Physics-Informed Neural Networks for Approximating Numerical Model Errors and Superresolution of Finite Element Solutions for a Two-Dimensional Elastic Plate
Integrating physics-informed loss functions into neural networks enhances their ability to approximate numerical model errors and perform superresolution of finite element solutions, surpassing purely data-driven approaches.
복잡한 경계 조건을 가진 Navier-Stokes 방정식 해결을 위한 Soft 및 Hard 제약 조건의 상호 보완적 Physics-Informed Neural Network
복잡한 경계 조건을 가진 Navier-Stokes 방정식을 효과적으로 풀기 위해 Soft 및 Hard 제약 조건을 결합한 새로운 Physics-Informed Neural Network 방법론을 제시한다.
Physics-Informed Neural Networks for Solving Allen-Cahn Equations with Preserved Energy Dissipation: A Novel Approach
This research paper introduces a novel Physics-Informed Neural Network (PINN) approach for solving Allen-Cahn equations, enhancing accuracy by incorporating energy dissipation as a constraint within the learning process.
뉴럴 컨쥬게이트 플로우: 플로우 구조를 갖춘 물리 정보 기반 아키텍처
뉴럴 컨쥬게이트 플로우(NCF)는 위상 켤레를 통해 정확한 플로우 구조를 갖추도록 설계되어, 일반 미분 방정식(ODE)의 잠재적 dynamcis를 효율적으로 추정하고 외삽할 수 있는 새로운 물리 정보 기반 신경망 아키텍처입니다.
Neural Conjugate Flows: A Novel Physics-Informed Neural Network Architecture for Solving and Extrapolating Dynamical Systems
Neural Conjugate Flows (NCFs) offer a novel architecture for physics-informed neural networks, outperforming traditional PINNs and Neural ODEs in extrapolating dynamical systems by leveraging topological flow conjugation for enhanced causality and efficiency.
KH-PINN: Using Physics-Informed Neural Networks to Predict Kelvin-Helmholtz Instability in Multiscale Flows
KH-PINN, a novel physics-informed neural network framework, accurately reconstructs complex Kelvin-Helmholtz instability flows and infers unknown parameters from sparse, noisy data by incorporating multiscale embedding and small-velocity amplification strategies.
Regression-Based Physics-Informed Neural Networks (Reg-PINNs) for Improved Magnetopause Location Prediction
Integrating physics-inspired empirical models into neural networks (Reg-PINNs) enhances the accuracy and generalizability of magnetopause location prediction, outperforming traditional empirical models and standard neural networks.
可分離物理信息化柯爾莫哥洛夫-阿諾德網路 (SPIKANs)
SPIKANs，一種新型可分離物理信息化神經網路架構，有效解決了傳統 PINNs 在處理高維偏微分方程時遇到的計算瓶頸，顯著提升了訓練速度和效率。
분리 가능한 물리 정보 기반 콜모고로프-아놀드 네트워크 (SPIKAN) 소개
SPIKAN은 고차원 편미분 방정식을 효율적으로 풀기 위해 변수 분리 원리를 PIKAN에 적용한 새로운 신경망 아키텍처로, 정확도를 유지하면서도 훈련의 계산 복잡성을 크게 줄여줍니다.
Separable Physics-Informed Kolmogorov-Arnold Networks (SPIKANs): A Novel Architecture for Solving High-Dimensional PDEs
SPIKANs, a novel architecture for physics-informed machine learning, leverages the principle of separation of variables to enhance the efficiency of Kolmogorov-Arnold Networks (KANs) in solving high-dimensional partial differential equations (PDEs).
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