arXiv:2606.18759v1 Announce Type: cross Abstract: The concept of geodesic-like curves was introduced by Chen in 2010 as a method for estimating shortest paths (geodesics) on parametric surfaces, with its convergence established theoretically. However, an efficient numerical computational framework has not yet been developed. In this paper, we propose an elegant and efficient approach for computing geodesic-like curves by leveraging deep learning and Physics-Informed Neural Networks (PINNs). Under the proposed framework, not only can single parametric surfaces be handled efficiently, but a broa
The increasing maturity of AI, particularly Physics-Informed Neural Networks (PINNs), is enabling breakthroughs in computationally intensive problems previously theoretical or inefficient.
This development allows for more accurate and efficient computation of complex geometric paths, which has implications across engineering, design, and simulation, reducing development cycles and improving product performance.
The prior theoretical understanding of geodesic-like curves can now be practically and efficiently applied using deep learning, transforming their utility from conceptual to an accessible computational tool.
- · AI/ML researchers
- · Computer graphics
- · CAD/CAE software developers
- · Robotics
- · Traditional numerical methods (in specific applications)
- · Manual geodesic approximation techniques
More efficient and accurate path planning in complex 3D environments becomes feasible.
This could lead to advancements in areas like autonomous navigation, material science (for optimal stress distribution), and medical imaging (for surgical path guidance).
The broader application of PINNs to other challenging physics problems might accelerate innovation in diverse scientific and engineering fields, leading to new design paradigms and possibly new industries.
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Read at arXiv cs.LG