1. Random walk method: This is a basic sampling method, and particles move in random steps and random directions. According to the formula of continuous diffusion model, the motion of particles can be simulated from the initial position according to the specified step size and direction. Repeat the simulation several times to obtain a set of samples.
2. Monte Carlo method: Monte Carlo method is a numerical calculation method based on random sampling. In the continuous diffusion model, Monte Carlo method can be used for sampling. The diffusion process of particles is simulated by generating random numbers that obey random distribution, such as normal distribution (Gaussian distribution).
3. Stochastic differential equation method: The continuous diffusion model can be expressed by stochastic differential equation (SDE). Numerical methods, such as Euler-Maruyama method, are used to solve stochastic differential equations numerically, thus obtaining sample paths. This method is more suitable for complex continuous diffusion model.
4. Monte Carlo Markov chain Monte Carlo method: the continuous diffusion model can be regarded as a stochastic process with Markov properties. Monte Carlo Markov Chain Monte Carlo (MCMC) method combines Markov chain and Monte Carlo sampling, and can be used to generate samples from continuous diffusion models.
These methods have their own advantages and disadvantages and are suitable for different types of continuous diffusion models. Which method to choose depends on the characteristics of the model, computing resources and sampling requirements. In the application, it is suggested that the appropriate sampling method should be selected according to the requirements of specific problems and the characteristics of numerical calculation technology.