Deep learning for simulating the evolution of condensed matter systems at the continuum scale: methods and...

Area of Science:

• Condensed matter physics
• Computational science

Background:

• Continuum models are crucial for studying complex systems but face computational challenges at high resolutions.
• Advancements in computational methods have been made, yet limitations persist for large-scale simulations.

Purpose of the Study:

• To review the state-of-the-art of neural network approaches for time-evolution problems.
• To systematize strategies and architectures used in neural network-based simulations.
• To showcase diverse applications and successful uses of these novel methods.

Main Methods:

• Literature inspection to identify and categorize neural network strategies for time-dependent evolutions.
• Distinguishing between data-driven and physics-informed neural network approaches.
• Analyzing hybrid methods and novel concepts combining data and physics.

Main Results:

• Neural networks show potential as fast and accurate alternatives to conventional numerical schemes.
• Various architectures and strategies are employed for time-dependent evolution simulations.
• Successful applications demonstrate the efficacy of neural networks in complex system modeling.

Conclusions:

• Neural network-based approaches present a promising avenue for accelerating scientific simulations.
• Challenges and drawbacks remain, requiring further development for widespread adoption as surrogates for conventional methods.
• Future research directions and potential developments are identified.