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Information-optimal error enclosures from a residual and one operator action: Applications to neural operators and PDE solver
September, 2026 • Model
Chen, Xiaoliang, Chang, Le
Reproducibility package
This repository implements numerical routines for SPD attainable-set enclosures, relative-error decisions, and low-rank trust-region calculations.
Quick start
Python 3.11+ is r…
Reproducibility package
This repository implements numerical routines for SPD attainable-set enclosures, relative-error decisions, and low-rank trust-region calculations.
Quick start
Python 3.11+ is required. From this directory:
python -m pip install torch==2.10.0 --index-url https://download.pytorch.org/whl/cpu python -m pip install -e '.[test]' python -m pytest -q python scripts/audit_results.py python scripts/plot_results.py --output-dir results/recomputed/figures
--tables-dir results/recomputed/tables
The supplied results/ contain the reference numerical outputs, including the reported tables, figures, and timing measurements.
To recompute all studies without modifying the reference copy:
python scripts/run_experiments.py --stage all --output results/recomputed python scripts/audit_results.py --results-dir results/recomputed python scripts/plot_results.py --results-dir results/recomputed/certification
--comparison-dir results/recomputed
--output-dir results/recomputed/figures
--tables-dir results/recomputed/tables
All studies use one CPU thread. Required data and 35 selected model checkpoints are included locally; no retraining or TeX installation is required. Installation may require network access. The tested software stack is recorded in requirements.txt.
Study stages
Stage: models Scope: 35 models, two grids, 8,960 predictions
Stage: comparisons Scope: Residual weighting, effectivity, scaling, timing, and analytic forcing
Stage: residual_bounds Scope: Ball-bound comparisons and high-contrast cases
Stage: certification Scope: 600 matrix witnesses, 960 distance checks, 576 PDE approximations, and 3,840 neural predictions
For individual certification studies, use --stage trust, separation, screened, or learned.
Repository layout
ione/: numerical library
configs/: experiment configurations
checkpoints/: fixed model weights
data/: input arrays
metadata/: model-selection records, training history, provenance, and code/result mapping
figures/, tables/: numerical outputs
Historical training and parameter-refinement runs are not rerun by this repository; their configurations and summaries are retained in metadata/.
Numerical scope
The retained information consists of spectral bounds, a residual, and one observed operator action. Set equalities refer to exact arithmetic for the prescribed discrete system. The implementation uses float64 arithmetic, so its numerical checks and optimization tolerances are not directed-rounding certificates.
Reference solutions are excluded from decision functions and are used only for independent checks. Timing results are host-dependent and are not included in numerical equality tests. Bitwise repeatability refers to the tested CPU/software stack rather than a cross-platform guarantee.
Hydrodynamic Forces in Stationary Bidisperse Particle Assemblies
September, 2026 • Dataset
Kandari, Lowkya, Taborda Ceballos, Manuel Alejandro, van Wachem, Berend
Dataset accompanying the paper
L. Kandari, M. A. Taborda, B. van Wachem, "Predicting hydrodynamic forces in stationary bidisperse particle assemblies using microstructure-based models".
If you use thi…
Dataset accompanying the paper
L. Kandari, M. A. Taborda, B. van Wachem, "Predicting hydrodynamic forces in stationary bidisperse particle assemblies using microstructure-based models".
If you use this dataset, please cite the paper above and this dataset.
Authors: Lowkya Kandari, Manuel A. Taborda, Berend van WachemChair of Mechanical Process Engineering, Otto-von-Guericke-Universitaet Magdeburg, GermanyContact: berend.van.wachem@multiflow.org
Description
This dataset contains the hydrodynamic forces on the individual particles of random, fixed (stationary) bidisperse assemblies of spheres. The forces were obtained from particle-resolved direct numerical simulations (PR-DNS), carried out with the immersed boundary method (IBM) and adaptive mesh refinement in the finite-volume code MultiFlow (https://www.multiflow.org).
For every particle, the dataset also contains the Minkowski scalars, vectors and tensors describing its local microstructure, computed from a radius-weighted Voronoi tessellation (voro++), together with the list of its Voronoi neighbours. For two of the simulations, the full Eulerian flow field and Lagrangian particle data are also provided.
Simulation setup
Domain: tri-periodic cube of side length L = 1.
The flow is driven in the x-direction by a uniform body force, the imposed mean pressure gradient dP. The value of dP is set from a bidisperse drag correlation for the target Reynolds number and solid volume fraction.
