Research

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Cell on a soft gel with measured displacements, and the traction force map reconstructed by the model
01

Deep learning for traction force microscopy

I develop hybrid Vision Transformer + U-Net networks that reconstruct the forces cells exert on soft substrates directly from microscopy data, for 2D and 3D traction force microscopy. The models generalize across spatial scales and noise levels and can take metadata such as cell type as extra input. They build on my Bayesian inference methods with automatic regularization, released as open-source software.

02

Physics-constrained neural PDE surrogates

I design symmetry-equivariant convolutional networks with hard physical constraints: new input and output layers for staggered grids that enforce rotation symmetry and the conservation of mass and momentum. These surrogates give accurate, stable long rollouts for shallow-water flow and turbulence and generalize beyond the training data (ICML 2025). The video compares the reference solver with our network.

Lorenz attractor and Turing patterns, examples of equations identified from data
03

Machine learning for discovering governing equations

Which equation produced this data? My sparse Bayesian learning algorithm with automatic thresholding selects the few terms that govern a system and quantifies the uncertainty of every coefficient, while an active-learning loop decides which perturbations to apply next. It recovers ODEs, PDEs and stochastic differential equations, from the Lorenz attractor to Turing patterns.

Publications

(2014). Consolidation modelling of second grade porous media by homogenization. Master Thesis at University Joseph Fourier-Grenoble 1, France, 2014.

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Projects

Double_constraints_PDE

Neural PDE surrogates with geometric and physical constraints that give more accurate and stable long-term predictions (ICML 2025).

Teaching

Advance: Practical Deep Learning with Climate Data, 2024

At the University of Hamburg, I have given the exercise sessions.

Practical Deep Learning with Climate Data, 2023

At the University of Hamburg, I have given the exercise sessions.