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This paper introduces Geometric Kolmogorov-Arnold Networks (GeoKAN), a family of geometry-aware models that learn Riemannian metrics to adapt coordinates for improved function approximation and physics-informed learning.
This paper proposes a new architecture that augments Flux Neural Operators with recurrent Vision Transformers to solve conservation laws as a foundation model. It demonstrates robust generalization and long-time prediction capabilities across diverse conservative systems without explicit access to governing equations.
This paper proposes a self-supervised physics-informed neural network (PINN) framework with a learnable blending neuron to adaptively balance physics-based and data-driven losses, and integrates transfer learning to improve efficiency under data scarcity. It is validated on liquid-metal miniature heat sink CFD data with only 87 datapoints, achieving under 8% error.