Fokker--Planck
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Related Articles from SNS
Operator learning for solving Fokker-Planck equations with various initial conditions
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...
Logarithmic Sobolev inequality and hypercontractivity for the Navier-Stokes Fokker-Planck operator
Announce Type: cross Abstract: The stochastic incompressible Navier-Stokes equations on $\TT^3$, completed by the fluctuation-dissipation noise, have a Fokker-Planck generator that decomposes into a self-adjoint Ornstein-Uhlenbeck (dissipative) part and an antisymmetric (convective) part. We prove two results about this generator. First, the logarithmic Sobolev inequality holds with the same optimal constant as the pure Ornstein-Uhlenbeck operator, $c_\mathrm{LSI} = \nu\lambda_1$ (where...
Safe and Energy-Aware Multi-Robot Density Control via PDE-Constrained Optimization for Long-Duration Autonomy
arXiv:2604.15524v3 Announce Type: replace Abstract: This paper presents a novel density control framework for multi-robot systems with spatial safety and energy sustainability guarantees. Stochastic robot motion is encoded through the Fokker-Planck Partial Differential Equation (PDE) at the density level. Control Lyapunov and control barrier functions are integrated with PDEs to enforce target density tracking, obstacle region avoidance, and energy sufficiency over multiple charging cycles.
Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundaries
Announce Type: new Abstract: One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn...
Learning collision operators from plasma phase space data using differentiable simulators
arXiv:2601.10885v2 Announce Type: replace-cross Abstract: We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker-Planck solver, with a gradient-based optimisation method to learn the collisional operators that best describe the phase space dynamics. We test our method using data from two-dimensional Particle-in-Cell simulations of...
Learning collision operators from plasma phase space data using differentiable simulators
arXiv:2601.10885v2 Announce Type: replace Abstract: We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker-Planck solver, with a gradient-based optimisation method to learn the collisional operators that best describe the phase space dynamics. We test our method using data from two-dimensional Particle-in-Cell simulations of spatially...
The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport
arXiv:2606.05217v1 Announce Type: cross Abstract: We exhibit an exact correspondence between sampling with score-based diffusion models and adiabatic transport of ground states for a family of Schr\"odinger operators we call Score Hamiltonians, built from the learned score's quantum potential. We obtain novel density reconstruction bounds and principled annealing schedules via adiabatic theorems for Fokker-Planck equations with time-varying potentials. We find the fundamental limit of...
The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport
arXiv:2606.05217v1 Announce Type: cross Abstract: We exhibit an exact correspondence between sampling with score-based diffusion models and adiabatic transport of ground states for a family of Schr\"odinger operators we call Score Hamiltonians, built from the learned score's quantum potential. We obtain novel density reconstruction bounds and principled annealing schedules via adiabatic theorems for Fokker-Planck equations with time-varying potentials. We find the fundamental limit of...
Flow-Regulated Suprathermal Particle Acceleration in Weakly Collisional Astrophysical Plasmas
Announce Type: new Abstract: We investigate the formation of suprathermal particle populations in weakly collisional plasmas using a one-dimensional Fokker-Planck framework. A key element of this work is the introduction of a systematic velocity-space drift term that represents net energization relative to a background streaming flow. This term provides a minimal phenomenological description of competing relaxation and acceleration processes, enabling the incorporation of large-scale plasma...
Riemannian Diffusion Models on General Manifolds via Physics-Informed Neural Networks
arXiv:2605.31106v1 Announce Type: new Abstract: Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a...