522 research outputs found
Supplemental data for "Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators"
No full textThis repository contains supplemental data for the article
Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators,
accepted for publication in the International Journal for Numerical Methods in Engineering (IJNME) by Julius Herb and Felix Fritzen [1].
In this publication, we introduce UNO-CG, a hybrid solver that accelerates conjugate gradient (CG) solvers using specially designed machine-learned preconditioners, while ensuring convergence by construction.
As a preconditioner, we propose Unitary Neural Operators (UNOs) as a modification of the established Fourier Neural Operators.
Our method can be interpreted as a data-driven discovery of Green's functions, which are then used much like expert knowledge to accelerate iterative solvers.
The data contained in this DaRUS repository acts as an extension to the GitHub repository that contains a software package for UNO-CG, including a GPU-accelerated implementation of the hybrid solver in PyTorch, an implementation for PETSc, and the training procedures proposed in our article.
All results and figures in the article can be reproduced using the mentioned software package together with the data sets available in this DaRUS repository.
As part of the training data and evaluation data, we consider bi-phasic two-dimensional microstructures with a resolution of 400 × 400 pixels, as published in [2], and three-dimensional microstructures with a resolution of 192 × 192 × 192 voxels, as published in [3].
Further information is available in the `README.md` file of this repository.
[1] Herb, J. and Fritzen, F. (2026), Accelerating Conjugate Gradient Solvers for Homogenization Problems with Unitary Neural Operators. Int J Numer Methods Eng. https://doi.org/10.1002/nme.70277
[2] Lißner, J. (2020). 2d microstructure data (Version V2) [dataset]. DaRUS.
https://doi.org/10.18419/DARUS-1151
[3] Prifling, B., Röding, M., Townsend, P., Neumann, M., and Schmidt, V. (2020). Large-scale statistical learning for mass transport prediction in porous materials using 90,000 artificially generated microstructures [dataset]. Zenodo. https://doi.org/10.5281/zenodo.4047774</a
Supplemental data for "Spectral Normalization and Voigt–Reuss net: A universal approach to microstructure‐property forecasting with physical guarantees"
No full textThis repository contains supplemental data for the article
"Spectral Normalization and Voigt-Reuss net: A universal approach to microstructure‐property forecasting with physical guarantees",
accepted for publication in GAMM-Mitteilungen by Sanath Keshav, Julius Herb, and Felix Fritzen [1]. The data contained in this DaRUS repository acts as an extension to the GitHub repository for the so-called Voigt-Reuss net. The data in this dataset is generated by solving thermal homogenization problems for an abundance of different microstructures. The microstructures are defined by periodic representative volume elements (RVE) and periodic boundary conditions are applied to the temperature fluctuations.
We consider bi-phasic two-dimensional microstructures with a resolution of 400 × 400 pixels, as published in [2], and three-dimensional microstructures with a resolution of 192 × 192 × 192 voxels, as published in [3]. For both microstructure datasets, we provide the effective thermal conductivity tensor that is obtained by solving homogenization problems on the full microstructure for different material parameters in the two phases. For the simulation, we used our implementation of Fourier-Accelerated Nodal Solvers (FANS, [4]) that is based on a Finite Element Method (FEM) discretization. Further details are provided in the README.md file of this dataset, in our manuscript [1], and in the GitHub repository.
[1] Keshav, S., Herb, J., and Fritzen, F. (2025). Spectral Normalization and Voigt–Reuss net: A universal approach to microstructure‐property forecasting with physical guarantees, GAMM‐Mitteilungen. (2025), e70005.
https://doi.org/10.1002/gamm.70005
[2] Lißner, J. (2020). 2d microstructure data (Version V2) [dataset]. DaRUS.
https://doi.org/doi:10.18419/DARUS-1151
[3] Prifling, B., Röding, M., Townsend, P., Neumann, M., and Schmidt, V. (2020). Large-scale statistical learning for mass transport prediction in porous materials using 90,000 artificially generated microstructures [dataset]. Zenodo. https://doi.org/10.5281/zenodo.4047774
[4] Leuschner, M., and Fritzen, F. (2018). Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems. Computational Mechanics, 62(3), 359-392.
https://doi.org/10.1007/s00466-017-1501-5 <br
Replication Data for: Flow in Porous Media with Fractures of Varying Aperture
No full textThis data set contains the simulation data for the results presented in [S. Burbulla, M. Hörl, and C. Rohde (2022). "Flow in Porous Media with Fractures of Varying Aperture." Submitted for publication, <a href="
https://doi.org/10.48550/arXiv.2207.09301">
https://doi.org/10.48550/arXiv.2207.09301].
