In fields such as physics and engineering
Partial differential equations (PDEs) are used to model complex physical processes and gain insight into the functioning of intricate natural systems. However, solving these equations can be time-consuming and computationally expensive. To address this, researchers have developed data-driven surrogate models that focus on computing the desired property of a solution rather than the entire solution itself. These surrogate models are trained on data generated by high-fidelity numerical solvers, but this approach is data-intensive and costly due to the need for a large number of simulations.
A new method for developing data-driven surrogate models
In a recent paper published in Nature Machine Intelligence, MIT’s professor of applied mathematics Steven G. Johnson, along with researchers from the MIT-IBM Watson AI Lab, IBM Research, Julia Lab, and Georgia Tech, propose a new method called “physics-enhanced deep surrogate” (PEDS) for developing data-driven surrogate models for complex physical systems. PEDS combines a low-fidelity physics simulator with a neural network generator, which is trained to match the output of the high-fidelity numerical solver. This approach aims to replace the inefficient trial-and-error process with systematic computer-aided simulation and optimization.
The advantages of PEDS surrogates
The authors demonstrate that PEDS surrogates can be up to three times more accurate than an ensemble of feedforward neural networks with limited data. They also show that PEDS significantly reduces the amount of training data required to achieve a target error of 5 percent, by at least a factor of 100. Developed using the Julia programming language, PEDS is efficient in terms of both computing resources and data.
Bridging the gap between simplified physical models and numerical solvers
PEDS provides a general data-driven strategy to bridge the gap between simplified physical models and brute-force numerical solvers that model complex systems. It offers accuracy, speed, data efficiency, and valuable physical insights into the process. By choosing its parameters smartly and leveraging automatic differentiation, PEDS achieves accuracy with a small number of parameters.
Overcoming the curse of dimensionality
One of the main challenges in using surrogate models in engineering is the curse of dimensionality, where the required training data increases exponentially with the number of model variables. PEDS addresses this challenge by incorporating information from both the data and field knowledge in the form of a low-fidelity model solver. This approach has the potential to enhance the accuracy of minimal models and make them predictive for surrogate model applications.
Potential applications and future prospects
The researchers believe that PEDS has the potential to be applied beyond the scope of their study. Complex physical systems governed by PDEs, such as climate modeling and seismic modeling, could greatly benefit from physics-inspired fast and explainable surrogate models like PEDS. These models can complement other emerging techniques and contribute to a wide range of applications. The research was supported by the MIT-IBM Watson AI Lab and the U.S. Army Research Office through the Institute for Soldier Nanotechnologies.Kindly read our copyright disclaimer here: https://cere-sync.com/dmca-copyrights-disclaimer/