Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains
arXiv:2606.31342v1 Announce Type: cross Abstract: Partial differential equations on unbounded domains are challenging because the exterior region must be represented without excessive truncation error. Truncation-based methods often require problem-dependent artificial boundary conditions, while global spectral bases may be inefficient for localized structures, irregular geometries, or solutions with different near-field and far-field behaviors. We propose a domain-decomposed randomized neural network framework for such problems. Different randomized subnetworks are assigned to different spati
The increasing complexity of scientific computing and the rapid advancements in AI/ML techniques for solving differential equations drive the need for more robust and efficient methods.
This development offers a more effective approach to solving complex physics-based problems in unbounded domains, which are common in engineering and scientific research, potentially accelerating simulation and design processes.
The proposed framework provides a generalized and potentially more accurate method for handling domain boundary conditions in partial differential equations, reducing truncation errors and the need for problem-specific artificial conditions.
- · Machine Learning Researchers
- · Computational Scientists
- · Engineering Simulation Software Providers
- · Aerospace and Defense Sectors
- · Traditional numerical methods reliant on manual boundary condition tuning
Improved accuracy and efficiency in physical simulations involving infinite or large domains using AI.
Faster design cycles and enhanced predictive capabilities in fields like fluid dynamics, electromagnetics, and astrophysics.
The democratization of complex simulation tools, allowing more researchers and engineers to tackle previously intractable problems with reduced expertise in numerical analysis.
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Read at arXiv cs.LG