Physics-enhanced deep surrogates for partial differential equations
This work addresses the need for faster and more data-efficient surrogate models in physics and engineering applications, offering an incremental improvement over existing data-driven methods.
The paper tackles the problem of efficiently evaluating Partial Differential Equations (PDEs) by proposing a physics-enhanced deep surrogate (PEDS) approach, which combines a low-fidelity physics simulator with a neural network to match high-fidelity solver outputs, resulting in up to 3× higher accuracy with limited data and reducing training data needs by at least a factor of 100 to achieve a 5% error target.
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 significant cost of training. Emerging applications would benefit from surrogates with an improved accuracy-cost tradeoff, while 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 testcases, diffusion, reaction-diffusion, and electromagnetic scattering models, show that a PEDS surrogate can be up to 3$\times$ more accurate than an ensemble of feedforward neural networks with limited data ($\approx 10^3$ 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 modeling complex systems, offering accuracy, speed, data efficiency, as well as physical insights into the process.