Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a data-driven closure approach based on memory embedding to provide physically correct boundary conditions at the interface. To enable the interface learning for hyperbolic systems by considering the domain of influence and wave structures into account, we put forth the concept of upwind learning toward a physics-informed domain decomposition. The promise of the proposed approach is shown for a set of canonical illustrative problems. We highlight that high-performance computing environments can benefit from this methodology to reduce communication costs among processing units in emerging machine-learning-ready heterogeneous platforms toward exascale era.

中文翻译：

---

多物理场和多尺度系统的界面学习

复杂的自然或工程系统包含多个特征尺度，多个时空域，甚至多个物理封闭定律。为了解决这些挑战，我们引入了一种界面学习范例，并提出了一种基于内存嵌入的数据驱动的闭合方法，以在界面上提供物理上正确的边界条件。为了通过考虑影响范围和波浪结构来实现双曲系统的界面学习，我们提出了迎风学习的概念走向物理信息域分解。对于一组规范的说明性问题，显示了所提出方法的前景。我们着重指出，高性能计算环境可以从这种方法中受益，以降低面向百亿美元时代的新兴机器学习就绪异构平台中处理单元之间的通信成本。