Bi-orthogonal fPINN: A physics-informed neural network method for solving time-dependent stochastic fractional PDEs

Understand

Fractional partial differential equations (FPDEs) can effectively represent anomalous transport and nonlocal interactions.

• However, inherent uncertainties arise naturally in real applications due to random forcing or unknown material properties.
• Mathematical models considering nonlocal interactions with uncertainty quantification can be formulated as stochastic fractional partial differential equations (SFPDEs).
• There are many challenges in solving SFPDEs numerically, especially for long-time integration since such problems are high-dimensional and nonlocal.