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Since the time of Isaac Newton, the fundamental laws of nature in optics, acoustics, engineering, electronics, etc. all boil down to important broad equations. Now, researchers have discovered a new way to use brain-inspired neural networks to solve these equations much more efficiently than before, with numerous potential applications in science and engineering. It is now possible.

In modern science and engineering, __partial differential equation__ help model __complex physical systems with multiple rates of change, such as those that vary over both space and time__.they will help __model__ It can be all kinds of events, such as the flow of air past the wings of an airplane, the spread of pollutants in the air, or the collapse of a star into a black hole.

To solve these difficult equations, scientists have traditionally used high-precision numerical methods. However, these executions can be very time-consuming and computationally resource intensive.

A simpler alternative now exists, known as a data-driven surrogate model.These models include: __neural network__, trained on data from a numerical solver to predict what answers will be produced. However, these still require large amounts of data from numerical solvers for training. As the size of these models grows, the amount of data required increases exponentially, making this strategy difficult to scale, said study lead author Raphael, a computational scientist at Georgia Tech in Atlanta.・Mr. Pestory said.

In a new study, researchers developed a new approach to developing surrogate models. This strategy uses a physics simulator to train a neural network to match the output of a high-precision numerical system. The goal is to leverage expertise in a field (in this case, physics) to produce accurate results, rather than simply throwing large amounts of computational resources at these problems and finding solutions by brute force. That’s it.

The researchers say that numerical surrogates (symbolized here as a cartoon of James Clerk Maxwell) solve difficult mathematical problems that previously required precision and brute-force mathematics, symbolized by the Maxwell daguerreotype. discovered that it is possible to arrive at a solution. Massachusetts Institute of Technology

The scientists tested what they call a physically enhanced deep surrogate (PEDS) model on three different physical systems. These include diffusion, such as dyes that spread through a liquid over time. reaction diffusion. such as diffusion that can occur after a chemical reaction. and electromagnetic scattering.

The researchers found that these new models can achieve up to three times more accuracy than other neural networks when tackling partial differential equations. At the same time, these models required only about 1,000 training points. This reduces the training data required to achieve a target error of 5% by at least a factor of 100.

“The idea is very intuitive: you let the neural network do the learning, and you let the scientific model do the science,” Pestory says. “PEDS shows that the combination of both is much greater than the sum of its parts.”

Potential uses for the PEDS model include “accelerating the simulation of complex systems that appear everywhere in engineering, including weather forecasting, carbon capture, and nuclear reactors, to name a few,” PEDS says. says Mr.

scientists explained in detail __their discoveries__ in diary *nature machine intelligence*.

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