The particles are fixed, spherical, and belong to two size classes: small (diameter d_s) and large (diameter d_l). The configurations are generated by random sequential addition, with 382-417 particles per simulation.
All dimensional quantities are in consistent simulation units: L = 1, fluid density rho_f = 1, superficial velocity <u> approximately 1. The viscosity mu_f is chosen to obtain the target Reynolds number.
Only the converged (steady) state of each simulation is reported.
Definitions (N_i is the number of particles of class i, i = s, l):
Solid volume fraction
eps_p = eps_l + eps_s, with eps_i = N_i pi d_i^3 / (6 L^3)
Large-particle volume ratio
eps* = eps_l / eps_p
Diameter ratio
d* = d_l / d_s
Sauter mean diameter
<d> = sum(N_i d_i^3) / sum(N_i d_i^2)
Superficial velocity
<u> = (1/V) * integral over V of (I_f u) dV, where I_f is 1 in the fluid and 0 in the particles
Reynolds number
Re = rho_f <u> <d> / mu_f, using the x-component of <u>
Stokes drag of particle k
F_S = 3 pi mu_f d_k <u>, using the particle's own diameter d_k
Normalised force
F = F_dim / F_S, where F_dim is the dimensional hydrodynamic force
Hydrodynamic force convention
The particle forces in the CSV files follow Eq. (5) of the paper:
F_dim = - sum_j (S_j dV_j) - dP V_p e_x
The first term is the IBM feedback force summed over the Lagrangian markers j of the particle. The second term removes the contribution of the imposed mean pressure gradient dP, where V_p is the particle volume and e_x the unit vector in the x-direction.
NOTE: the "Force" stored in the HDF5 particle files of Simulation_output is the first term only, i.e. the force BEFORE this correction:
Force (HDF5) = F_dim + dP V_p e_x
The streamwise component of "Force" in the HDF5 files is therefore larger than the drag in the CSV files. The transverse (y, z) components are identical, apart from small differences. dP itself is not stored in the CSV files.
Parameter space
The dataset contains 324 simulations with 130,203 particles in total. Each parameter was varied over the following values:
Parameter
Nominal values
Actual values in the CSV files
eps_p (Vfrac)
0.1, 0.2, 0.3, 0.4
within 0.2% of nominal
Re (Reynolds)
0.1, 1, 100
within -5.6% / +7.8% of nominal
d* (DiamRatio)
1.5, 2, 3
exact (up to round-off)
eps* (VLarge_vfrac)
1/3, 1/2, 2/3
0.334-0.366, 0.500-0.521, 0.666-0.683
Realisation (Array)
1, 2, 3
-
The paper and the folder names use the NOMINAL values. The CSV files contain the ACTUAL values of each simulation:
eps_p and eps* differ from nominal because the number of particles is an integer.
Re is computed from the superficial velocity that the simulation actually reached, which differs from the target because dP is prescribed from a drag correlation.
To select a case by its nominal values, round the actual values. The script read_data.py does this for you, in the columns Re_nom, Vfrac_nom, DiamRatio_nom and VLarge_vfrac_nom.
For a given eps_p, d*, eps* and realisation index, the same particle configuration is used at all three Reynolds numbers, with one exception. For eps_p = 0.4, d* = 3, eps* = 1/3:
at Re = 1 and Re = 100, realisations 1 and 2 have the same particle configuration;
at Re = 0.1, realisation 2 has the configuration of realisation 3 at Re = 1 and 100, and realisation 3 has a configuration that appears only there.
Files
README
this file
data-vfrac-0.1.csv ... data-vfrac-0.4.csv
particle data, one file per nominal eps_p (54-55 MB each)
read_data.py
Python script to read the CSV files, with examples
Simulation_output/
Eulerian and Lagrangian data of two simulations (13 GB)
CSV files
Each row of a CSV file describes one particle of one simulation (case). A case is identified by the columns Vfrac, Reynolds, DiamRatio, VLarge_vfrac and Array, which are constant within the case. The rows of a case are stored as one contiguous block; the cases themselves are not sorted. All files have the same 87 columns.
Case parameters (constant within a case)
Vfrac
eps_p, total solid volume fraction
VLarge_vfrac
eps*, large-particle volume ratio eps_l/eps_p
DiamRatio
d*, diameter ratio d_l/d_s
Array
realisation index of the random configuration (1, 2, 3)
Viscosity
mu_f, dynamic viscosity
u_avg_ZH
x-component of the superficial velocity <u>
v_avg_ZH
y-component of the superficial velocity
w_avg_ZH
z-component of the superficial velocity
Reynolds
Re, computed with u_avg_ZH and <d>
Forces
Stokes_[Fs]
F_S, Stokes drag 3 pi mu_f d_k <u> of the particle (dimensional)
Fx_Fs_[-]
F_{i,x}, normalised drag force (x)
Fy_Fs_[-]
F_{i,y}, normalised lift force (y)
Fz_Fs_[-]
F_{i,z}, normalised lift force (z)
To obtain the dimensional force, multiply the normalised force by Stokes_[Fs].
Particle
X, Y, Z
coordinates of the particle centre, in [0, 1)
Diameter
particle diameter d_K; each case has exactly two values, d_s and d_l
Voronoi cell and Minkowski descriptors (Section 3.2 and Table 1 of the paper)
The suffixes -0, -1, -2 denote the x, y, z components of a vector. The suffixes -ab (a, b in {0, 1, 2}) denote the xx ... zz components of a tensor. Positions and normals are taken in a reference frame centred on the particle. Unless stated otherwise, the quantities are dimensionless as defined in Table 1 of the paper, with A_ref = 4 pi (3 V_K / (4 pi))^(2/3) and L_ref = d_K / eps_p^(1/3).
Voro-Volume
V_K, volume of the Voronoi cell (dimensional); the volumes sum to L^3 = 1 per case
Voro-Surface
A_K, surface area of the Voronoi cell (dimensional)
Voro-LocalVolumeFraction
eps_K, local solid volume fraction (pi/6) d_K^3 / V_K
Voro-StretchingVector-a
D, stretching vector sum_j(A_j n_j / r_j) / sum_j(A_j / r_j)
Voro-WOneZeroZeroVector-a
W^{1,0}_0 / V_K^(4/3)
Voro-WOneZeroOneVector-a
W^{1,0}_1 / (A_ref L_ref)
Voro-WTwoZeroZeroTensor-ab
W^{2,0}_0 / V_K^(5/3)
Voro-WTwoZeroOneTensor-ab
W^{2,0}_1 / (A_ref L_ref^2)
Voro-WZeroTwoOneTensor-ab
W^{0,2}_1 / A_ref
Voro-InertiaTensor-ab
inertia tensor of the Voronoi cell without the particle, Eq. (22), divided by V_K^(5/3): [-W^{2,0}_0 + tr(W^{2,0}_0) Q - (pi/60) d_K^5 Q] / V_K^(5/3), with Q the identity tensor
<Tensor>-Eigen0/1/2
eigenvalues of the tensor; they are NOT sorted
<Tensor>-Beta
anisotropy index: smallest / largest eigenvalue
<Tensor>-Trace
trace of the tensor
In the last three entries, <Tensor> stands for each of the four rank-2 tensors.
Voronoi neighbours
nfaces
number of faces of the Voronoi cell, which equals the number of Voronoi neighbours
adjacent_cells
list of the neighbouring particles, stored as a string "[i, j, ...]"
The indices in adjacent_cells are 0-based row positions WITHIN THE SAME CASE: index 0 is the first row of the case block, in file order. The neighbour relation is symmetric. The tessellation is periodic, so a neighbour may lie across a periodic boundary. The string can be parsed with ast.literal_eval (see neighbours() in read_data.py).
read_data.py
The script requires Python >= 3.8, numpy and pandas. Running
python read_data.py [directory]
reads all CSV files and prints two examples:
the forces and Voronoi neighbours of a particle of one case;
the class-averaged drag F_{i,D} with its standard deviations sigma_{i,x} and sigma_{i,y}, which reproduces cases A-D of Table 4 of the paper.
The script also provides the following functions:
load_data() reads all CSV files into one table. It adds a case index, the particle index within the case, the particle class (small/large), the nominal parameter values and the dimensional forces.
neighbours() parses the adjacent_cells column.
tensor() returns a 3x3 Minkowski tensor.
class_averaged_drag() computes the class-averaged drag statistics.
Simulation_output
This folder contains the flow field and particle data of two of the 324 simulations. Each folder is named
Re<Re>-Vfrac<eps_p>-VFracLarge<eps*>-DiamRatio<d*>-Array<realisation>
using the nominal parameter values; VFracLarge corresponds to the CSV column VLarge_vfrac. The two simulations are:
Re1-Vfrac0.1-VFracLarge0.33-DiamRatio1.5-Array1: Re = 1, eps_p = 0.1, eps* = 1/3, d* = 1.5, realisation 1 (413 particles).
Re100-Vfrac0.3-VFracLarge0.50-DiamRatio2.0-Array1: Re = 100, eps_p = 0.3, eps* = 1/2, d* = 2, realisation 1 (398 particles).
Their particles are the same as the corresponding rows of data-vfrac-0.1.csv and data-vfrac-0.3.csv.
Each folder contains the following files:
Meshes/mesh_0.h5: the adaptively refined mesh (vertices and cells).
Fields/fields_<n>.h5: the Eulerian fields, one value per cell:
velocity vector;
pressure;
AMR level;
other data relevant for the coupling between the IBM particles and the fluid.
Particles/IBMparticles_<n>.h5: the Lagrangian particle data:
coordinates;
diameter;
hydrodynamic force components (see "Hydrodynamic force convention" above);
torque components;
translational velocity components (zero; the particles are fixed);
rotational velocity components (zero).
results.xmf and results_IBM.xmf: XDMF wrappers for reading the fluid and particle data directly in ParaView.
Only the converged state of each simulation is provided, due to storage limits.
Acknowledgements
This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project-ID 422037413 - TRR 287.
An open-source Early Information System (EIS) that predicts dissolved oxygen and hypoxia risk in the tidal Elbe River using auto-regressive statistical time-series models based on lagged environmental…
An open-source Early Information System (EIS) that predicts dissolved oxygen and hypoxia risk in the tidal Elbe River using auto-regressive statistical time-series models based on lagged environmental variables (air temperature, water temperature, historic oxygen measurements, and, for short lead times, upstream chlorophyll-a from the Schmilka gauging station at Elbe km 0).Models are trained on historic data from the highest-quality period (2000-2010), evaluated against the full 1996-2024 record to assess skill, and then used operationally to forecast oxygen levels and hypoxia likelihood at monitoring stations along the tidal Elbe, including Bunthaus, Seemannshöft, and Blankenese.
Elbe Riverdissolved oxygenhypoxiaforecastingtime-series model
QCB_Monthly_2007_2026: A monthly dataset of Qatari interest rates, credit and deposits constructed from ten issues of the Qatar Central Bank Monthly Monetary Bulletin
September, 2026 • Dataset
Ijla, Salah Eldean M.
Monthly series, January 2007 to July 2026 (235 observations, 53 variables), assembled from ten issues of the Qatar Central Bank Monthly Monetary Bulletin: January 2009, 2011, 2013, 2015, 2017, 2019, 2…
Monthly series, January 2007 to July 2026 (235 observations, 53 variables), assembled from ten issues of the Qatar Central Bank Monthly Monetary Bulletin: January 2009, 2011, 2013, 2015, 2017, 2019, 2021, 2023 and 2025, and July 2026. The Bulletin reports each series over a rolling twenty-five-month window; the ten issues were combined into an uninterrupted record and cross-checked in overlapping months. The deposit includes the dataset, a variable dictionary, and the Python code that reproduces the estimates in the related paper submitted to the International Journal of Financial Studies.
interest rate pass-throughQatar bank lending ratesNARDL
Metaanalyse der Evaluationen österreichischer FTI-Politik. Technischer Report
September, 2026 • Report
Wagner, Isabella Elisabeth, König, Thomas, de Koning, Paloeka
Das FTI-System wird fortlaufend auf unterschiedlichen Ebenen evaluiert - von Einzelmaßnahmen und Programmen bis hin zu institutionellen und systemischen Fragestellungen. Es mangelt daher hä…
Das FTI-System wird fortlaufend auf unterschiedlichen Ebenen evaluiert - von Einzelmaßnahmen und Programmen bis hin zu institutionellen und systemischen Fragestellungen. Es mangelt daher häufig nicht an Evaluationswissen. Dieses bleibt jedoch häufig an den jeweiligen Evaluationsgegenstand und -kontext gebunden. Mit Blick auf eine kommende Systemevaluation führt die Metaanalyse die bislang verstreuten Erkenntnisse zusammen, ordnet sie systematisch ein und macht sie über ihre ursprünglichen Kontexte hinaus bewertbar und nutzbar.Der technische Bericht fasst die Vorgehensweise zur Datenaufbereitung und -auswertung zusammen. Ziel ist es daher, das in Studien, Evaluationen und Analysen der vergangenen fünfzehn Jahre enthaltene Wissen über das österreichische FTI-System zu bündeln, übergreifend einzuordnen bestehende Erkenntnislücken und blinde Flecken sichtbar zu machen. Damit soll eine belastbare Wissensgrundlage für die Ausrichtung und Schwerpunktsetzung künftiger systemischer Betrachtungen geschaffen werden.
