论文标题
实体模拟的无限限制区域性化
Infinite-Fidelity Coregionalization for Physical Simulation
论文作者
论文摘要
在与物理模拟相关的应用程序中,多保真建模和学习很重要。它可以利用低保真性和高保真示例进行培训,以降低数据生成成本,同时仍取得良好的性能。尽管现有方法仅模型有限,离散的保真度,但实际上,忠诚度的选择通常是连续且无限的,这可能对应于连续的网格间距或有限的元素长度。在本文中,我们提出了无限的保真度核心化(IFC)。鉴于数据,我们的方法可以在连续无限的保真度中提取和利用丰富的信息来增强预测准确性。我们的模型可以插值和/或推断出对新型保真度的预测,这甚至可以高于训练数据的保真度。具体而言,我们引入了一个低维的潜在输出,作为保真度和输入的连续函数,并具有带有基矩阵的多个IT以预测高维解决方案输出。我们将潜在输出建模为神经普通微分方程(ODE),以捕获内部的复杂关系并整合整个连续保真度。然后,我们使用高斯工艺或其他颂歌来估计忠诚度变化的碱基。为了有效的推断,我们将碱基重组为张量,并使用张量 - 高斯变异后部为大规模输出开发可扩展的推理算法。我们在计算物理学的几个基准任务中显示了我们方法的优势。
Multi-fidelity modeling and learning are important in physical simulation-related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation while still achieving good performance. While existing approaches only model finite, discrete fidelities, in practice, the fidelity choice is often continuous and infinite, which can correspond to a continuous mesh spacing or finite element length. In this paper, we propose Infinite Fidelity Coregionalization (IFC). Given the data, our method can extract and exploit rich information within continuous, infinite fidelities to bolster the prediction accuracy. Our model can interpolate and/or extrapolate the predictions to novel fidelities, which can be even higher than the fidelities of training data. Specifically, we introduce a low-dimensional latent output as a continuous function of the fidelity and input, and multiple it with a basis matrix to predict high-dimensional solution outputs. We model the latent output as a neural Ordinary Differential Equation (ODE) to capture the complex relationships within and integrate information throughout the continuous fidelities. We then use Gaussian processes or another ODE to estimate the fidelity-varying bases. For efficient inference, we reorganize the bases as a tensor, and use a tensor-Gaussian variational posterior to develop a scalable inference algorithm for massive outputs. We show the advantage of our method in several benchmark tasks in computational physics.