Public articles linked to the same research event.
arXiv This work develops a deep learning framework for solving high-dimensional stationary Fokker-Planck equations by combining Monte Carlo weak supervision, energy-variational physics constraints, and quasi-Newton refinement: Monte Carlo statistics anchor the scale of the stationary density, a free-energy variational loss enforces equilibrium physics, the formulation also applies to stationary systems with pointwise orthogonal rotational components and, using a family of test functions, to systems with more general non-gradient drift, and numerical results demonstrate accurate and robust density approximations across a range of high-dimensional stationary Fokker-Planck problems, including rough-potential and noisy-data settings.
This work develops a deep learning framework for solving high-dimensional stationary Fokker-Planck equations by combining Monte Carlo weak supervision, energy-variational physics constraints, and quasi-Newton refinement: Monte Carlo statistics anchor the scale of the stationary density, a free-energy variational loss enforces equilibrium physics, the formulation also applies to stationary systems with pointwise orthogonal rotational components and, using a family of test functions, to systems with more general non-gradient drift, and numerical results demonstrate accurate and robust density approximations across a range of high-dimensional stationary Fokker-Planck problems, including rough-potential and noisy-data settings.
This work develops a deep learning framework for solving high-dimensional stationary Fokker-Planck equations by combining Monte Carlo weak supervision, energy-variational physics constraints, and quasi-Newton refinement: Monte Carlo statistics anchor the scale of the stationary density, a free-energy variational loss enforces equilibrium physics, the formulation also applies to stationary systems with pointwise orthogonal rotational components and, using a family of test functions, to systems with more general non-gradient drift, and numerical results demonstrate accurate and robust density approximations across a range of high-dimensional stationary Fokker-Planck problems, including rough-potential and noisy-data settings.
This work develops a deep learning framework for solving high-dimensional stationary Fokker-Planck equations by combining Monte Carlo weak supervision, energy-variational physics constraints, and quasi-Newton refinement: Monte Carlo statistics anchor the scale of the stationary density, a free-energy variational loss enforces equilibrium physics, the formulation also applies to stationary systems with pointwise orthogonal rotational components and, using a family of test functions, to systems with more general non-gradient drift, and numerical results demonstrate accurate and robust density approximations across a range of high-dimensional stationary Fokker-Planck problems, including rough-potential and noisy-data settings.