Discretization-independent surrogate modeling of physical fields around variable geometries using coordinate-based networks

Abstract Numerical solutions of partial differential equations require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques aim to decrease computational expense while retaining dominant solution features and characteristics. Existing frameworks based on convolutional neural networks and snapshot-matrix decomposition often rely on lossy pixelization and data-preprocessing, limiting their effectiveness in realistic engineering scenarios. Recently, coordinate-based multilayer perceptron networks have been found to be effective at representing 3D objects and scenes by regressing volumetric implicit fields. These concepts are leveraged and adapted in the context of physical-field surrogate modeling. Two methods toward generalization are proposed and compared: design-variable multilayer perceptron (DV-MLP) and design-variable hypernetworks (DVH). Each method utilizes a main network which consumes pointwise spatial information to provide a continuous representation of the solution field, allowing discretization independence and a decoupling of solution and model size. DV-MLP achieves generalization through the use of a design-variable embedding vector, while DVH conditions the main network weights on the design variables using a hypernetwork. The methods are applied to predict steady-state solutions around complex, parametrically defined geometries on non-parametrically-defined meshes , with model predictions obtained in less than a second. The incorporation of random Fourier features greatly enhanced prediction and generalization accuracy for both approaches. DVH models have more trainable weights than a similar DV-MLP model, but an efficient batch-by-case training method allows DVH to be trained in a similar amount of time as DV-MLP. A vehicle aerodynamics test problem is chosen to assess the method’s feasibility. Both methods exhibit promising potential as viable options for surrogate modeling, being able to process snapshots of data that correspond to different mesh topologies.