#numerical — Public Fediverse posts

#numerical : relating to or expressed as numbers

- French: numérique

- German: zahlenmäßig

- Italian: numerico

- Portuguese: numérico

- Spanish: numérico

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Fill in missing or incorrect translations @ https://wordofthehour.org/r/translations

JNum: A Pure Java Numerical Library

#analysis #java #numerical

https://github.com/CH-Abhinav/JNum

JNum: A Pure Java Numerical Library

#analysis #java #numerical

https://github.com/CH-Abhinav/JNum

RE: https://mast.hpc.social/@msleigh/116562490685026434

Are you dealing with large #legacy code bases, #numerical models with strict validation requirements, or operational #workflows? Are you maintaining #Fortran code?

Please consider submitting an abstract, we are genuinely interested in how you're approaching #software #sustainability and evolution! Especially if you come from outside the #weather and #climate domain!

RE: https://mast.hpc.social/@msleigh/116562490685026434

Are you dealing with large #legacy code bases, #numerical models with strict validation requirements, or operational #workflows? Are you maintaining #Fortran code?

Please consider submitting an abstract, we are genuinely interested in how you're approaching #software #sustainability and evolution! Especially if you come from outside the #weather and #climate domain!

Transport and settling of suspended particles in a simulated estuary: particle-laden freshwater enters a basin filled with seawater. The white iso-surface indicates 50% of the original particle density. Kelvin-Helmholtz instabilities evolve in the shear flow and drive the turbulent mixing. Rayleigh–Taylor instabilities can be observed in the initial settling phase. Based on Direct #Numerical #Simulation.

#sedimentation #estuary #fluiddynamics #turbulence #CFD #computationalfluiddynamics

Transport and settling of suspended particles in a simulated estuary: particle-laden freshwater enters a basin filled with seawater. The white iso-surface indicates 50% of the original particle density. Kelvin-Helmholtz instabilities evolve in the shear flow and drive the turbulent mixing. Rayleigh–Taylor instabilities can be observed in the initial settling phase. Based on Direct #Numerical #Simulation.

#sedimentation #estuary #fluiddynamics #turbulence #CFD #computationalfluiddynamics

Another one from the archive: turbulent mixing of sediment-laden freshwater and seawater (black). The white iso-surface indicates a 50/50 mix. The freshwater enters the basin at the bottom left. Direct #Numerical #Simulation.

#sedimentation #estuary #fluiddynamics #turbulence #CFD #computationalfluiddynamics

Another one from the archive: turbulent mixing of sediment-laden freshwater and seawater (black). The white iso-surface indicates a 50/50 mix. The freshwater enters the basin at the bottom left. Direct #Numerical #Simulation.

#sedimentation #estuary #fluiddynamics #turbulence #CFD #computationalfluiddynamics

Snapshot of the turbulent mixing of sediment-laden freshwater (black) and seawater (white / grey) in a modelled estuary. The scene is seen from the top. The freshwater enters from the bottom of the picture.

The results were obtained from a Direct #Numerical #Simulation. Only half of the domain is simulated (the other half is mirrored). Only the interesting part is shown (the simulated domain is actually a lot bigger).

#sedimentation #estuary #fluiddynamics #CFD #computationalfluiddynamics

Snapshot of the turbulent mixing of sediment-laden freshwater (black) and seawater (white / grey) in a modelled estuary. The scene is seen from the top. The freshwater enters from the bottom of the picture.

The results were obtained from a Direct #Numerical #Simulation. Only half of the domain is simulated (the other half is mirrored). Only the interesting part is shown (the simulated domain is actually a lot bigger).

