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Echo state network for coarsening dynamics of charge density waves.
Clement Dinh1, Yunhao Fan1, Gia-Wei Chern1
1University of Virginia, Department of Physics, Charlottesville, Virginia 22904, USA.
Physical Review. E
|January 21, 2026
Summary
Echo state networks (ESNs) efficiently model charge-density wave (CDW) dynamics in materials. This approach captures complex spatial-temporal patterns, offering scalable and transferable simulations for functional electron materials.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Computational Physics
Background:
- Echo state networks (ESNs) are a type of reservoir computing utilizing recurrent neural networks with sparse hidden layers.
- ESNs offer a simplified training process compared to other recurrent neural networks while effectively capturing complex spatial-temporal dynamics.
Purpose of the Study:
- To develop an ESN model for simulating the coarsening dynamics of charge-density waves (CDWs).
- To investigate the application of ESNs in modeling pattern formation in functional electron materials.
Main Methods:
- An ESN was constructed to model CDW dynamics within a semiclassical Holstein model.
- Inputs comprised local CDW order parameters; the output predicted the next time step's CDW order.
- Lattice symmetries were incorporated by carefully designing couplings between hidden layer and input nodes.
Main Results:
- The ESN successfully modeled the coarsening dynamics of CDWs, exhibiting checkerboard electron density modulation.
- The ESN demonstrated scalability and transferability, with models trained on smaller systems applicable to larger lattices.
Conclusions:
- ESNs provide an efficient and scalable method for dynamical modeling of pattern formation in electron materials.
- This work opens new possibilities for simulating complex dynamics in functional materials using reservoir computing.
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