Research projects
PDE-AI
A national research initiative on AI methods for PDEs. A small subset of this project uses Scimba.
ANR INFERNO
More details coming soon!
Exa-MA (PEPR NumPEx)
It is a project on methods and algorithms for exascale computing. Several contributions on PINNs and surrogate models are integrated into Scimba.
Publications
Non-linear control variate in δf particle-in-cell methods using symplectic neural networks
A δf particle-in-cell approach for kinetic plasma simulations in which the bulk density, used as a control variate, is evolved with symplectic neural networks (SympNets) approximating the backward flow, with a periodic SympNet variant validated on 1D1V and 3D3V Vlasov-Poisson configurations.
Enriching continuous Lagrange finite element approximation spaces using neural networks
A pipeline that enriches classical FEM approximation spaces with a neural network prior, with error estimates showing the enriched scheme reaches a given accuracy on coarser meshes than standard FEM, validated on parametric 1D, 2D and 3D problems.
Neural semi-Lagrangian method for high-dimensional advection-diffusion problems
A semi-Lagrangian scheme for high-dimensional advection-diffusion equations that projects the solution onto a finite-dimensional neural space at each time step, combining the unconditional stability of semi-Lagrangian methods with neural approaches that avoid the curse of dimensionality.
Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation
An assessment of Finite Basis Physics-Informed Neural Networks and their multilevel variants for the homogeneous Helmholtz equation in complex 2D domains, partitioning the computational domain into overlapping sub-domains each governed by a local network, and comparing the approach against conventional finite difference and finite element methods on high-frequency wave problems.
Volume-preserving geometric shape optimization of the Dirichlet energy using variational neural networks
A variational neural network approach to volume-constrained shape optimization of the Dirichlet energy, parametrizing admissible shapes so that the constraint is preserved throughout training instead of enforced through penalization.
Neural non-canonical Hamiltonian dynamics for long-time simulations
A study of learning non-canonical Hamiltonian dynamics from data while preserving structure in both the learned model and its numerical integration, identifying a gauge-dependency instability that arises when combining the two and proposing two training strategies (learning the vector field directly, or the time-discrete map through the integration scheme), validated on guiding-center dynamics from gyrokinetic plasma physics.
Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks
An enrichment of Discontinuous Galerkin bases with a Physics-Informed Neural Network prior approximating the steady solution, yielding schemes that are approximately well-balanced for hyperbolic systems of balance laws.