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Blockkurs
Supplementary physics course material wiki
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Blockkurs
Supplementary physics course material wiki
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BlockkursELEC446.Blockkurs HistoryHide minor edits - Show changes to output Changed line 42 from:
*'' to:
*''[[https://www.mathcomp.uni-heidelberg.de/curriculum/ | HGS MathComp Curriculum page]]'' Added lines 41-42:
*'' [[https://www.mathcomp.uni-heidelberg.de/curriculum/ | HGS MathComp Curriculum page]]"" Changed lines 34-35 from:
*''Lecture 4'' * to:
*''Lecture 4'' [[Attach:Lecture4Slides.pdf | slides]] Changed lines 32-34 from:
*Some good books on FEM to:
*Some good books on FEM are [[http://www.springer.com/us/book/9783540548225 | Hackbusch]] and [[http://www.springer.com/us/book/9780387205748 | Ern and Guermond]] Changed line 43 from:
*Template for counting MCMC with moves [[Attach: to:
*Template for counting MCMC with moves [[Attach:countingMCMCtemplate | countingMCMCtemplate.m]] Changed lines 41-43 from:
*Image of good and bad cells [[Attach:slide.tif|slide.tif]]. to:
*Image of good and bad cells [[Attach:slide.tif|slide.tif]]. *Matlab code [[Attach:makefake | makefake.m]] that generated the image, and uses functions [[Attach:putgood | putgood.m]] and [[Attach:putbad | putbad.m]]. *Template for counting MCMC with moves [[Attach:counting_MCMC_template | counting_MCMC_template.m]] Changed lines 37-38 from:
*[[Attach: to:
*[[Attach:Lecture4Slides.pdf | slides]] Changed lines 40-41 from:
*[[Attach: *Image of good and bad cells to:
*[[Attach:Compute4.pdf | Task sheet]] *Image of good and bad cells [[Attach:slide.tif|slide.tif]]. Matlab code [[Attach:makefake | makefake.m]] that generated the image, and uses functions [[Attach:putgood | putgood.m]] and [[Attach:putbad | putbad.m]]. Changed line 27 from:
*[[Attach: to:
*[[Attach:DJacc |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 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? 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 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 27 from:
*[[Attach:DJac |DJac.m]] function to return Jacobian matrix, built using secant approximation to:
*[[Attach:DJac |DJac.m]] function to return Jacobian matrix for inverse coefficient problem, built using secant approximation Changed line 26 from:
*[[Attach:heatIPsvals |heatIPsvals.m]] to:
*[[Attach:heatIPsvals |heatIPsvals.m]] plot the singular values for the inverse-source problem in the 1-dim heat equation Changed lines 26-27 from:
*[[Attach:heatIPsvals | to:
*[[Attach:heatIPsvals |heatIPsvals.m]] script file the plots the singular values for the inverse-source problem in the 1-dim heat equation *[[Attach:DJac |DJac.m]] function to return Jacobian matrix, built using secant approximation Changed line 26 from:
*[[Attach: to:
*[[Attach:heatIPsvals |heatIPevals.m]] script file the plots the singular values for the inverse-source problem in the 1-dim heat equation Added line 26:
*[[Attach:heatIPevals |heatIPevals.m]] script file the plots the singular values for the inverse-source problem in the 1-dim heat equation Changed line 18 from:
*[[Attach:heatfem | heatfem.m]] that builds FEM to:
*[[Attach:heatfem | heatfem.m]] that builds FEM mass and stiffness matrices for 1-dim heat problem Deleted lines 13-14:
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*[[Attach:robfem |robfem.m]] that builds FEM to:
*[[Attach:robfem |robfem.m]] that builds FEM matrix for 1-dim operator -cu'' + alpha u Changed lines 28-29 from:
to:
*[[Attach:robfem |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:
*[[Attach:heatfem | heatfem.m]] that builds FEM matrices for heat problem Deleted lines 24-27:
*''Compute 3'' *[[Attach:heatfem | heatfem.m]] that builds FEM matrices for heat problem Added lines 26-28:
*''Compute 3'' Changed line 27 from:
*[[Attach:heatfem to:
*[[Attach:heatfem | heatfem.m]] that builds FEM matrices for heat problem Changed line 28 from:
*''Python code:'' Andres' python code [[Attach:Minicourse.zip |zip file]] to:
*''Python code:'' Andres' python code [[Attach:Minicourse.zip |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'' *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 [[Attach:Minicourse.zip |zip file]] for heat FEM Changed line 36 from:
*''Lecture to:
*''Lecture 4'' Changed line 39 from:
*''Compute to:
*''Compute 4'' Deleted lines 42-44:
