通过自动提取背景知识，让算法真正发现未知微分方程。
Knowledge-aware equation discovery with automated background knowledge extraction
- 用知识引导进化搜索，动态调整方程结构空间
- 在伯格斯、波动和科特韦格-德弗里斯方程上优于SINDy
- 兼顾专家经验与自由探索，适合复杂方程发现任务
在微分方程发现算法中，先验专家知识通常隐式约束方程形式，导致算法无法真正发现新方程。现有方法多局限于已知结构的系数恢复。本文提出一种新算法，利用自动或手动提取的背景知识，动态调整进化过程中的交叉与变异操作，使特定项更可能被生成，从而模拟专家选择但保留发现任意方程形式的可能性。实验表明，该方法在搜索稳定性和鲁棒性上优于SINDy算法，在伯格斯（Burgers）、波动（wave）和科特韦格-德弗里斯（Korteweg--De Vries）等合成方程上表现优异。
原文摘要 · Abstract (English)
In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations. Instead, most differential equation discovery algorithms try to recover the coefficients for a known structure. In this paper, we describe an algorithm that allows the discovery of unknown equations using automatically or manually extracted background knowledge. Instead of imposing rigid constraints, we modify the structure space so that certain terms are likely to appear within the crossover and mutation operators. In this way, we mimic expertly chosen terms while preserving the possibility of obtaining any equation form. The paper shows that the extraction and use of knowledge allows it to outperform the SINDy algorithm in terms of search stability and robustness. Synthetic examples are given for Burgers, wave, and Korteweg--De Vries equations.
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