Robust Variational Physics-Informed Neural Networks: A Detailed Analysis
Robust Variational Physics-Informed Neural Networks provide reliable error estimations in energy norms.
Fourier PINNs: Enhancing Physics-Informed Neural Networks with Adaptive Fourier Bases for Improved Accuracy in High-Frequency and Multi-Scale Solution Prediction
Fourier PINNs improve the accuracy of physics-informed neural networks (PINNs) in predicting high-frequency and multi-scale solutions by augmenting the architecture with adaptive Fourier bases, addressing the limitations of standard PINNs and strong boundary condition PINNs.
푸리에 PINN: 강력한 경계 조건에서 적응형 푸리에 기저까지
고주파수 및 다중 스케일 솔루션을 학습하는 데 어려움을 겪는 기존 PINN의 문제점을 해결하기 위해, 본 논문에서는 강력한 경계 조건(BC) 기반 PINN 아키텍처를 제안하고 푸리에 분석을 통해 그 효과를 입증합니다. 또한, 특정 경계 조건이나 문제 영역에 제한 없이 고주파수 성분 학습을 향상시키는 푸리에 PINN이라는 새로운 방법을 제시합니다.
HyResPINNs: A Novel Physics-Informed Neural Network Architecture for Solving Partial Differential Equations with Enhanced Accuracy and Robustness
HyResPINNs, a new class of physics-informed neural networks, leverage adaptive hybrid residual blocks combining standard neural networks and radial basis function networks to solve partial differential equations with superior accuracy, robustness, and the ability to capture both smooth and discontinuous solutions.
物理情報モデリングのためのニューラルネットワークとRBFコンポーネントの最適な組み合わせを学習する適応型ハイブリッド残差ネットワーク：HyResPINNs
HyResPINNsは、標準的なニューラルネットワークとRBFネットワークを組み合わせた新しい物理情報ニューラルネットワークアーキテクチャであり、滑らかさと非滑らかさの両方の特徴を効果的に捉え、従来のPINNよりも高い精度と堅牢性を実現する。
물리 정보 모델링을 위한 신경망 및 RBF 구성 요소의 최적 조합 학습을 위한 적응형 하이브리드 잔차 네트워크: HyResPINNs
HyResPINNs는 표준 신경망과 방사 기저 함수(RBF) 네트워크를 결합하여 기존 PINN보다 정확하고 효율적으로 복잡한 물리 시스템을 모델링하는 새로운 종류의 Physics-Informed Neural Network(PINN) 아키텍처입니다.
Enhancing Physics-Informed Neural Networks with Densely Multiplied Architectures for Improved Accuracy and Efficiency
Densely multiplied architectures significantly improve the accuracy and efficiency of Physics-Informed Neural Networks (PINNs) by enhancing their expressive power without increasing trainable parameters.
밀집 곱셈 연산을 활용한 고정밀 물리 정보 신경망 구조
본 논문에서는 기존의 완전 연결 신경망(FC-NN) 기반 물리 정보 신경망(PINN)의 정확도를 향상시키기 위해 밀집 곱셈 연산을 활용한 새로운 PINN 구조를 제안합니다.
Sinc Kolmogorov-Arnold Networks (SincKANs): A Novel Approach for Physics-Informed Neural Networks with Enhanced Singularity Handling
This paper introduces Sinc Kolmogorov-Arnold Networks (SincKANs), a novel neural network architecture that leverages Sinc interpolation to improve the handling of singularities in physics-informed neural networks (PINNs), making them more robust and accurate in solving partial differential equations.
Transport-Embedded Neural Networks for Simulating Fluid Mechanics
A novel neural network architecture, Transport-Embedded Neural Network (TENN), shows promise in simulating fluid mechanics problems by embedding physical transport laws directly into its structure, leading to improved accuracy and stability compared to traditional Physics-Informed Neural Networks (PINNs).
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