论文标题
深层物理校正器：一种物理学增强了用于求解随机微分方程的深度学习体系结构
Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations
论文作者
论文摘要
我们为由随机微分方程（SDE）控制的物理系统提出了一种新型的灰色盒建模算法。所提出的方法（称为深物理校正器（DPC））将用SDE代表的物理学与深神经网络（DNN）相结合。这里的主要思想是利用DNN来建模缺失的物理学。我们假设将不完整的物理与数据相结合将使模型可解释并允许更好地概括。与随机模拟器训练替代模型相关的主要瓶颈通常与选择合适的损耗函数有关。在文献中可用的不同损失函数中，我们在DPC中使用有条件的最大平均差异（CMMD）损失函数，因为其证明了其性能。总体而言，物理数据融合和CMMD允许DPC从稀疏数据中学习。我们说明了拟议的DPC在文献中的四个基准示例上的性能。获得的结果高度准确，表明它可能将其作为随机模拟器的替代模型的应用。
We propose a novel gray-box modeling algorithm for physical systems governed by stochastic differential equations (SDE). The proposed approach, referred to as the Deep Physics Corrector (DPC), blends approximate physics represented in terms of SDE with deep neural network (DNN). The primary idea here is to exploit DNN to model the missing physics. We hypothesize that combining incomplete physics with data will make the model interpretable and allow better generalization. The primary bottleneck associated with training surrogate models for stochastic simulators is often associated with selecting the suitable loss function. Among the different loss functions available in the literature, we use the conditional maximum mean discrepancy (CMMD) loss function in DPC because of its proven performance. Overall, physics-data fusion and CMMD allow DPC to learn from sparse data. We illustrate the performance of the proposed DPC on four benchmark examples from the literature. The results obtained are highly accurate, indicating its possible application as a surrogate model for stochastic simulators.
