Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however, while these methods have demonstrated state-of-the-art performance in both accuracy and computational efficiency, a significant challenge remains in their interpretability. Most existing methodologies prioritize predictive accuracy over clarity in the underlying mechanisms driving the model's decisions. Interpretability is crucial for trustworthiness and broader applicability, especially in scientific and engineering domains where neural PDE solvers might see the most impact. In this context, a notable gap in current research is the integration of symbolic frameworks (such as symbolic regression) into these solvers. Symbolic frameworks have the potential to distill complex neural operations into human-readable mathematical expressions, bridging the divide between black-box predictions and solutions.

翻译：偏微分方程（PDEs）在自然界中无处不在，从热传导、声波传播到量子系统等现象均由其建模。深度学习的最新进展催生了强大的神经求解器；然而，尽管这些方法在精度与计算效率上均展现出最优性能，其可解释性仍是一大关键挑战。现有方法大多将预测准确性置于模型决策机制透明性之上。在神经PDE求解器可能产生最大影响的科学与工程领域，可解释性对于提升模型可信度与拓宽应用范围至关重要。在此背景下，当前研究的一个显著空白在于将符号化框架（如符号回归）融入求解器中。符号化框架能够将复杂的神经运算提炼为人类可读的数学表达式，从而弥合黑箱预测与物理意义解之间的鸿沟。