Feb. 13, 2024, 5:42 a.m. | Zheyuan Hu Zhongqiang Zhang George Em Karniadakis Kenji Kawaguchi

cs.LG updates on arXiv.org arxiv.org

The Fokker-Planck (FP) equation is a foundational PDE in stochastic processes. However, curse of dimensionality (CoD) poses challenge when dealing with high-dimensional FP PDEs. Although Monte Carlo and vanilla Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimension increases, surpassing the precision of numerical simulations and resulting in …

challenge cs.ai cs.lg cs.na dimensionality dimensions equation errors math.ds math.na networks neural networks numerical physics physics-informed processes stat.ml stochastic

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