We present BenCzechMark (BCM), the first comprehensive Czech language benchmark designed for large language models, offering diverse tasks, multiple task formats, and multiple evaluation metrics. Its …
We present BenCzechMark (BCM), the first comprehensive Czech language benchmark designed for large language models, offering diverse tasks, multiple task formats, and multiple evaluation metrics. Its duel scoring system is grounded in statistical significance theory and uses aggregation across tasks inspired by social preference theory.Our benchmark encompasses 50 challenging tasks, with corresponding test datasets, primarily in native Czech, with 14 newly collected ones. These tasks span 8 categoriesand cover diverse domains, including historical Czech news, essays from pupils or language learners, and spoken word. Furthermore, we collect and clean BUT-Large Czech Collection, the largest publicly available clean Czech language corpus, and use it for (i) contamination analysis and (ii) continuous pretraining of the first Czech-centric7B language model with Czech-specific tokenization. We use our model as a baseline for comparison with publicly available multilingual models. Lastly, we release and maintain a leaderboard with existing 50 model submissions, where new model submissions can be made at https://huggingface.co/spaces/CZLC/BenCzechMark.
Requirements for Use Case 1: Identity management for enhanced privacy pre-serving Digital Wallet (D3.1)
May, 2025 • Project deliverable
Samiei, Salma, Cauchie, Stéphane
This deliverable reports on the results of Task 3.1, providing a technical review of digital wallets and the requirements for developing FHE-based biometric authentication.
Digital WalletFacial BiometryTechnical RequirementsPrivacy PreservingFHE
Biochemical Engineering: Bioprocesses, Fermentation and Applications
September, 2026 • Lesson
Prep4Uni.Online
Biochemical Engineering: Bioprocesses, Fermentation and Applications | Student Guide serves as an open educational resource (OER) curriculum framework and foundational reference manual connecting mole…
Biochemical Engineering: Bioprocesses, Fermentation and Applications | Student Guide serves as an open educational resource (OER) curriculum framework and foundational reference manual connecting molecular cellular biology to industrial-scale process engineering. Developed by Prep4Uni.Online, this module details upstream cell culture systems, bioreactor configurations, transport phenomena in cellular matrices, downstream bioseparations, and modern biomanufacturing paradigms.
Core Pedagogical Coverage:
Systems Engineering & IDEF0 Modeling: Translates biological inputs (microbial growth dynamics, metabolic kinetics, nutrient media) into engineered outputs (therapeutics, bulk enzymes, biofuels) under strict biosafety standards, GMP guidelines, and quality assurance controls.
Fermentation Paradigms & Reactor Design: Operating principles, fluid dynamics, and mass transfer trade-offs across Batch, Fed-Batch, and Continuous fermentation, including Stirred-Tank (STR), Airlift, and Packed-Bed bioreactors.
Downstream Processing & Purification Trains: Primary clarification (centrifugation, microfiltration), capture, chromatographic fractionation (affinity, ion-exchange, size-exclusion), ultrafiltration, and aseptic formulation.
Molecular & Synthetic Engineering: Biocatalysis, enzyme immobilization, metabolic flux redirection, CRISPR-Cas genome editing, and continuous biomanufacturing pipelines.
Self-Assessment & Quantitative Calculations: Rigorous foundational, scenario-based, and analytical practice problems with step-by-step solutions evaluating Monod cell growth kinetics and biomass yield coefficients.
Interactive Companion & Curriculum Navigation: This student guide accompanies the interactive digital learning module featuring dynamic Monod growth kinetic simulators, interdisciplinary curriculum pathways, and the Prep4Uni career diagnostic portal.
Permanent Webpage URL: https://prep4uni.online/stem/physical-technologies/chemical-engineering/biochemical-engineering/
There is an increasing interest in upgrading the EModel, a parametric tool for speech quality estimation, to the wideband and super-wideband contexts. The
Contemporary models of Unmanned Aerial Vehicles (UAVs) are largely developed using simulators. In a typical scheme, a flight simulator is dovetailed with a
Undertaking engineering research can be compounding for beginning graduate students and thwarting even for seasoned researchers. With a wealth of academic
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