Numerical methods
Examine floating-point behavior and reference calculations.
Questions to work through.
Find a numerical failure before trusting an experiment
Does an apparently sensible floating-point answer survive a separately formulated reference calculation?
Separate a solver's stopping signal from solution accuracy
When does a tiny residual or smaller step fail to imply a more accurate scientific result?
Explore the sources.
All 71 resources →NumPy
Upstream project repository
Multidimensional array operations and numerical linear algebra for scientific Python.
Investigate How do sequential and pairwise array reductions behave on cancellation-heavy inputs?
SciPy
Upstream project repository
Numerical routines for integration, differential equations, optimization, transforms, and statistical analysis.
Investigate Which declared tolerances are attained by adaptive quadrature on a fixed family of endpoint-singular integrals?
[Re] Curve-Fitting with Piecewise Parametric Cubics
ReScience C
A replication of piecewise parametric cubic curve fitting, useful for studying how a geometric approximation is constructed and checked.
Investigate Can the fitting procedure meet a fixed geometric error tolerance on evaluator-generated curves with different curvature?
[Re] Learning Neural PDE Solvers with Convergence Guarantees ICLR Reproducibility Challenge 2019
ReScience C
A replication of learning-based PDE solvers with convergence guarantees as the target topic.
Investigate On an evaluator-chosen PDE with an analytic solution, does the observed residual contract over a fixed iteration budget?
[Re] Numerical influence of ReLU'(0) on backpropagation
ReScience C
A replication about the numerical influence of the derivative convention for ReLU at zero during backpropagation.
Investigate On a controlled network with exact-zero activations, how do alternative zero-derivative conventions change gradients and subsequent updates?
[Re] The principal components of natural images
ReScience C
A Julia replication about principal components of natural images.
Investigate How do the leading subspaces change when centering and scaling choices are varied explicitly?
[Re] Volume computation for polytopes: Vingt ans après
ReScience C
A C replication about computing volumes of polytopes.
Investigate Can the implementation recover known simplex and box volumes across controlled coordinate scales?
[Re] Weighted Voronoi Stippling
ReScience
A replication of weighted Voronoi stippling, a geometric method for distributing sample points according to image intensity.
Investigate How closely do generated stipple densities match evaluator-defined synthetic intensity maps at fixed point counts?
[Rp] Gifa V.4: A complete package for NMR data set processing
ReScience C
A FORTRAN77 reproduction report on the Gifa V.4 NMR data-processing package.
Investigate Can a bounded recovered processing step preserve known peak locations and amplitudes in evaluator-generated signals?
[Rp] Parallelization of an object-oriented FEM dynamics code
ReScience C
A C++ reproduction about parallelizing an object-oriented finite-element dynamics program using OpenMP.
Investigate Does parallel execution preserve a chosen dynamics observable within a declared tolerance across thread counts?
[Rp] Reproduction of interaction second virial coefficient calculation for H₂--CO interactions [J. Chem. Phys. vol. 112, 4417 (2000)]
ReScience C
A Fortran reproduction of a molecular-interaction second-virial-coefficient calculation for hydrogen and carbon monoxide.
Investigate Can a simplified potential with a known integral expose quadrature or unit-conversion errors before the original model is attempted?
[Rp] Structural flexibility in proteins - impact of the crystal environment
ReScience C
A Python reproduction concerning protein structural flexibility and the effect of a crystal environment on normal-mode calculations.
Investigate Which low-dimensional synthetic stiffness model can test eigenmode normalization and environment sensitivity independently?