We consider the numerical solutions of single-phase fluid flow governed by Darcy's law in a fractured porous medium for four different scenarios. For each scenario, we provide the raw vtk-files (*.vtu and *.vtp) of the pressure field for different values of the fracture aperture and for discontinuous Galerkin discretizations of four different discrete fracture models and one full-dimensional reference model. These files can be reproduced by running the script main_comparison.py of the corresponding source code (see [S. Burbulla, M. Hörl, C. Rohde (2022). "Source Code for: Flow in Porous Media with Fractures of Varying Aperture", https://doi.org/10.18419/darus-3012, DaRUS.]). Moreover, we provide visualizations (*.pdf) of the simulation results for each scenario that can be reproduced by running the script plot_comparison.py which is part of the corresponding source code. This includes, for each value of the fracture aperture, a visualization of the full-dimensional reference pressure and velocity, as well as a plot of the effective fracture pressure and the corresponding absolute error (compared to the full-dimensional reference solution) for the different discrete models. In addition, the L2-error of the effective fracture pressure is plotted as function of the fracture aperture for the different reduced models.
Scenario 1a (section-6.1.1.tar.gz): Flow perpendicular to a sinusoidal fracture with constant total aperture (two-dimensional).
Scenario 1b (section-6.1.2.tar.gz): Flow perpendicular to a sinusoidal fracture with constant total aperture (three-dimensional).
Scenario 2 (section-6.2.tar.gz): Flow perpendicular to an axisymmetric sinusoidal fracture (two-dimensional).
Scenario 3 (section-6.3.tar.gz): Tangential flow through an axisymmetric sinusoidal fracture (two-dimensional).
A detailed description of the different scenarios can be found in Section 6 in [S. Burbulla, M. Hörl, and C. Rohde (2022). "Flow in Porous Media with Fractures of Varying Aperture." Submitted for publication, <a href="
https://doi.org/10.48550/arXiv.2207.09301">
https://doi.org/10.48550/arXiv.2207.09301]
Supplementary Videos for: Robustly optimal dynamics for active matter reservoir computing (Gaimann and Klopotek, 2025)
No full text
This dataset contains supplementary videos for the publication "Robustly optimal dynamics for active matter reservoir computing" (Gaimann and Klopotek, 2025)
The videos show active matter systems (swarms) driven by an external force. These swarm systems can be used to predict the future trajectory of the external driving force using reservoir computing. Their default external driving protocol is the chaotic attractor Lorenz-63, but we also employ the attractors Hénon-Heiles, Rössler, Chua, and Lorenz-96 as benchmarks. Agents are colored by their current speed. The driver is marked as a black spiked ball, follows a fixed trajectory specified by the driving protocol, and exerts a repulsive force on the agents. The past positions of agents and drivers in a time window of 0.1 time units (5 integration time steps of 0.02 time units as default) are displayed as traces. Agents experience local alignment, local repulsion, global attraction (homing) to the center of the simulation box, speed control towards a constant agent speed, and local driver repulsion. A sigmoid force clamp (wrapper) processes and limits the total force experienced by each agent. The simulation uses periodic boundary conditions. Velocity fluctuations are colored by their orientation; the green cross indicates the center of mass.
Each video corresponds to a specific parameter combination or a point in a parameter scan presented in the corresponding publication, or to a specific parameter combination.
We provide videos for the following parameter scans:
speed-controller
speed-controller (velocity fluctuations)
speed-controller, with an integration time step of 2e-3
speed-controller, without external driving (undriven)
speed-controller, with a single agent
speed-controller, with 500 agents (overdamped phenomenology)
speed-controller, with initial transient (burn-in phase)
speed-controller, with Hénon-Heiles driving protocol
speed-controller, with Rössler driving protocol
speed-controller, with Chua driving protocol
speed-controller, with Lorenz-96 driving protocol
damping analysis, with non-interacting agents
damping analysis, with interacting agents
alignment force, with speed-controller settings of Lymburn et al. (2021)
homing force, with varied speed-controller strength
reproduction of the dynamical regimes analyzed in Lymburn et al. (2021) (Fig. 7)
We also provide visualizations of the time evolution of chaotic attractors that we use as driving protocols:
Lorenz-63
Hénon–Heiles
Rössler
Chua
Lorenz-96
The raw data used to generate these videos is published as:
Gaimann, M. U., & Klopotek, M. (2025). Replication Data for: Robustly optimal dynamics for active matter reservoir computing (Gaimann and Klopotek, 2025). DaRUS. https://doi.org/10.18419/DARUS-4620.
