Domain decomposition for physics-informed neural networks (Alexandre Heinlein, Delft University)

20.02.2024 14:00 – 15:00

Physics-informed neural networks (PINNs) are a class of methods for
solving differential equation-based problems using a neural network as
the discretization. They have been introduced by Raissi et al. and
combine the pioneering collocation approach for neural network functions
introduced by Lagaris et al. with the incorporation of data via an
additional loss term. PINNs are very versatile as they do not require an
explicit mesh, allow for the solution of parameter identification
problems, and are well-suited for high-dimensional problems. However,
the training of a PINN model is generally not very robust and may
require a lot of hyper parameter tuning. In particular, due to the
so-called spectral bias, the training of PINN models is notoriously
difficult when scaling up to large computational domains as well as for
multiscale problems.

In this talk, overlapping domain decomposition-based techniques for
PINNs are being discussed. Compared with other domain decomposition
techniques for PINNs, in the finite basis physics-informed neural
networks (FBPINNs) approach, the coupling is done implicitly via the
overlapping regions and does not require additional loss terms. Using
the classical Schwarz domain decomposition framework, a very general
framework, that also allows for mult-level extensions, can be
introduced. The method outperforms classical PINNs on several types of
problems, including multiscale problems, both in terms of accuracy and
efficiency. Furthermore, the combination of the multi-level domain
decomposition strategy with multifidelity stacking PINNs for
time-dependent problems will be discussed. It can be observed that the
combination of multifidelity stacking PINNs with a domain decomposition
in time clearly improves the reference results without a domain
decomposition.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre