Time-Fractional Diffusions
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Transformed Diffusion-Wave fPINNs: Enhancing Computing Efficiency for PINNs Solving Time-Fractional Diffusion-Wave Equations
arXiv:2506.11518v2 Announce Type: replace Abstract: We propose transformed Diffsuion-Wave fractional Physics-Informed Neural Networks (tDWfPINNs) for efficiently solving time-fractional diffusion-wave equations with fractional order $\alpha\in(1,2)$. Conventional numerical methods for these equations often compromise the mesh-free advantage of Physics-Informed Neural Networks (PINNs) or impose high computational costs when computing fractional derivatives. The proposed method avoids...
Convergence Rates of Continuous-Time Random Walks to Time-Fractional Diffusions with Unbounded Coefficients
arXiv:2605.31471v1 Announce Type: cross Abstract: We investigate uniform weak convergence rates for probabilistic numerical methods applied to backward time-fractional diffusion equations whose dynamics are driven by diffusions with possibly unbounded coefficients, such as the Geometric Brownian Motion. The fractional structure is represented through a random time-change by the inverse of a stable subordinator. To approximate the underlying fractional dynamics, we combine discrete Markov...