Changelog
V2
Added videos showing active matter systems with random uniform driving with different driver update intervals (every 1, 2, 5, 10 steps) for parameter combinations of the speed-controller parameter scan, used for the computation of the short-term memory capacity
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TRChallenge - experimental results 2022
No full textThis dataset contains experimental data acquired from the benchmark system of the Tribomechadynamics Research Challenge [1]. The tests were part of Project 3 of the Tribomechadynamics Research Camp 2022 in Stuttgart [2]. CAD models, technical drawings and design documentation are available in [4].
Data obtained by linear modal testing is available, along with data obtained by three types of nonlinear tests, Phase Resonance Testing (PRT), Response Controlled Testing (RCT), and Excitation Controlled Testing (ECT). The test methods are described in [3].
Velocity data was acquired using a multi-point vibrometer (MPV). The 17 sensor locations are indicated in Figure 3 in [3]. Single-point/differential vibrometers (SPVs) were used for feedback control during the nonlinear tests. The SPV data is redundant with the MPV data, and is thus not contained in this dataset.
The naming and the content of each data file type is described in the file “README”.
REFERENCES
[1] http://tmd.rice.edu/ tribomechadynamics-research-challenge-2021/
[2] http://tmd.rice.edu/tribomechadynamics-research-camp/2022-graduate-projects/
[3] https://arxiv.org/abs/2403.07438
[4] https://doi.org/10.18419/darus-3147
ACKNOWLEDGEMENTS
M. Krack is grateful for the funding received by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [Project 450056469, 495957501].
This work presents results of the Tribomechadynamics Research Camp (TRC). The authors thank MTU Aero Engines AG for sponsoring the TRC 2022.
The support from NSF grant No: 1847130 is appreciated by A. Bhattu.
S. Hermann is grateful for the funding received by the EIPHI Graduate School, ANR-17-EURE-0002.
N. Jamia gratefully acknowledges the support of the Engineering and Physical Sciences Research Council through the award of the Programme Grant “Digital Twins for Improved Dynamic Design”, grant number EP/R006768/1
Replication Data for: Robustly optimal dynamics for active matter reservoir computing (Gaimann and Klopotek, 2025)
No full text
This repository contains raw and post-processed replication data for the publication "Robustly optimal dynamics for active matter reservoir computing" (Gaimann and Klopotek, 2025).
The datasets contain physical observables recorded during non-equilibrium simulations of active matter systems (swarms) driven by an external force. These simulations serve as information processors in a reservoir computing setup.
We provide replication data for all figures and supplementary videos shown in our publication:
speed-controller
speed-controller, with an integration time step of 2e-3
speed-controller, with a maximum correlation delay time of 75 integration time steps
speed-controller, without external driving (undriven)
speed-controller, with a single agent
speed-controller, with two agents
speed-controller, with 500 agents (overdamped phenomenology)
speed-controller, with initial transient (burn-in phase)
speed-controller, with 12 integration time steps predicted ahead
speed-controller, with 50 integration time steps predicted ahead
speed-controller, with 100 integration time steps predicted ahead
speed-controller, with Hénon-Heiles driving protocol
speed-controller, with Hénon-Heiles driving protocol, Lyapunov time-adjusted prediction (638 integration time steps), and maximum correlation delay time of 75 integration time steps
speed-controller, with Rössler driving protocol
speed-controller, with Rössler driving protocol, Lyapunov time-adjusted prediction (150 integration time steps), and maximum correlation delay time of 75 integration time steps
speed-controller, with Chua driving protocol
speed-controller, with Chua driving protocol, Lyapunov time-adjusted prediction (18 integration time steps), and maximum correlation delay time of 75 integration time steps
speed-controller, with Lorenz-96 driving protocol
speed-controller, with Lorenz-96 driving protocol, Lyapunov time-adjusted prediction (17 integration time steps), and maximum correlation delay time of 75 integration time steps
speed-controller, with a larger correlation recording delay time of 500 integration time steps
damping analysis, with non-interacting agents
damping analysis, with interacting agents
damping analysis, with non-interacting agents and an integration time step of 2e-3
damping analysis, with interacting agents and an integration time step of 2e-3
alignment force, with speed-controller settings of Lymburn et al. (2021)
alignment force, with overdamped speed-controller settings
homing force strength vs. speed-controller strength, with speed-controller settings of Lymburn et al. (2021)
homing force strength vs. speed-controller strength, with overdamped speed-controller settings
homing force strength vs. speed-controller target agent speed
number of agents vs. Gaussian white noise strength, with speed-controller settings of Lymburn et al. (2021)
number of agents vs. Gaussian white noise strength, with overdamped speed-controller settings
reproduction of the dynamical regimes analyzed in Lymburn et al. (2021) (Fig. 7)
reproduction of the (driven) alignment strength vs. repulsion strength parameter scans in Lymburn et al. (2021) (Fig. 6B, Fig. 8A)
reproduction of the undriven alignment strength vs. repulsion strength parameter scan in Lymburn et al. (2021) (Fig. 6A)
The Lorenz-63 driving protocol was generated on the fly during the simulation. We also provide the raw chaotic time series used as benchmark driving protocols:
Hénon-Heiles
Rössler
Chua
Lorenz-96
Each dataset typically contains 400 parameter combinations. Each parameter combination contains four files:
config.yaml: controlled variables
simulation_output_train.h5: physical simulation observables in first (training) run
simulation_output_test.h5: physical simulation observables in second (testing) run
reservoir_computer_output.h5: observables related to reservoir computing and time series prediction
The second run has a different chaotic driving protocol, using the same underlying dynamical system (chaotic attractor) but different initial conditions.
