Development and Application of Hypernetworks for Discretization-Independent Surrogate Modeling of Physical Fields

Abstract

High-fidelity models (HFMs) of physical phenomena are frequently expressed using partial differential equations which require expensive and complex numerical methods for solution. This thesis develops discretization independent data-driven approaches for complexity reduction.

Recently, coordinate-based multi-layer-perceptron networks have been found to be effective at representing 3D objects and scenes by regressing volumetric implicit fields, with applications in computer graphics. A key distinction is that coordinate-inputs are taken pointwise instead of as full-domain solution snapshots, as is required for existing techniques based on convolutional neural networks and matrix decomposition, such as proper orthogonal decomposition. These concepts are leveraged and adapted in the context of physical-field surrogate modeling, and allow for full discretization independence where each solution may have a unique and varying domain, boundary, mesh topology, and operating condition.

Generalization across solution instances is achieved by conditioning the neural networks through a combination of local and global variables. Local conditioning relates to use of the signed-distance or minimum-distance function as an additional network input to provide geometric information. Global conditioning utilizes the problem design variables as the conditional input. Various methods of global conditioning are explored, including concatenation-based conditioning and the use of hypernetworks for full or partial network-weight conditioning. The methods are applied to predict solutions around complex, parametrically-defined geometries on non-parametrically-defined meshes with model predictions obtained many orders of magnitude faster than the full-order models.

The HFM surrogates are applied to a variety of steady-state problems, including 2D vehicle aerodynamics, jet-engine-compressor aerodynamics, the 2D Poisson equation with a source term, and finally 3D Ahmed body aerodynamics. Additionally, the HFM surrogates are used to drive aerodynamic design optimization of jet-engine-compressor airfoils in subsonic and transonic regimes, with orders-of-magnitude reduction in online time to attain optimal designs as compared to CFD-driven optimization. In summary, this work develops and demonstrates HFM surrogates with promising potential as practical tools in industrial analysis and design.