Physics-enhanced deep surrogates for partial differential equations

Many physics and engineering applications demand partial differential equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an efficient alternative but come with a substantial cost of training. Emerging applications would benefit from surrogates with an improved accuracy–cost tradeoff when studied at scale. Here we present a ‘physics-enhanced deep-surrogate’ (PEDS) approach towards developing fast surrogate models for complex physical systems, which is described by PDEs. Specifically, a combination of a low-fidelity, explainable physics simulator and a neural network generator is proposed, which is trained end-to-end to globally match the output of an expensive high-fidelity numerical solver. Experiments on three exemplar test cases, diffusion, reaction–diffusion and electromagnetic scattering models, show that a PEDS surrogate can be up to three times more accurate than an ensemble of feedforward neural networks with limited data (approximately 103 training points), and reduces the training data need by at least a factor of 100 to achieve a target error of 5%. Experiments reveal that PEDS provides a general, data-driven strategy to bridge the gap between a vast array of simplified physical models with corresponding brute-force numerical solvers modelling complex systems, offering accuracy, speed and data efficiency, as well as physical insights into the process. Data-driven surrogate models are used in computational physics and engineering to greatly speed up evaluations of the properties of partial differential equations, but they come with a heavy computational cost associated with training. Pestourie et al. combine a low-fidelity physics model with a generative deep neural network and demonstrate improved accuracy–cost trade-offs compared with standard deep neural networks and high-fidelity numerical solvers.