arXiv:2605.25786v1 Announce Type: new Abstract: Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural operators offer a fast alternative, they typically rely on large-scale labeled datasets or struggle with unstable training dynamics when using physics-informed residual losses. We propose \textsc{NPSolver}, a neural Poisson solver trained without solution labels via iterative physics supervision. Instead of rely
Advances in neural networks are allowing for more sophisticated and efficient approaches to long-standing computational challenges in scientific computing, driven by increasing compute availability and algorithmic innovation.
Efficiently solving complex scientific equations is foundational for breakthroughs across many engineering and scientific disciplines, and improved speed without large datasets could democratize advanced simulation capabilities.
The ability to solve complex Poisson equations rapidly and without extensive labeled datasets significantly reduces the computational bottleneck for various scientific and engineering applications, potentially accelerating R&D cycles.
- · Scientific computing researchers
- · Engineering R&D sectors
- · AI hardware manufacturers
- · Simulation software developers
- · Traditional iterative solver developers
- · Organizations reliant on large labeled datasets for neural operators
Faster and more accurate simulations in fields like fluid dynamics, electromagnetics, and material science become widely accessible.
Accelerated design and optimization cycles for new materials, devices, and industrial processes, leading to novel products and efficiencies.
Reduced time-to-market for complex scientific and engineering solutions, potentially impacting global competitiveness and technological leadership.
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