Physics-guided machine learning (PGML) has become a prevalent approach in studying scientific systems due to its ability to integrate scientific theories for enhancing machine learning (ML) models. However, most PGML approaches are tailored to isolated and relatively simple tasks, which limits their applicability to complex systems involving multiple interacting processes and numerous influencing features. In this paper, we propose a \textit{\textbf{P}hysics-\textbf{G}uided \textbf{F}oundation \textbf{M}odel (\textbf{PGFM})} that combines pre-trained ML models and physics-based models and leverages their complementary strengths to improve the modeling of multiple coupled processes. To effectively conduct pre-training, we construct a simulated environmental system that encompasses a wide range of influencing features and various simulated variables generated by physics-based models. The model is pre-trained in this system to adaptively select important feature interactions guided by multi-task objectives. We then fine-tune the model for each specific task using true observations, while maintaining consistency with established physical theories, such as the principles of mass and energy conservation. We demonstrate the effectiveness of this methodology in modeling water temperature and dissolved oxygen dynamics in real-world lakes. The proposed PGFM is also broadly applicable to a range of scientific fields where physics-based models are being used.

翻译：物理引导机器学习已成为研究科学系统的主流方法，因其能够整合科学理论以增强机器学习模型。然而，大多数物理引导机器学习方法针对孤立且相对简单的任务定制，这限制了其在涉及多个相互作用过程及众多影响特征的复杂系统中的适用性。本文提出一种**物理引导基础模型**，该模型结合了预训练的机器学习模型与基于物理的模型，并利用其互补优势以改进对多个耦合过程的建模。为有效进行预训练，我们构建了一个模拟环境系统，该系统涵盖广泛的影响特征以及由基于物理的模型生成的各种模拟变量。模型在此系统中通过多任务目标引导自适应地选择重要的特征交互进行预训练。随后，我们使用真实观测数据对每个特定任务进行模型微调，同时保持与已确立的物理理论（如质量与能量守恒原理）的一致性。我们在真实湖泊的水温和溶解氧动态建模中验证了该方法的有效性。所提出的物理引导基础模型也广泛适用于其他正在使用基于物理模型的科学领域。