DAS-PINNs for high-dimensional partial differential equations: extending deep adaptive sampling to spacetime domains
arXiv:2606.06314v1 Announce Type: cross Abstract: Time-dependent high-dimensional partial differential equations (PDEs) with spatially localised and dynamically evolving solutions pose a fundamental challenge for physics-informed neural networks (PINNs), as uniform collocation sampling becomes increasingly ineffective in high-dimensional spatiotemporal domains. In this work, a deep adaptive sampling framework for PINNs is extended to the time-dependent setting by treating space and time as a unified domain without any explicit time marching. A normalising flow neural network model effectively
The continuous development in AI and machine learning techniques, particularly in physics-informed neural networks (PINNs), is driving new approaches to solve complex scientific computing problems.
This development enhances the capability of AI to solve high-dimensional partial differential equations, which are fundamental to simulations across various scientific and engineering fields.
The extension of deep adaptive sampling to spacetime domains for PINNs improves efficiency and accuracy in modeling complex time-dependent systems without traditional time-marching methods.
- · AI/ML researchers
- · Scientific computing sectors
- · Engineering simulation industries
- · High-performance computing
- · Traditional numerical methods for PDEs
- · Manual parameter tuning in complex simulations
More accurate and faster simulations become possible for complex physical phenomena, from fluid dynamics to quantum mechanics.
Accelerated discovery and design cycles in fields like materials science, drug discovery, and climate modeling due to enhanced simulation capabilities.
Potential for autonomous scientific discovery systems that can model, simulate, and predict complex systems with minimal human intervention.
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Read at arXiv cs.LG