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This paper presents AD-TLERT, a unified GPU-accelerated framework for time-lapse electrical resistivity tomography inversion based on automatic differentiation, enabling efficient and flexible hydrologic monitoring with significant speedup.
This arXiv paper introduces the Edge-Conditioned Spectral Operator (ESO), a spectral neural operator that uses local edge-wise variations to adapt global spectral mixing, improving performance on physics-sensitive PDE benchmarks.
This paper proposes FALM-PINN, an alternating Levenberg-Marquardt training framework for physics-informed neural networks that uses Fourier-enhanced features to address spectral bias and representation-coefficient coupling, achieving up to two orders of magnitude lower errors on high-frequency and nonlinear PDEs.
Introduces LLT, a transformer-based neural operator that combines linear global attention with local spatial mixing for PDE learning. It achieves competitive accuracy and faster training compared to baselines on multiple PDE problems.
AutoPDE is a code agent that explicitly represents solver strategies for partial differential equations, improving pass rate by 14.2% over baselines on the PDE Agent Bench.
Functional Attention is a novel attention mechanism that reinterprets attention as a functional correspondence between adaptive bases, replacing softmax affinities with structured linear operators inspired by geometric functional maps. The method achieves state-of-the-art performance on operator learning tasks including PDE solving and 3D segmentation while remaining resolution-invariant.
This paper investigates the generalization behavior of Fourier Neural Operators and Deep Operator Networks under distribution shifts in a variable-coefficient wave equation, revealing that FNO struggles with high-frequency inputs while DeepONet shows milder degradation.
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.