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"... In a new study, researchers developed a new approach to developing surrogate models. This strategy uses physics simulators to help train neural networks to match the output of the high-precision numerical systems. The aim is to generate accurate results with the help of expert knowledge in a field—in this case, physics—instead of merely throwing a lot of computational resources at these problems to find solutions using brute force.
The scientists tested what they called physics-enhanced deep surrogate (PEDS) models on three kinds of physical systems. These included diffusion, such as a dye spreading in a liquid over time; reaction-diffusion, such as diffusion that might take place following a chemical reaction; and electromagnetic scattering.
The researchers found these new models can be up to three times as accurate as other neural networks at tackling partial differential equations. At the same time, these models needed only about 1,000 training points. This reduces the training data required by at least a factor of 100 to achieve a target error of 5 percent. ..."
From the abstract:
"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."
Physics-enhanced deep surrogates for partial differential equations (no public access)
Fig. 1: Diagram of PEDS. Researchers have found that numerical surrogates (symbolized here as a cartoon of James Clerk Maxwell) can arrive at solutions to hard mathematical problems that had previously required high-precision, brute-force math—symbolized by the Maxwell daguerreotype.
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