Kernel-Adaptive PI-ELMs for Forward and Inverse Problems in PDEs with Sharp Gradients

arXiv — cs.LGTuesday, November 25, 2025 at 5:00:00 AM
  • The introduction of the Kernel-Adaptive Physics-Informed Extreme Learning Machine (KAPI-ELM) addresses challenges in solving partial differential equations (PDEs) with sharp gradients, enhancing the capabilities of existing physics-informed machine learning frameworks like PINNs and PI-ELMs. This new approach utilizes Bayesian optimization to refine Radial Basis Function (RBF) parameters, improving performance in both sharp gradient and smooth-flow scenarios.
  • This development is significant as it offers a more effective solution for complex PDEs, which are critical in various scientific and engineering applications. By overcoming limitations faced by traditional methods, KAPI-ELM can potentially lead to more accurate modeling and simulation in fields such as fluid dynamics and material science.
  • The advancement of KAPI-ELM reflects a broader trend in machine learning where adaptive methods are increasingly employed to tackle specific challenges in numerical simulations. This aligns with ongoing efforts to enhance the predictive capabilities of physics-informed frameworks, as seen in various studies focusing on hyperbolic flow equations and optimal sensor placements, indicating a growing interest in integrating physics with machine learning for improved problem-solving.
— via World Pulse Now AI Editorial System

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