*[[Attach:Fox_IMI_PL.pdf | slides]] *[[Attach:Fox_IMI_movie.mp4 | movie]] Changed lines 18-19 from:
*[[Attach:tauvsw *[[Attach:Dmcmc to:
*[[Attach:tauvsw |Code to plot IACT as function of window using mcgauss.m]] *[[Attach:Dmcmc |Code to sample inverse heat problem]] *''Compute 3'' Changed lines 26-27 from:
*''Python code'' to:
*''Python code'' Deleted lines 27-28:
*''Compute 2'' Changed lines 11-13 from:
*[[Attach: to:
*[[Attach:mcgaus | mcgaus.m]] MH for sampling a Gaussian in 1-dim *[[Attach:mcgaus_demo | mcgaus_demo.m]] Traces of Gaussian sampler for different window sizes Deleted line 16:
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*''Compute 1'' (for m-files, right click to 'Save As' to get formatting correct *[[Attach:mcmc.m | mcmc to:
*''Compute 1'' (for m-files, right click to 'Save As' to get formatting correct, and add .m extension (my silly Wiki does not allow .m extensions)) *[[Attach:mcmc | mcmc.m]].m is a basic Metropolis-Hastings algorithm, with acceptance prob. for exponential distribution Deleted line 8:
Added lines 10-14:
*[[Attach:mcmc.m | mcmc.m]] is a basic Metropolis-Hastings algorithm *[[Attach:mcgauss.m | mcgauss.m]] MH for sampling a Gaussian in 1-dim, with mean and covariance *''Compute 2'' (for m-files, right click to 'Save As' to get formatting correct) Changed line 22 from:
*Andres' to:
*Andres' python code [[Attach:Minicourse.zip |zip file]] for heat FEM Changed lines 3-4 from:
Instructors: [[http://elecphysics.otago.ac.nz/w/index.php/Colin_Fox|Colin Fox to:
Instructors: [[http://elecphysics.otago.ac.nz/w/index.php/Colin_Fox|Colin Fox]] Changed lines 6-7 from:
* *Gareth Roberts' to:
* Book by Jun Liu: [[https://www.springer.com/de/book/9780387763699 | Monte Carlo Strategies in Scientific Computing]] * Gareth Roberts' [[Attach:notes2012partiii.pdf | notes on Statistical Inference]] has useful statements of basic MCMC methods and theorems Changed line 1 from:
'+Resources for [[https://www.mathcomp.uni-heidelberg.de/curriculum/ | Blockkurs]] on Markov Chain Monte Carlo for Inverse Problems in PDEs+' to:
'+Resources for [[https://www.mathcomp.uni-heidelberg.de/curriculum/ | Blockkurs]] on Markov Chain Monte Carlo for Inverse Problems in [=PDEs=]+' Changed line 1 from:
'+Resources for [[https://www.mathcomp.uni-heidelberg.de/curriculum/ | Blockkurs]] on Markov Chain Monte Carlo for Inverse Problems in PDEs to:
'+Resources for [[https://www.mathcomp.uni-heidelberg.de/curriculum/ | Blockkurs]] on Markov Chain Monte Carlo for Inverse Problems in PDEs+' Changed line 1 from:
'+Resources for to:
'+Resources for [[https://www.mathcomp.uni-heidelberg.de/curriculum/ | Blockkurs]] on Markov Chain Monte Carlo for Inverse Problems in PDEs:+' Added lines 1-40:
'+Resources for BUC5 computing labs:+' Instructors: [[http://elecphysics.otago.ac.nz/w/index.php/Colin_Fox|Colin Fox]] and [[http://www.cimat.mx/~jac/| J Andres Christen]] *''Some Reading '' * [[Attach:BUC5notes.pdf | lecture notes]] (so far) *Gareth Roberts' [[http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/roberts/st911/notes2012partiii.pdf | notes on Statistical Inference]] has useful statements of basic MCMC methods and theorems *''Compute 1'' (for m-files, right click to 'Save As' to get formatting correct) *[[Attach:mcgauss.m | mcgauss.m]] *Ulli Wollf's [[http://www.physik.hu-berlin.de/com/ALPHAsoft/ | UWerr MatLab code]] and documentation *[[Attach:tauvsw.m |Code to plot IACT as function of window using mcgauss.m]] *[[Attach:Dmcmc.m |Code to sample inverse heat problem]] *[[Attach:heatfem.m | heatfem.m]] that builds FEM matrices for heat problem *''Python code'' *Andres' [[Attach:Minicourse.zip |zip file]] *''Compute 2'' *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. *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? *Some good books on FEM *[[http://www.springer.com/us/book/9783540548225 | Hackbusch]] *[[http://www.springer.com/us/book/9780387205748 | Ern and Guermond]] *''Lecture 3'' *[[Attach:Lecture3Slides.pdf | slides]] *''Compute 3'' *[[Attach:Compute3.pdf | Task sheet]] *Image of good and bad cells in Matlab mat format [[Attach:slide.mat | slide.mat]], or as [[Attach:slide.tif|slide.tif]]. Matlab code [[Attach:makefake.m | makefake.m]] that generated the image, and uses functions [[Attach:putgood.m | putgood.m]] and [[Attach:putbad.m | putbad.m]]. *''Public Lecture'' *[[Attach:Fox_IMI_PL.pdf | slides]] *[[Attach:Fox_IMI_movie.mp4 | movie]] |