Extensive deep neural networks for transferring small scale learning to large scale systems.

Area of Science:

• Computational Physics
• Materials Science
• Artificial Intelligence

Background:

• Accurate prediction of system properties (energy, entropy) is crucial for understanding large-scale physical phenomena.
• Current methods like density functional theory (DFT) are computationally intensive, limiting their application to smaller systems.
• Deep neural networks (DNNs) offer potential for faster simulations but require efficient architectures for large-scale problems.

Purpose of the Study:

• To introduce a novel, physically-motivated deep neural network (DNN) architecture for efficient inference of extensive parameters in large systems.
• To demonstrate the scalability and accuracy of this DNN approach across diverse physical systems.
• To enable rapid, high-accuracy predictions for systems at scales previously inaccessible to traditional computational methods.

Main Methods:

• Developed an energy-driven neural network (EDNN) utilizing domain decomposition with overlapping context regions, informed by physical interaction length scales.
• Trained and validated the EDNN on the Ising model and hexagonal/graphene-like lattice datasets.
• Evaluated EDNN performance against Density Functional Theory (DFT) for accuracy and speed.

Main Results:

• The EDNN accurately predicted the total energy of a 60-atom system in 57 milliseconds, comparable to DFT.
• Demonstrated the EDNN's capability for massively parallel evaluation without inter-node communication.
• Achieved DFT-comparable accuracy for a 35.2 million atom system (1.0 μm²) in under 25 minutes.

Conclusions:

• Physically-motivated DNNs, specifically EDNNs, provide a scalable and efficient solution for inferring properties of large physical systems.
• EDNNs offer a significant speedup over traditional methods like DFT, enabling simulations at unprecedented scales.
• This approach opens new possibilities for materials science and condensed matter physics research at mesoscopic and macroscopic length scales.