ELEC446 »
Blockkurs
Supplementary physics course material wiki
|
|
BlockkursELEC446.Blockkurs HistoryHide minor edits - Show changes to markup Changed line 42 from:
to:
Changed lines 32-34 from:
to:
Changed line 43 from:
*Template for counting MCMC with moves counting_MCMC_template.m Δ to:
*Template for counting MCMC with moves countingMCMCtemplate.m Changed lines 41-43 from:
*Image of good and bad cells slide.tif. Matlab code makefake.m that generated the image, and uses functions putgood.m and putbad.m. to:
*Image of good and bad cells slide.tif. *Matlab code makefake.m that generated the image, and uses functions putgood.m and putbad.m. *Template for counting MCMC with moves counting_MCMC_template.m Δ Changed lines 37-38 from:
to:
Changed lines 40-41 from:
*Task sheet Δ *Image of good and bad cells in Matlab mat format slide.mat Δ, or as slide.tif. Matlab code makefake.m Δ that generated the image, and uses functions putgood.m Δ and putbad.m Δ. to:
*Task sheet *Image of good and bad cells slide.tif. Matlab code makefake.m that generated the image, and uses functions putgood.m and putbad.m. Changed line 27 from:
*DJac.m function to return Jacobian matrix for inverse coefficient problem, built using secant approximation to:
*DJac.m function to return Jacobian matrix for inverse coefficient problem, built using secant approximation Changed line 29 from:
*Task: Evaluate the Jacobian (linearized forward map) for D(x)->u(x,T), using the secant method in D Jac?, and FEM program in heatfem (or your own). What is the effective rank of this map? What happens to the rank as the discretization of D (and u) is refined?
to:
*Task: Evaluate the Jacobian (linearized forward map) for D(x)->u(x,T), using the secant method in DJac, and FEM program in heatfem (or your own). What is the effective rank of this map? What happens to the rank as the discretization of D (and u) is refined? Changed line 29 from:
*Evaluate the linearized forward map for D(x)->u(x,T), using the secant method and robfem.m FEM program (or your own). What is the effective rank of this map? to:
Changed line 27 from:
*DJac.m function to return Jacobian matrix, built using secant approximation to:
*DJac.m function to return Jacobian matrix for inverse coefficient problem, built using secant approximation Changed line 26 from:
*heatIPsvals.m script file the plots the singular values for the inverse-source problem in the 1-dim heat equation to:
*heatIPsvals.m plot the singular values for the inverse-source problem in the 1-dim heat equation Changed lines 26-27 from:
*heatIPevals.m script file the plots the singular values for the inverse-source problem in the 1-dim heat equation to:
*heatIPsvals.m script file the plots the singular values for the inverse-source problem in the 1-dim heat equation *DJac.m function to return Jacobian matrix, built using secant approximation Changed line 26 from:
*heatIPevals.m Δ script file the plots the singular values for the inverse-source problem in the 1-dim heat equation to:
*heatIPevals.m script file the plots the singular values for the inverse-source problem in the 1-dim heat equation Added line 26:
*heatIPevals.m Δ script file the plots the singular values for the inverse-source problem in the 1-dim heat equation Changed line 18 from:
*heatfem.m that builds FEM matrices for heat problem to:
*heatfem.m that builds FEM mass and stiffness matrices for 1-dim heat problem Deleted lines 13-14:
Changed line 26 from:
*robfem.m that builds FEM mass and stiffness matrices for 1-dim space part to:
*robfem.m that builds FEM matrix for 1-dim operator -cu'' + alpha u Changed lines 28-29 from:
*Evaluate the linearized forward map for D(x)->u(x,T), using the secant method and the simple FEM program supplied. What is the effective rank of this map? to:
*robfem.m that builds FEM mass and stiffness matrices for 1-dim space part *Evaluate the linearized forward map for D(x)->u(x,T), using the secant method and robfem.m FEM program (or your own). What is the effective rank of this map? Added line 20:
*heatfem.m that builds FEM matrices for heat problem Deleted lines 24-27:
Added lines 26-28:
Changed line 28 from:
*Python code: Andres' python code zip file for heat FEM to:
*Python code: Andres' python code zip file plus IP text Changed lines 20-23 from:
to:
* Write a sampler for the inverse heat-conductivity problem in (constant) D (or use my awful code, above) * Tune the window size for your RWM sampler, or better still (challenge question) plot a graph of IACT as function of window w to find the optimal w *Consider error in the final time T, T~Unif[1.8,2.2]. Perform joint inference for D and T, and say whether inference for D is significantly altered. Changed lines 28-32 from:
*Python code *Andres' python code zip file for heat FEM *Complete your sampler for the inverse problem in (constant) D *Tune the window size for your RWM sampler, or better still (challenge question) plot a graph of IACT as function of window w to find the optimal w *Consider error in the final time T, T~Unif[1.8,2.2]. Perform joint inference for D and T, and say whether inference for D is significantly altered. to:
*Python code: Andres' python code zip file for heat FEM Changed line 36 from:
to:
Changed line 39 from:
to:
Deleted lines 42-44:
Changed lines 18-19 from:
to:
*Code to plot IACT as function of window using mcgauss.m *Code to sample inverse heat problem
Changed lines 26-27 from:
to:
*Python code Deleted lines 27-28:
Changed lines 11-13 from:
to:
*mcgaus.m MH for sampling a Gaussian in 1-dim *mcgaus_demo.m Traces of Gaussian sampler for different window sizes Deleted line 16:
Changed lines 9-10 from:
to:
Deleted line 8:
Added lines 10-14:
*mcmc.m Δ is a basic Metropolis-Hastings algorithm *mcgauss.m Δ MH for sampling a Gaussian in 1-dim, with mean and covariance
Changed line 22 from:
*Andres' zip file to:
*Andres' python code zip file for heat FEM Changed lines 3-4 from:
Instructors: Colin Fox and J Andres Christen to:
Instructors: Colin Fox Changed lines 6-7 from:
* lecture notes Δ (so far) *Gareth Roberts' notes on Statistical Inference has useful statements of basic MCMC methods and theorems to:
* Book by Jun Liu: Monte Carlo Strategies in Scientific Computing * Gareth Roberts' notes on Statistical Inference has useful statements of basic MCMC methods and theorems Changed line 1 from:
to:
Resources for Blockkurs on Markov Chain Monte Carlo for Inverse Problems in PDEs Changed line 1 from:
to:
Added lines 1-40:
Resources for BUC 5 computing labs: Instructors: Colin Fox and J Andres Christen
|