Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To overcome this limitation, we propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations, including varying initial conditions, PDE coefficients, and training time horizons. PIDO exploits the shared underlying structure of dynamical systems with different properties by projecting PDE solutions into a latent space using auto-decoding. It then learns the dynamics of these latent representations, conditioned on the PDE coefficients. Despite its promise, integrating latent dynamics models within a physics-informed framework poses challenges due to the optimization difficulties associated with physics-informed losses. To address these challenges, we introduce a novel approach that diagnoses and mitigates these issues within the latent space. This strategy employs straightforward yet effective regularization techniques, enhancing both the temporal extrapolation performance and the training stability of PIDO. We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations. Additionally, we demonstrate the transferability of its learned representations to downstream applications such as long-term integration and inverse problems.

本研究针对物理信息神经网络（PINNs）在不同场景下泛化能力有限的问题，提出了一种新颖的物理信息神经偏微分方程求解器PIDO。PIDO通过将偏微分方程解投影到潜在空间，学习动态的潜在表示，显著提升了对多样偏微分方程配置的泛化能力，验证结果显示其在长期积分和逆问题等下游应用中的可转移性。 

通过潜在空间表示提升物理信息神经网络的泛化能力