Only the first file is generated if the dataset contains a simulation without an external driving force (undriven). By default, for all driven simulations, physical observables are only recorded for the test run for a full reservoir computing train/test cycle. Each simulation typically consists of 1,000.00 time units (50,000 integration time steps of 0.02 time units by default). A burn-in phase of 20.0 simulation time units (1,000 integration time steps of 0.02 time units by default) takes place at the beginning of each simulation, which is not recorded by default (only recorded in the "speed-controller, with initial transient" dataset). Controlled variables are stored as HDF5 attributes. At each step, we predict by default 25 integration time steps ahead (=0.45283 L63-Lyapunov times). For Lyapunov times adjusted attractor predictions, we predict n integration time steps ahead that equal 0.45283 Lyapunov times of the corresponding attractor.
The simulation output files contain:
agent_observables: positions, velocities, total forces, velocity fluctuations for all agents; for the first 20.0 simulation time units
frame_observables: driver position (external driving trajectory / input time series), center of mass (taking periodic boundary conditions into account), agent-averaged observables, scalar polarity, scalar rotation; for the full simulation
histograms: binned agent observables and derived quantities; for the full simulation
radially_binned: radial distribution function (agent count), connected velocity correlation, cumulative velocity correlation
time_lags: auto-correlations of agent observables and derived quantities, two-time correlations of agent observables and derived quantities
reference_frame_steps: reference frames (measured in integration steps) for the recording of delay-based quantities in time_lags
The reservoir computer output files contain:
linear_regression_model: the weights of the linear model (readout layer)
observer_kernel_params: placement positions and widths of the Gaussian observation kernels
predictions_train: n-steps-ahead prediction using the trained linear model, on training data
predictions_test: n-steps-ahead prediction using the trained linear model, on testing data
Aggregates of physical observables across all parameter combinations in a single dataset are stored as CSV files for convenience, the relevant observable is indicated by the file name. Files that carry the "time_avg" tag are averaged over all simulation time steps, for the "ensemble_avg" averaged over all seeds (only one seed is used here), and for the "array_avg" averaged over all recorded entries (typically samples at different time steps). We provide the following aggregated observables that were processed to generate figures in our associated publication:
lymburn_correlation_coefficient: Correlation coefficient, predictive performance
agent_avg_msd_at_lyapunov_time_step=55: Agent-averaged mean squared displacement at the Lyapunov integration time step of the Lorenz-63 attractor (after 55 integration time steps of 0.02 each)
first_local_min.array_avg.h5?connected_velocity_correlation: First local minimum of the connected velocity correlation function, averaged over all recorded samples
mean_speed: Agent-averaged speed
scalar_polarity: Scalar polarity
scalar_rotation: Scalar rotation
attanasi_susceptibility: Dynamical susceptibility
The supplementary videos generated using this raw data are published as: Gaimann, M. U., & Klopotek, M. (2025). Supplementary Videos for: Robustly optimal dynamics for active matter reservoir computing (Gaimann and Klopotek, 2025). DaRUS. doi:10.18419/DARUS-4619.
