Neural Nets Speed Simulations

 Very interesting piece, Often the speed of complex simulations can be key for their use.  Below an introductory text, makes a good case.  Think of it as a way to insert learned knowledge into  a model.  More at the link.

Neural Networks Learn to Speed Up Simulations  By Chris Edwards

Communications of the ACM, May 2022, Vol. 65 No. 5, Pages 27-29   101145/3524015

Physical scientists and engineering research and development (R&D) teams are embracing neural networks in attempts to accelerate their simulations. From quantum mechanics to the prediction of blood flow in the body, numerous teams have reported on speedups in simulation by swapping conventional finite-element solvers for models trained on various combinations of experimental and synthetic data.

At the company's technology conference in November, Animashree Anandkumar, Nvidia's director of machine learning research and Bren Professor of Computing at the California Institute of Technology, pointed to one project the company worked on for weather forecasting. She claimed the neural network that team created could achieve results 100,000 times faster than a simulation that used traditional numerical methods to solve the partial differential equations (PDEs) on which the model relies.

Nvidia has packaged the machine learning techniques that underpin the weather-forecasting project into the Simnet software package it provides to customers. Its engineers have used the same approach to model the heat-sinks that cool the graphics processing units (GPUs) that power many other machine learning systems.

Other engineering companies are following suit. Both Ansys and Siemens Digital Industries Software are working on their own implementations to support their mechanical simulation product lines, adding to a growing body of open source initiatives such as the DeepModeling community.

A key reason for using machine learning for scientific simulations is that a collection of fully connected artificial neurons can act as a universal function approximator. Though training those neurons is computationally intensive, during the inference phase the neural network often will provide faster results than running simulators based on finite-element or numerical approximations to PDEs.

One approach to training a neural network for scientific simulation is to record experimental data and augment that with simulated data using numerical methods. For example, a simulation of the motion of a shock wave in a fluid-filled pipe might use a combination of sensor recordings and the solutions of the Bateman-Burgers equation.

The simulated data can be used to supply usable data for points where it is impossible to place a sensor to record pressure or simply to provide a higher density of data points. In principle, the machine learning model then will interpolate reasonable values for points where no data has been supplied. But the learned approximation can easily diverge from reality when checked against traditional models. The neural network likely will not learn the underlying patterns, just those that let it approximate the data points used for training.  .... '