Sepehr Mousavi


Last Name

Mousavi

First Name

Sepehr

ORCID

0009-0008-2919-1978

Organisational unit

09697 - De Lorenzis, Laura / De Lorenzis, Laura

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Publications 1 - 1 of 1
  • Region Interaction Graph Neural Operator: Solving Multi-Scale Time-Dependent Partial Differential Equations with Graph Neural Networks
    Item type: Master Thesis
    Mousavi, Sepehr (2024)
    Operator learning has emerged in recent years as a supervised machine learning framework for differentiable and fast physics simulations, with applications in PDE-constrained optimization, uncertainty quantification, and real-time decision support systems. In this thesis, we introduce a graph neural network architecture for operator learning that is discretization invariant, easily adaptable to unstructured meshes, and robust to input noise. Focusing on time-dependent partial differential equations, we aim to approximate a time-dependent solution operator. We present training techniques with temporal solution trajectories applicable to any neural operator to im- pose continuity in time, demonstrating that these techniques allow trained operators to effectively perform time interpolation and time extrapolation without compromising accuracy. The proposed architecture, with its relatively low number of parameters, is resilient to overfitting and scales well with both the size of the training dataset and the model size. The flexibility of graphs allows for the convenient imposition of complex boundary conditions. We present a method for imposing periodic boundary conditions and show that the architecture performs well for Dirichlet boundary conditions without any structural imposition on the boundaries. By introducing randomness into the model, we demonstrate the ability to quantify epistemic uncertainties, using them as indicators for potential approximation errors. Finally, we explore the working mechanisms of trained models by inspecting their intermediate latent states.
Publications 1 - 1 of 1