Numerical methods for solving stochastic differential equations.
| Week | Summary |
|---|---|
| 8/5 - 8/11 | Animations (wiener process). Explored discontinuous ODE's and SDE's. |
| 7/29 - 8/4 | Matthews pg. 149 - 153, 156 (numerical methods with holonomic constraints), 161 - 162 (SHAKE and RATTLE), 317 - 319 (constrained Langevin dynamics) Differential forms: 2-forms, exactness and conservation. |
| 7/22 - 7/28 | Matthews pg. 98 - 106 (modified Hamiltonian, Lie derivatives and Poisson brackets), 139 - 144 (implicit schemes), 150 - 153, 281 - 282. Differential forms: multivariable calculus review, wedge product. Partial differential equations: introduction, heat equation, explicit scheme. Estimators, mean error (bias), mean squared error (MSE), strong and weak convergence. |
| 7/15 - 7/21 | Applications of rejection sampling and importance sampling, basic Monte Carlo estimation, Markov Chain Monte Carlo (MCMC), Langevin dynamics with harmonic potential, splitting methods. |
| 7/8 - 7/14 | On break. |
| 7/1 - 7/7 | Topology: introduction to topological spaces (Chapter 1). Real analysis: continuous functions, metric spaces. Functional analysis: linear spaces, normed linear spaces. Lab 5: integrators for SDEs (Euler-Maruyama). Random walk and Wiener process in multiple dimensions. Differential equations: nondimensionalization. |
| 6/24 - 6/30 | Matthews pg. 60 - 70 (Verlet method). Equations of motion. |
| 6/17 - 6/23 | Matthews pg. 211 - 258 (chapter 6 review). |
| 6/10 - 6/16 | Matthews pg. 216 - 258 (canonical distributions, stochastic differential equations), 407 - 411 (appendix: probability theory). Ito process. |
| 6/7 - 6/9 | Matthews pg. 1 - 7 (introduction), 18 - 28 (N-body problem, Hamiltonian, and flow maps), 44 - 46 (variational equations), 211 - 214 (canonical ensemble). Stochastic processes and stochastic differential equations. Matrix calculus. |
- Leimkuhler and Matthews. Molecular Dynamics with Deterministic and Stochastic Methods.