Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
arXiv:2604.09361v3 Announce Type: replace Abstract: This paper introduces the Stochastic-Dimension Frozen Sampled Neural Network (SD-FSNN), a novel computational framework for solving high-dimensional Gross-Pitaevskii equation (GPE) on unbounded domain. The proposed method circumvents the curse-of-dimensionality that plagues traditional discretizations and the computational bottlenecks of gradient-based neural network solvers through a synergistic combination of techniques. First, a prescribed Gaussian envelope encodes the far-field decay of the wavefunction, enabling a space-time separation w
The continuous drive to overcome computational limitations in complex scientific simulations, particularly in quantum mechanics, makes new algorithmic approaches like SD-FSNN highly relevant.
This development represents a significant step towards enabling more accurate and efficient simulation of high-dimensional quantum systems, which is crucial for advancements in materials science, drug discovery, and quantum computing.
The ability to solve high-dimensional Gross-Pitaevskii equations more efficiently on unbounded domains circumvents a major 'curse-of-dimensionality' bottleneck, opening new avenues for theoretical and applied research.
- · Quantum computing research
- · Materials science
- · Drug discovery
- · Computational physicists
- · Traditional simulation methods
- · Researchers dependent on gradient-based neural network solvers
More accurate and faster simulations of complex quantum phenomena become feasible.
Accelerated discovery of novel materials and more efficient drug development through advanced computational modeling.
Potential for new industrial applications previously limited by the compute-intensive nature of high-dimensional quantum simulations.
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