#sedimentation #estuary #fluiddynamics #CFD #computationalfluiddynamics

#numerical : belonging to number

- French: numérique

- German: zahlenmäßig

- Italian: numerico

- Portuguese: numérico

- Spanish: numérico

------------

Fill in missing or incorrect translations @ https://wordofthehour.org/r/translations

#numerical : belonging to number

- French: numérique

- German: zahlenmäßig

- Italian: numerico

- Portuguese: numérico

- Spanish: numérico

------------

Fill in missing or incorrect translations @ https://wordofthehour.org/r/translations

From the archive: beautiful visualization of the boundary layer flow at the leading edge of a swept wing. Small disturbances introduced at the left transition to turbulence at the right.
The configuration is idealized for academic research (swept Hiemenz flow).
The results were obtained from a Direct #Numerical #CFD #simulation.
https://ethz.ch/content/dam/ethz/special-interest/mavt/fluid-dynamics/ifd-dam/research/documents/posters/transition-and-turbulent-flows/michael_john_swept_hiemenz_flow.pdf

🔄 Power transforms help reshape data toward a Gaussian distribution
💥 Overflow errors are common when implemented naively
🛠️ This post dives into the cause and shows practical solutions

https://xuefeng-xu.github.io/blog/power-transform.html

#Numerical #Statistics #Python

🔄 Power transforms help reshape data toward a Gaussian distribution
💥 Overflow errors are common when implemented naively
🛠️ This post dives into the cause and shows practical solutions

https://xuefeng-xu.github.io/blog/power-transform.html

#Numerical #Statistics #Python

Many animal species, including primates, birds, and fish, exhibit a sense of number known as #Numerical #Competence, allowing them to discriminate and compare quantities of objects.

This foundational ability is thought to be an ancient cognitive trait, suggesting that the basic mechanics for perceiving quantity are shared by humans and other animals.

https://knowledgezone.co.in/posts/Animals-that-could-do-Math-6762bb557b620f019ff7fbb3

Many animal species, including primates, birds, and fish, exhibit a sense of number known as #Numerical #Competence, allowing them to discriminate and compare quantities of objects.

This foundational ability is thought to be an ancient cognitive trait, suggesting that the basic mechanics for perceiving quantity are shared by humans and other animals.

https://knowledgezone.co.in/posts/Animals-that-could-do-Math-6762bb557b620f019ff7fbb3

After quite some weeks of work I have quantified the #numerical error of several #FFT implementations compared to my own.

This was done by implementing an arbitrary precision FFT to compute the true value.

For each implementation we compare the L1, L2 and Linfinity norms as well as #rms

The theoretical l2 bound is derived by Nicholas J.Higham in his famous book 'accuracy and stability of numerical algorithms'

The Linf bound from P. Henrici 'Applied and Computational Complex Analysis'

#numerical : belonging to number

- French: numérique

- German: zahlenmäßig

- Italian: numerico

- Portuguese: numérico

- Spanish: numérico

------------

Fill in missing or incorrect translations @ https://wordofthehour.org/r/translations

Stuart McAlpine - Creating a Bayesian digital twin of our Universe (Sept. 18, 2025) https://www.youtube.com/watch?v=q5eSO_YOZR8

The Manticore Project I: a digital twin of our cosmic neighbourhood from Bayesian field-level analysis
https://arxiv.org/abs/2505.10682

"Leveraging field-level Bayesian inference with data from the
2M++ galaxy survey, our model incorporates refined galaxy bias modelling, high-fidelity reconstructions, and rigorous posterior predictive validation. As a result, Manticore-Local accurately reproduces the spatial distribution, mass hierarchy, and velocity fields of observed cosmic structures within the local Universe, outperforming previous state-of-the-art constrained simulations and velocity field reconstructions across multiple key metrics."

#numerical #bayesian #cosmology #simulation

Stuart McAlpine - Creating a Bayesian digital twin of our Universe (Sept. 18, 2025) https://www.youtube.com/watch?v=q5eSO_YOZR8

The Manticore Project I: a digital twin of our cosmic neighbourhood from Bayesian field-level analysis
https://arxiv.org/abs/2505.10682

"Leveraging field-level Bayesian inference with data from the
2M++ galaxy survey, our model incorporates refined galaxy bias modelling, high-fidelity reconstructions, and rigorous posterior predictive validation. As a result, Manticore-Local accurately reproduces the spatial distribution, mass hierarchy, and velocity fields of observed cosmic structures within the local Universe, outperforming previous state-of-the-art constrained simulations and velocity field reconstructions across multiple key metrics."

