AI 中文总结
本研究提出Kastor微调策略，通过两阶段推理、均值预测正则化等方法改进物理基础模型，在The Well数据集上实现比Walrus更优的PDE仿真性能，降低预测误差并提升效率。
AI 中文摘要
机器学习提供了一条有前景的途径，可通过将计算成本高昂的传统偏微分方程（PDE）求解器替换为快速、可微分的代理模型，从而加速物理仿真。然而，标准的自回归机器学习模拟器往往会在长时序范围内出现误差累积，且难以捕捉复杂物理系统的随机性。在本文中，我们提出了Kastor这一综合方法，用于将确定性物理基础模型适配为高效且准确的生成式代理模型。首先，我们引入了两阶段推理方案，将大步长因果自回归模型与非因果时间超分辨率网络相结合，在显著降低误差累积的同时最小化计算成本。其次，我们提出了均值预测正则化（MPR）这一新的训练目标，该目标约束生成式模型在零噪声条件下预测确定性分布均值，这种正则化大幅提升了功能生成网络（FGN）和基于扩散的模拟器的性能与稳定性。最后，我们证明，结合空间梯度匹配可提升仿真的准确性和物理保真度，这一点通过功率谱密度得到了衡量。在基准The Well的各类仿真数据集上进行的广泛评估表明，借助这些组件，我们的模型在预测准确性、频谱一致性和计算效率方面优于对比方法。与基于Walrus微调方法的参考模型相比，我们的模型在预测方面平均降低了42.9%的误差，且在方差归一化均方根误差（VRMSE）指标上，在10个数据集中有8个优于Walrus。
英文摘要
Machine learning offers a promising avenue to accelerate physical simulations by replacing computationally expensive traditional Partial Differential Equation (PDE) solvers with fast, differentiable surrogate models. However, standard auto-regressive ML emulators often suffer from error accumulation over long horizons and struggle to capture the stochasticity of complex physical systems. In this paper, we propose Kastor, a comprehensive methodology to adapt a deterministic physics foundation model into a highly efficient and accurate generative surrogate. First, we introduce a two-stage inference scheme that combines a large-stride causal auto-regressive model with a non-causal temporal super-resolution network, significantly reducing error accumulation while minimizing computational cost. Second, we present Mean prediction regularization (MPR), a novel training objective that constrains the generative model to predict the deterministic distribution mean under null noise conditioning. This regularization dramatically improves the performance and stability of both Functional Generative Networks (FGN) and diffusion-based emulators. Finally, we demonstrate that incorporating spatial gradient matching improves the accuracy and physical fidelity of the simulations as measured by power spectrum density. Extensive evaluations on diverse simulation datasets of the benchmark The Well show that with these components, our model outperforms competing methods in forecasting accuracy, spectral consistency, and computational efficiency. Our model achieves a 42.9% average reduction in forecasting compared to our reference based on the Walrus finetuning methodology, and outperforms Walrus for 8 out of 10 datasets on variance-normalized RMSE (VRMSE).
Comments34 pages, 32 figures
