Sampling conditioned diffusions via Pathspace Projected Monte Carlo

• URL: http://arxiv.org/abs/2506.15743v1
• Date: Tue, 17 Jun 2025 23:01:24 GMT
• Title: Sampling conditioned diffusions via Pathspace Projected Monte Carlo
• Authors: Tobias Grafke,
• Abstract summary: We present an algorithm to sample differential equations conditioned on rather general constraints.<n>The algorithm is a pathspace-adjusted manifold sampling scheme, which samples paths on the submanifold of realizations that adhere to the conditioning constraint.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace Metropolis-adjusted manifold sampling scheme, which samples stochastic paths on the submanifold of realizations that adhere to the conditioning constraint. We demonstrate the effectiveness of the algorithm by sampling a dynamical condensation phase transition, conditioning a random walk on a fixed Levy stochastic area, conditioning a stochastic nonlinear wave equation on high amplitude waves, and sampling a stochastic partial differential equation model of turbulent pipe flow conditioned on relaminarization events.

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