PDE-NET:一个灵活的深度架构,可以从数据中学习pde;我们用“u(t,·):t = t0,t1,···}”的问题来解决空间域上一系列物理量的测量问题,“u(t,·):t = t0,t1,···}”Ω今天的问题是价值取向的问题,我们的问题是“u(t,·):Ω7→R”。我们假设观测数据与PDE相关联,其一般形式如下: 我们的目标...
Comparing with existing approaches, PDE-Net 2.0 has the most flexibility and expressive power by learning both differential operators and the nonlinear response function of the underlying PDE model. Numerical experiments show that the PDE-Net 2.0 has the potential to uncover the hidden PDE of the ...
The basic idea of the proposed PDE-Net is to learn differential operators by learning convolution kernels (filters), and apply neural networks or other machine learning methods to approximate the unknown nonlinear responses. Comparing with existing approaches, which either assume the form of the ...
Numerical experiments show that the PDE-Net has the potential to uncover the hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment. 展开 关键词: Mathematics - Numerical Analysis Computer Science - Learning Computer Science ...
董彬团队在PDE-Net(2018)中探索机理与数据融合的方法论 董彬的研究历程从小波、偏微分方程(PDE)等传统数学方法的深入探索开始,这些工具曾为他的计算成像和医学影像分析研究奠定了重要理论和算法基础。2016年,他敏锐地察觉到深度学习技术在这些问题上可能带来的颠覆性变革,于是转向深度学习研究。在原有的理论研究思想指引...
PDE-Net 2.0has the most f l exibility and expressive power by learning both differential operators and the nonlinearresponse function of the underlying PDE model. Numerical experiments show that the PDE-Net 2.0has the potential to uncover the hidden PDE of the observed dynamics, and predict the ...
Comparing with existing approaches, PDE-Net 2.0has the most f l exibility and expressive power by learning both differential operators and the nonlinearresponse function of the underlying PDE model. Numerical experiments show that the PDE-Net 2.0has the potential to uncover the hidden PDE of the ...
hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment. 中文翻译: PDE-Net 2.0:使用数字符号混合深度网络从数据中学习PDE 偏微分方程(PDE)通常是根据经验观察得出的。但是,技术的最新发展使我们能够收集和存储大量数据,这为数据驱动的...
python train.py --cuda --gpu "0" --dataset "CAVE" --upscale_factor 4 --model_name "template" --nEpochs 50 python train.py --cuda --gpu "0" --dataset "CAVE" --upscale_factor 4 --model_name "pde-net" --nEpochs 100 --resume checkpoints/CAVE_x4/template_4_epoch_50.pth Tes...
TaylorPDENet Theory In this repository the code for theTaylorPDENetcan be found. It is based on the estimation of the derivatives contained in the PDE (Partial Differential Equation) with the Taylor Polyinomial. Pn(x,y)=∑q=0Q∑r=0Q−j(x−x0)j(y−y0)kq!r!⋅∂(q+r)f∂...