Frequency-compensated PINNs for Fluid-dynamic Design Problems
This work addresses the need for efficient surrogate models in fluid-dynamic design problems, such as for offshore structures or heat exchangers, but it is incremental as it builds on existing PINN methods by adding Fourier features.
The authors tackled the problem of learning a high-accuracy surrogate for incompressible fluid flow around a cylinder, a classical fluid-dynamics problem relevant to engineering designs like offshore structures, by proposing a physics-informed neural network (PINN) architecture that incorporates Fourier features. Their results show that this approach improves generalization performance over temporal domains and design spaces.
Incompressible fluid flow around a cylinder is one of the classical problems in fluid-dynamics with strong relevance with many real-world engineering problems, for example, design of offshore structures or design of a pin-fin heat exchanger. Thus learning a high-accuracy surrogate for this problem can demonstrate the efficacy of a novel machine learning approach. In this work, we propose a physics-informed neural network (PINN) architecture for learning the relationship between simulation output and the underlying geometry and boundary conditions. In addition to using a physics-based regularization term, the proposed approach also exploits the underlying physics to learn a set of Fourier features, i.e. frequency and phase offset parameters, and then use them for predicting flow velocity and pressure over the spatio-temporal domain. We demonstrate this approach by predicting simulation results over out of range time interval and for novel design conditions. Our results show that incorporation of Fourier features improves the generalization performance over both temporal domain and design space.