arXiv:2606.10562v1 Announce Type: cross Abstract: We propose a new optimization method, the Nystr\"om-enhanced relaxed scalar auxiliary variable method (N-RSAV), which incorporates curvature information into the RSAV framework to accelerate convergence while preserving an unconditional modified energy dissipation law. Existing RSAV-based methods rely solely on first-order information and often suffer from slow convergence, particularly for ill-conditioned problems such as those arising in physics-informed neural networks (PINNs). To address this limitation, we design the linear operator in the
The continuous growth in demand for more complex AI models and scientific computing necessitates more efficient optimization algorithms to handle large and ill-conditioned problems.
Improved optimization techniques, particularly for physics-informed neural networks (PINNs), are critical for accelerating AI development and scientific discovery, potentially lowering computational costs and reducing training times.
The proposed N-RSAV method offers a more robust and faster convergence for specific, challenging optimization problems, which could enable more sophisticated AI applications and scientific simulations.
- · AI researchers
- · High-performance computing (HPC) sector
- · Deep learning practitioners
- · Physics-informed neural network developers
- · Developers reliant solely on first-order optimization methods
Faster training and deployment of advanced AI models and complex scientific simulations.
Reduced computational resource needs for certain types of AI, potentially freeing up compute capacity or lowering the barrier to entry for developing complex models.
Acceleration of research in fields utilizing PINNs, leading to breakthroughs in areas like materials science, climate modeling, or drug discovery.
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