| Abstract: |
| We develop a pseudo-reversible normalizing flow to efficiently generate samples of the state of a stochastic differential equation (SDE) for various initial distributions. The goal of this work is to build an accurate and efficient sampler of the SDE to replace computationally expensive particle simulators. After training, the normalizing flow model can directly generate samples of the SDEs final state without simulating trajectories. Existing normalizing flows for SDEs depend on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a huge computational saving in studies of how the final state varies with the initial distribution. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow mode. |
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