#numerical #bayesian #cosmology #simulation

🤔 Everyone knows how to compute variance... right?
⚠️ But the textbook formula can be wildly wrong on computers
👇 Here is why and how to fix it in practice

https://xuefeng-xu.github.io/blog/variance.html

#Numerical #Python

🤔 Everyone knows how to compute variance... right?
⚠️ But the textbook formula can be wildly wrong on computers
👇 Here is why and how to fix it in practice

https://xuefeng-xu.github.io/blog/variance.html

#Numerical #Python

Analog optical computer for AI inference and combinatorial optimization
https://www.nature.com/articles/s41586-025-09430-z

AOC implements the following idealized iteration:

\({{{\bf{s}}}_{t+1}=\alpha (t){{\bf{s}}}_{t}+\beta W\,f({{\bf{s}}}_{t})+\gamma ({{\bf{s}}}_{t}-{{\bf{s}}}_{t-1})+{\bf{b}}} \)

The current small-scale AOC accelerates equilibrium models with up to 4,096 weights at 9-bit precision. Projected performance around 500 tera-operations per second (TOPS) per watt at 8-bit precision—over 100-times more efficient than leading graphics processing units (GPUs)"

Microsoft Research Project page: https://www.microsoft.com/en-us/research/project/aoc/
Digital Twin: https://github.com/microsoft/aoc

#numerical #computing #ml #optics

Analog optical computer for AI inference and combinatorial optimization
https://www.nature.com/articles/s41586-025-09430-z

AOC implements the following idealized iteration:

\({{{\bf{s}}}_{t+1}=\alpha (t){{\bf{s}}}_{t}+\beta W\,f({{\bf{s}}}_{t})+\gamma ({{\bf{s}}}_{t}-{{\bf{s}}}_{t-1})+{\bf{b}}} \)

The current small-scale AOC accelerates equilibrium models with up to 4,096 weights at 9-bit precision. Projected performance around 500 tera-operations per second (TOPS) per watt at 8-bit precision—over 100-times more efficient than leading graphics processing units (GPUs)"

Microsoft Research Project page: https://www.microsoft.com/en-us/research/project/aoc/
Digital Twin: https://github.com/microsoft/aoc

#numerical #computing #ml #optics

rant: i know there are a lot of alternative (typically anti-) definitions of "AI" flying around, but i just thought of another one: Actual Insanity! anyone who has done serious work with finite precision #arithmetic, #linear #algebra, #statistics, #computational #modeling, or #numerical analysis, knows that minimizing the number of parameters is essential for building truly explanatory models. but establishment scientists have collectively signed onto the idea that large models are intelligent

rant: i know there are a lot of alternative (typically anti-) definitions of "AI" flying around, but i just thought of another one: Actual Insanity! anyone who has done serious work with finite precision #arithmetic, #linear #algebra, #statistics, #computational #modeling, or #numerical analysis, knows that minimizing the number of parameters is essential for building truly explanatory models. but establishment scientists have collectively signed onto the idea that large models are intelligent

#numerical : belonging to number

- French: numérique

- German: zahlenmäßig

- Italian: numerico

- Portuguese: numérico

- Spanish: numérico

------------

See previous words @ https://wordofthehour.org/r/past

5 Steps to N-body Simulation in Python.

Link: https://alvinng4.github.io/grav_sim/5_steps_to_n_body_simulation/

#CompMath #simulation #math #compsci #numerical

#numerical : belonging to number

- French: numérique

- German: zahlenmäßig

- Italian: numerico

- Portuguese: numérico

- Spanish: numérico

------------

See previous words @ https://wordofthehour.org/r/past

Escalation Of Caldera Unrest Indicated By Increasing Emission Of Isotopically Light Sulfur
--
https://doi.org/10.1038/s41561-024-01632-w <-- shared paper
--
#GIS #spatial #mapping #geology #structuralgeology #volcano #vulcanism #caldera #numerical #model #modeling #eruption #risk #hazard #seismicity #deformation #gases #engineeringgeology #physicochemical #monitoring #CampiFlegrei #Italy #sulfur #fumaroles #hydrothermal #magma #dataanalysis #global

