Efficient Deep Learning-Based Models for Physics Simulation and Computational
Design
Advisor: Dr. Hadi Meidani
Scientific computing problems are widely used in an array of problems with applications
ranging from micro- to macro-world in the field of physics, biology, material science, and civil
and mechanical engineering. Many scientific computing problems such as design optimization,
and design space exploration require resource-intensive repetitive simulation runs of a model
with different input values. For systems characterized by numerous input parameters, the
response calculation is particularly challenging as one also has to deal with the curse of
dimensionality, which is the exponential increase in the volume of the input space, as the
number of parameters increases linearly. Many real-world computational problems, governed
by partial differential equations, require running high-fidelity simulations of physical systems,
using numerical methods such as finite element, and thus are often limited by the available
computational resources. While data-driven and physics-informed deep learning based
surrogate models have demonstrated success in tackling many of these problems, they still
grapple with limitations in generalizability across problems, ability to handle complex domains
and dependence on high data quality (for supervised models).
The overarching objective of this research is to take a step toward addressing these
computational challenges and contribute to the promotion of efficient computational
approaches based on deep learning for scientific computing problems such as physics
simulations and computational design. In particular, and in moving toward this objective, we
introduce various deep learning approaches, both data-driven and physics-informed, for fast
and efficient modeling of physical systems. First, we tackle supervised deep learning
algorithms, primarily Variational Autoencoders (VAEs) and Graph Neural Networks (GNNs)
and their applications for various array of problems such as Robust Topology Optimization
(RTO), time-independent physics simulations and multi-fidelity methods. In particular, we
introduce multi-fidelity architectures for VAE and GNN for improving the computational
efficiency of the models. We also propose novel GNN architectures for accurate evaluation of
time-independent physical systems. Then, we introduce two variants of physics-informed
neural network (PINN), an unsupervised model, namely FO-PINN and PINN-FEM, to tackle
some of the challenges of PINNs, including strong imposition of boundary conditions, and
solving higher-order PDEs and parameterized systems. We verify the accuracy and efficiency
of the proposed methods through a variety of engineering applications. The performance of the
proposed approaches in this research, thus, significantly extend the application of scientific
deep learning models for simulating complex systems in science and engineering.