGéolitheExailONERA