The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel method of the graph transformation model construction, combining generative and dynamical viewpoints to give a fully automated data-driven model inference method. The method takes the input dynamical properties, given as a "snapshot" of the dynamics encoded by explicit transitions, and constructs a compatible model. The obtained model is guaranteed to be minimal, thus framing the approach as model compression (from a set of transitions into a set of rules). The compression is permissive to a lossy case, where the constructed model is allowed to exhibit behavior outside of the input transitions, thus suggesting a completion of the input dynamics. The task of graph transformation model inference is naturally highly challenging due to the combinatorics involved. We tackle the exponential explosion by proposing a heuristically minimal translation of the task into a well-established problem, set cover, for which highly optimized solutions exist. We further showcase how our results relate to Kolmogorov complexity expressed in terms of graph transformation.

翻译：生命科学领域数据量的爆炸式增长，正推动着对表达性模型与计算方法的需求。图变换作为一种动态系统模型，具有广泛的应用场景。我们提出了一种新颖的图变换模型构建方法，通过结合生成性与动力学视角，实现完全自动化的数据驱动模型推断方法。该方法将输入动力学特性（以显式转换编码的动态"快照"形式给出）作为输入，并构建兼容的模型。所得模型被保证具有最小性，从而将该方法界定为模型压缩（从一组转换压缩为一组规则）。该压缩允许有损情况，即所构建模型可表现出输入转换之外的行为，从而实现对输入动态的补全。由于涉及组合优化，图变换模型推断任务自然具有极高挑战性。我们通过将任务启发式地最小化转化为成熟的集合覆盖问题（存在高度优化求解方案），以此应对指数级爆炸难题。进一步地，我们展示了研究结果如何与以图变换表达的柯尔莫哥洛夫复杂度相关联。