We introduce an adaptive refinement procedure for smart, and scalable abstraction of dynamical systems. Our technique relies on partitioning the state space depending on the observation of future outputs. However, this knowledge is dynamically constructed in an adaptive, asymmetric way. In order to learn the optimal structure, we define a Kantorovich-inspired metric between Markov chains, and we use it as a loss function. Our technique is prone to data-driven frameworks, but not restricted to. We also study properties of the above mentioned metric between Markov chains, which we believe could be of application for wider purpose. We propose an algorithm to approximate it, and we show that our method yields a much better computational complexity than using classical linear programming techniques.

翻译：我们提出了一种自适应细化方法，用于对动力系统进行智能且可扩展的抽象。我们的技术依赖于根据未来输出的观测结果划分状态空间，但这一知识是以自适应、非对称的方式动态构建的。为了学习最优结构，我们定义了一个受Kantorovich启发的马尔可夫链间度量，并将其作为损失函数。该技术适用于数据驱动框架，但并不局限于此。我们还研究了上述马尔可夫链间度量的性质，认为这些性质可能具有更广泛的应用价值。我们提出了一种近似该度量的算法，并证明该方法相比经典线性规划技术具有更好的计算复杂度。