Research interests

My current research lies at the intersection of physical models and kernel methods borrowed from machine learning. A promising perk of such kernel methods is that in the right context, they are a viable alternative to the now wide spread physics informed neural networks (PINNs), while remaining mathematically tractable.

Specifically, my research is a mix of the following topics:

  • Partial differential equations (PDEs), numerical schemes for PDEs.
  • Stochastic (Gaussian) processes, Gaussian process regression (Kriging), Gaussian measures over function spaces, reproducing kernel Hilbert spaces (RKHS).
  • Bayesian inverse problems for PDEs, physics informed Kriging.

I recently started working on conformal inference for time series.

Journal articles

  • I. Henderson, P. Noble, and O. Roustant. “Characterization of the second order random fields subject to linear distributional PDE constraints”. Bernoulli, Vol. 29(4) (2023), pp. 3396-3422. Journal homepage HAL File

  • I. Henderson, P. Noble, and O. Roustant. “Covariance models and Gaussian process regression for the wave equation. Application to related inverse problems”. Journal of Computational Physics, Vol 494 (2023), paper No 112519. Journal HAL File

  • I. Henderson. “Sobolev regularity of Gaussian random fields”. Journal of Functional Analysis, Vol. 286 (2024), paper No 110241. Journal HAL File

Conference proceedings

  • I. Henderson, Archontis Politis, and Stefan Bilbao. “Filter Design for Real-Time Ambisonics Encoding During Wave-based Acoustic Simulations”. In: Forum Acusticum. Lyon, France, Dec. 2020, pp. 517–521. HAL File

Some presentations and posters

  • ANR GAP and IMT/IMSV Bern "Fondue-Cassoulet" Workshop Presentation.
  • Poster presented at the MASCOT-NUM annual meeting (Jun. 2022) at Clermont-Ferrand. File
  • PhD defense slides (French).

Theses

  • PhD manuscript: "PDE constrained kernel methods". INSA Toulouse, Université Toulouse 3 Paul Sabatier. HAL File

  • Master's thesis (French): "Réduction de modèle non linéaire dans l’espace de Wasserstein et méta-modélisation pour certaines lois de conservation unidimensionnelles". Université Paris-Saclay, CentraleSupélec, IMT. File

Awards

  • Best video presentation, Graduate student category, at the LIKE22 (Lifting Inference with Kernel Embeddings) event, Jan. 2022 (500 Swiss francs prize)