Portrait de Tara Akhound-Sadegh n'est pas disponible

Tara Akhound-Sadegh

Doctorat - McGill
Superviseur⋅e principal⋅e
Siamak Ravanbakhsh
Co-supervisor
Laurence Perreault-Levasseur
Sujets de recherche
Apprentissage profond
Modèles génératifs

Publications

Physics-Informed Transformer Networks
Fabricio Dos Santos
F. Dos
Tara Akhound-Sadegh
Siamak Ravanbakhsh
Physics-informed neural networks (PINNs) have been recognized as a viable alternative to conventional numerical solvers for Partial Differen… (voir plus)tial Equations (PDEs). The main appeal of PINNs is that since they directly enforce the PDE equation, one does not require access to costly ground truth solutions for training the model. However, a key challenge is their limited generalization across varied initial conditions. Addressing this, our study presents a novel Physics-Informed Transformer (PIT) model for learning the solution operator for PDEs. Using the attention mechanism, PIT learns to leverage the relationships between its initial condition and query points, resulting in a significant improvement in generalization. Moreover, in contrast to existing physics-informed networks, our model is invariant to the discretization of the input domain, providing great flexibility in problem specification and training. We validated our proposed method on the 1D Burgers’ and the 2D Heat equations, demonstrating notable improvement over standard PINN models for operator learning with negligible computational overhead.
2023-10-31
NeurIPS.cc/2023/Workshop/DLDE (poster)
openreview.net
openreview.net
Lie Point Symmetry and Physics-Informed Networks
Tara Akhound-Sadegh
Laurence Perreault-Levasseur
Johannes Brandstetter
Max Welling
Siamak Ravanbakhsh
Symmetries have been leveraged to improve the generalization of neural networks through different mechanisms from data augmentation to equiv… (voir plus)ariant architectures. However, despite their potential, their integration into neural solvers for partial differential equations (PDEs) remains largely unexplored. We explore the integration of PDE symmetries, known as Lie point symmetries, in a major family of neural solvers known as physics-informed neural networks (PINNs). We propose a loss function that informs the network about Lie point symmetries in the same way that PINN models try to enforce the underlying PDE through a loss function. Intuitively, our symmetry loss ensures that the infinitesimal generators of the Lie group conserve the PDE solutions.. Effectively, this means that once the network learns a solution, it also learns the neighbouring solutions generated by Lie point symmetries. Empirical evaluations indicate that the inductive bias introduced by the Lie point symmetries of the PDEs greatly boosts the sample efficiency of PINNs.
openreview.net
Physics-Informed Transformer Networks
F. Dos
Santos
Tara Akhound-Sadegh
Siamak Ravanbakhsh
Physics-informed neural networks (PINNs) have been recognized as a viable alternative to conventional numerical solvers for Partial Differen… (voir plus)tial Equations (PDEs). The main appeal of PINNs is that since they directly enforce the PDE equation, one does not require access to costly ground truth solutions for training the model. However, a key challenge is their limited generalization across varied initial conditions. Addressing this, our study presents a novel Physics-Informed Transformer (PIT) model for learning the solution operator for PDEs. Using the attention mechanism, PIT learns to leverage the relationships between its initial condition and query points, resulting in a significant improvement in generalization. Moreover, in contrast to existing physics-informed networks, our model is invariant to the discretization of the input domain, providing great flexibility in problem specification and training. We validated our proposed method on the 1D Burgers’ and the 2D Heat equations, demonstrating notable improvement over standard PINN models for operator learning with negligible computational overhead.
2000-01-01
(publié)
www.semanticscholar.org