用状态空间模型解决物理信息网络初始条件传播难题，误差降低86.3%。
Sub-Sequential Physics-Informed Learning with State Space Model
- 引入子序列建模的SSM框架，实现连续与离散的精准衔接。
- 在多个PDE任务中，相比最优基线误差下降最高达86.3%。
- 适合需要高精度求解偏微分方程的研究者和工程应用。
物理信息神经网络（PINNs）是基于深度学习的偏微分方程（PDEs）数值求解器。现有PINNs常因无法有效传播初始条件而失效。我们发现，这源于神经网络的简化偏好，以及PDE连续性与PINN离散采样之间的不匹配。研究表明，状态空间模型（SSM）可作为连续-离散的桥梁，实现初始条件的有效传播；通过构建中等粒度序列，可消除简化偏差。为此，我们提出PINNMamba，一种基于SSM的子序列建模新框架。实验表明，该方法相比当前最优架构，误差最高可降低86.3%。代码已开源：https://github.com/miniHuiHui/PINNMamba。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks (PINNs) are a kind of deep-learning-based numerical solvers for partial differential equations (PDEs). Existing PINNs often suffer from failure modes of being unable to propagate patterns of initial conditions. We discover that these failure modes are caused by the simplicity bias of neural networks and the mismatch between PDE's continuity and PINN's discrete sampling. We reveal that the State Space Model (SSM) can be a continuous-discrete articulation allowing initial condition propagation, and that simplicity bias can be eliminated by aligning a sequence of moderate granularity. Accordingly, we propose PINNMamba, a novel framework that introduces sub-sequence modeling with SSM. Experimental results show that PINNMamba can reduce errors by up to 86.3\% compared with state-of-the-art architecture. Our code is available at https://github.com/miniHuiHui/PINNMamba.
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