Partial differential equations (PDEs) are used in fields like physics and engineering to model complex physical processes, offering insight into some of the world’s most intricate systems. To solve these equations, researchers use high-fidelity numerical solvers, which are time-consuming and computationally expensive. A simplified alternative, data-driven surrogate models, compute the goal property of a solution to PDEs rather than the full solution. These models are trained on data generated by the high-fidelity solver to predict the output of the PDEs for new inputs; however, this process can be data-intensive and costly.
Research from MIT published in Nature Machine Intelligence introduces a method for developing efficient data-driven surrogate models for complex physical systems. The paper, authored by MIT professor Steven G. Johnson and researchers from the MIT-IBM Watson AI Lab, Julia Lab, and Georgia Tech, presents a “physics-enhanced deep surrogate” (PEDS), which combines a low-fidelity, explainable physics simulator with a neural network generator trained to match the output of a high-fidelity numerical solver.
The team aims to replace inefficient trial-and-error processes with systematic, computer-aided simulations and optimizations, making training these models more affordable compared to AI processes that require vast computing resources. Under test conditions, PEDS surrogates proved up to three times more accurate than an ensemble of feedforward neural networks with limited data, and reduced the training data needed by at least a factor of 100 to achieve a target error of 5 percent.
The researchers report that PEDS bridged the gap between simplified physical models and their respective brute-force numerical solvers, offering accuracy, speed, data efficiency, and physical insights into the process. To counter the “curse of dimensionality”, where needed training data increases exponentially with the number of model variables, PEDS leverages automatic differentiation technology and includes information from the field in the form of a low-fidelity model solver.
PEDS has revival potential for minimal models – stripped down, intuitive models from pre-2000 literature. The application of PEDS extends beyond what was shown in this study, with potential use in modeling various complex physical systems governed by PDEs, from climate modeling to seismic modeling.
This research, supported by the MIT-IBM Watson AI Lab and the U.S. Army Research Office, presents an efficient, affordable alternative to the existing problem of solving complex physical systems.
