Although machine learning (ML) is increasingly employed recently for mechanistic problems, the black-box nature of conventional ML architectures lacks the physical knowledge to infer unforeseen input conditions. This implies both severe overfitting during a dearth of training data and inadequate physical interpretability, which motivates us to propose a new kinematically consistent, physics-based ML model. In particular, we attempt to perform physically interpretable learning of inverse problems in wave propagation without suffering overfitting restrictions. Towards this goal, we employ long short-term memory (LSTM) networks endowed with a physical, hyperparameter-driven regularizer, performing penalty-based enforcement of the characteristic geometries. Since these characteristics are the kinematical invariances of wave propagation phenomena, maintaining their structure provides kinematical consistency to the network. Even with modest training data, the kinematically consistent network can reduce the $L_1$ and $L_\infty$ error norms of the plain LSTM predictions by about 45% and 55%, respectively. It can also increase the horizon of the plain LSTM's forecasting by almost two times. To achieve this, an optimal range of the physical hyperparameter, analogous to an artificial bulk modulus, has been established through numerical experiments. The efficacy of the proposed method in alleviating overfitting, and the physical interpretability of the learning mechanism, are also discussed. Such an application of kinematically consistent LSTM networks for wave propagation learning is presented here for the first time.
翻译:虽然机械学习(ML)最近越来越多地被用于机械学问题,但常规ML结构的黑箱性质缺乏物理知识,无法推断出意外的投入条件,这意味着在缺乏培训数据期间严重过度适应,物理解释能力不足,这促使我们提出一个新的运动一致、以物理为基础的ML模式。特别是,我们试图在不受到过度限制的情况下,对波浪传播中的逆向问题进行物理解释性学习,不至于受到过度限制。为了实现这一目标,我们使用长期短期内存(LSTM)网络,配有物理的、超光量驱动的常规化器,对特有的地理偏差进行基于惩罚的执行。由于这些特征是波波传播现象的动态变异性,因此保持其结构与网络的动态一致性。即使使用少量的培训数据,动态一致的网络也可以将普通LSTM预测的短期内测值减少约45%和55%。此外,对普通LSTM测序的测算性测算系统第一次提高了视野,因此,通过最优的机算性化的机算方法,也实现了这种测测算方法。