arXiv:2606.09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics. In this work, we propose a conditional normalizing flow-based physics-informed neural network (PINN) framework for efficiently approximating the solution operator of the FPE for a whole range of initial conditions. Leveraging the Chapman-Kolmogorov equation for Markovian stochastic processes, the problem is reformulated into approximating a transition PDF starting at initial ti
The continuous advancements in AI and particularly neural network architectures are enabling new approaches to solving complex mathematical problems with higher efficiency, driving current research in fields like stochastic dynamics.
Efficiently solving Fokker-Planck equations is critical for modeling complex systems in physics, finance, and engineering, and this AI-driven approach can significantly accelerate scientific discovery and technological development.
The ability to approximate solution operators for Fokker-Planck equations across varying initial conditions using conditional normalizing flows will make these models more adaptable and less computationally intensive for real-world applications.
- · AI researchers
- · Quantitative finance
- · Computational fluid dynamics
- · Pharmaceutical R&D
- · Traditional numerical methods specialists
- · High-latency simulation platforms
Improved predictive models for systems governed by stochastic processes will become more accessible.
This could lead to faster development cycles for new materials, drug discovery, and financial risk models.
The integration of such AI operators into general-purpose AI agents could enhance their ability to model and interact with complex physical and economic realities.
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Read at arXiv cs.LG