A deep learning framework for jointly solving transient Fokker-Planck equations with arbitrary parameters and initial distributions
arXiv:2604.06001v2 Announce Type: replace-cross Abstract: Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting comprehensive parameter exploration and transient analysis. This paper introduces a deep learning-based pseudo-analytical probability solution (PAPS) that, via a single training process, simultaneously resolves transient FPE solutions for arbitrary multi-modal initial distributions, system parameters, a
The increasing complexity of stochastic systems and the computational demands of their analysis necessitate more efficient and scalable solutions, which deep learning is now positioned to provide.
This development significantly enhances the ability to model and understand complex dynamic systems with varying conditions, accelerating research and development in fields reliant on such simulations.
Traditional numerical methods for Fokker-Planck equations become less central, replaced by a deep learning framework capable of broader and more parallelized analysis across diverse parameters and initial states.
- · AI/ML researchers
- · Computational physicists
- · Engineers in complex systems design
- · Developers of traditional FPE solvers
- · Sectors reliant on slow, sequential computational analysis
More rapid and comprehensive exploration of parameter spaces in stochastic systems becomes feasible.
Accelerated design and optimization cycles for systems like autonomous agents, materials, or financial models.
New classes of AI models emerge that deeply integrate physical principles via enhanced equation solving capabilities.
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Read at arXiv cs.LG