Highlights
At CNMAC 2024, held in Porto de Galinhas, Larissa Miguez presented the talk
“Interplay of Physics-Informed Neural Networks and Multiscale Numerical Methods.”
The presentation explored the integration of Physics-Informed Neural Networks (PINNs)
with the Multiscale Hybrid-Mixed (MHM) framework. In this approach, PINN models are used
to approximate the multiscale basis functions that arise from the independent local problems
of the MHM method. Numerical experiments for the Poisson problem demonstrate the potential of
this strategy as a surrogate approach for efficiently capturing multiscale features in PDE simulations.
Technical meeting regarding the collaboration between Inria and LNCC on the design, study and development of AI-based innovative simulation methods based on the concept of Physics-Informed Neural Networks (PINNs), with applications to acoustic and electromagnetic wave propagation problems. Inria (Stéphane Lanteri) and LNCC (Antonio Tadeu Gomes and Frédéric Valentin) researchers have in particular discussed about a future joint roadmap for this collaboration, which is currently funded by the EOLIS and RISC2 projects.
We proposed a method that explores the idiosyncrasies of multiscale simulators to reduce the uncertainty when predicting the execution time of this type of HPC applications. The method is based on the knowledge about the influence of each parameter of the numerical method these simulators employ in the computational cost of a simulation. The result is a tree-based ML architecture (see figure below) with simple regression models at the leaves, which help with improving the interpretability of the obtained models. More information.