Escalation Of Caldera Unrest Indicated By Increasing Emission Of Isotopically Light Sulfur
--
https://doi.org/10.1038/s41561-024-01632-w <-- shared paper
--
#GIS #spatial #mapping #geology #structuralgeology #volcano #vulcanism #caldera #numerical #model #modeling #eruption #risk #hazard #seismicity #deformation #gases #engineeringgeology #physicochemical #monitoring #CampiFlegrei #Italy #sulfur #fumaroles #hydrothermal #magma #dataanalysis #global

Matti #Kujasalo – Painting, 17.10.2017, 2017

#abstract #art #numerical

Some time ago, we looked into #numerical #integration (Gauss Lobatto) methods that allow one to do flexible #survival analysis with Generalized Additive/Linear Models instead of the Cox model #rstats #stats

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0123784

I compare in a big data project of ours

Some time ago, we looked into #numerical #integration (Gauss Lobatto) methods that allow one to do flexible #survival analysis with Generalized Additive/Linear Models instead of the Cox model #rstats #stats

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0123784

I compare in a big data project of ours

Some time ago, we looked into #numerical #integration (Gauss Lobatto) methods that allow one to do flexible #survival analysis with Generalized Additive/Linear Models instead of the Cox model #rstats #stats journals.plos.org/plosone/arti... Here is a comparison in a big data project of ours

Deep Learning with Jax
https://www.manning.com/books/deep-learning-with-jax
#ycombinator #neural_networks #Python #Google #Flax #Haiku #gradient_processing #optimization #numerical #computations #federated_learning #parallelized #distributed #primitives #differentiable

Watershed Delineation On A Hexagonal Mesh Grid
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https://doi.org/10.1016/j.envsoft.2020.104702 <-- shared paper
--
#GIS #spatial #mapping #model #modeling #Hydrology #Hexagon #WatershedDelineation #DigitalGlobalGridSystem #DGS #watershed #water #delineation #scaling #discretization #discretisation #simulations #numerical #adjacency #d8 #HexWatershed #watersheds #catchments #drainageareas

'Stable Implementation of Probabilistic ODE Solvers', by Nicholas Krämer, Philipp Hennig.

http://jmlr.org/papers/v25/20-1423.html

#numerical #solvers #odes

The extraction seems to be working really well, but can't tell how well yet

Has two repeating sections. One is very clearly good data that looks as expected

The other looks like noise, but is very repeatable and (partially) points in a way that true noise wouldn't point. Also partially larger than the real effect could be

What I really need is more example data. Fortunately bosses/partners are listening enough to make that happen (maybe)

#numerical #math #space #python #numpy #matplotlib

Actually...those effects must not be an issue or I'd already be seeing them at apogee in a high-e #orbit.

My interpolation is only non-flat at perigee, which is exactly where pos, vel and acc are changing fastest and #numerical methods are going to be noisiest.

So I think I just need to reduce noise well below .1mm/s^2 and I should be good...?

The smooth elset is for a high-e orbit For Reasons which also means the hard part is perigee.

My first naive method was to subtract adjacent velocities. That's awful.

Learning some #numerical methods, I then tried (v(t+1) - v(t-1))/2t. That gives me a 25 mm/s^2 residual acc. Meh.

Lagrange #interpolation gives me 5 mm/s^2. Getting somewhere.

Going back to central diffs but using t-2, t-1, t+1, t+2 I do even better at 1.5 mm/s^2 residual.

I am still in this rabbit hole, learning a bunch of new #numerical methods.

What I want at the end is *thrust* acceleration values recovered from satellite position and velocity data given at 1m intervals.

Any method will obviously also have the acc due to gravity and other effects. Methods will differ in how much numerical "noise" they add to the process.

Subtracting the Earth is easy with F=ma=GMm/r^2.

To compare the noise, I'm using a smooth #keplerian element set that has no thrusts.

So....#Lagrange #polynomials. They are pretty dang clever and pretty dang amazing. You can get an analytic (if that's the word I want) polynomial fit! That you can take a continuous derivative!

For arbitrary data, I can see why it might not work.

But for a physical object that actually is moving according to a 2nd-order kinematics (piecewise--really 3rd-order overall) but all you have data for the the first two orders, it might be a good way to recover the higher order(s).

#math #numerical