Changelog
V2
Added raw random uniform driver trajectory files confined to a circle with radius 4.0, with different change intervals (used to compute the short-term memory capacity)
Added datasets for the computation of the short-term memory capacity for parameter combinations of the speed-controller parameter scan, with different driving protocols (Lorenz-63, random uniform with different change intervals). These datasets provide the full recorded Gaussian kernel observations of the simulation runs; datasets labeled with "memory-capacity" contain observables related to the memory capacity.
Added datasets of a simple Echo State Network (ESN) comparison, following the recipe in Hinaut and Trouvain (2021) (https://inria.hal.science/hal-03203318v2)
Added a dataset for the undriven active matter simulation of the homing-speed-controller-strength dataset with parameter combination K_h=483 and K_sc=0.0207 (highly condensed droplet case)
Updated datasets used for figures in the main text with aggregates of more performance metrics (NMSE, NRMSE, sMAPE, Pearson correlation coefficient of the y coordinate computed according to Lymburn et al. (2021))
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Measured hydrometeorologic data
No full textSolving the energy balance at the atmosphere-subsurface interface drives heat input (in the summer) into the subsurface. We use this subsequently to calculate heat transport and water flow into the subsurface and then to calculate temperature s around drinking-water supply pipes.
This data is from the weather station of the University of Stuttgart.
We are providing the measured Boundary Conditions, needed to compute the interface boundary conditions:
long wave radiation incoming
short wave radiation incoming
air temperature in 2 m above ground
wind velocity in 2 m above ground
relative humidity in 2 m above ground
precipitation intensity
Data is given tabulated, a readme-file explains the column names
Digital rock physics: A geological driven workflow for the segmentation of anisotropic Ruhr sandstone: segmented subvolumes
No full textThe Ruhr sandstone is assigned to the Upper Carboniferous and is part of the Ruhr cyclothem located in North Rhine-Westphalia, which consists of clays, siltstones, mudstones, sandstones, and interbedded coal seams. The sediment was chemically and mechanically compacted, folded, and faulted during the Hercynian orogeny. The studied microstructure of the Ruhr sandstone indicates depths of up to 6000 m and reconstructed, possible temperatures of over 120 ºC. This results in a complex mineralogical structure compared to other sandstones such as the Berea sandstone or the Fontainbleau sandstone. As part of the Balcewicz et al. (2021) publication, we made a first attempt to study the Ruhr Sandstone using Digital Rock Physics (DRP).
This dataset contains two different binned subvolumes of the micro-XRCT data set presented in Ruf et al. (2021). Based on a 1600³ voxel subvolume from the original data set, an 800³ voxel cube subvolume ("subvolume_2x2x2_binned.rar"), and a 400³ voxel cube subvolume ("subvolume_4x4x4_binned.rar") were generated by a 2x2x2 and 4x4x4 binning procedure, subsequently. This means that both data sets show the same physical region but distinguishing in the resolution. Both data sets were then segmented into a total of eight phases: (1) clean pore, (2) soiled pore, (3) quartz, (4) sericite, (5) albite, (6) orthoclase, (7) pyrite, and (8) high angle quartz grain boundaries. The idea of dividing the pore space into two distinct phases was inspired by thin-section studies of the microstructure. Here we found that there is a difference between (1) open pores and (2) pores filled with rock fragments of the host rock. A detailed description of the segmentation workflow can be looked up in Balcewicz et al. (2021) publication.<br
Coupled mass-spring-damper system for nonlinear system identification - actuated with random static inputs - synthetically generated
No full textOverview
This dataset contains input-output data of a coupled mass-spring-damper system with a nonlinear force profile. The data was generated with statesim [1], a python package for simulating linear and nonlinear ODEs, for the system coupled-msd. The configuration .json files for the corresponding datasets (in-distribution and out-of-distribution) can be found in the respective folders. After creating the dataset, the files are stored in the raw folder. Then, they are split into subsets for training, testing, and validation and can be found in the processed folder; details about the splitting are found in the config.json file.
The dataset can be used to test system identification algorithms and methods that aim to identify nonlinear dynamics from input-output measurements. The training dataset is used to optimize the model parameters, the validation set for hyperparameter optimization, and the test set only for the final evaluation.
In [2], the authors use the same underlying dynamics to create their dataset.
Input generation
Input trajectories are piecewise constant trajectories.
Noise
Gaussian white noise of approximately 30dB is added at the output.
Statistics
The input and output size is one.
In-distribution data: 1,500,000 data points
Training: 120 trajectories of length 7500
Validation: 20 trajectories of length 7500
Test: 60 trajectories of length 7500
Out-of-distribution data: 10 times 3000 data points
10 different datasets were only used for testing. Each dataset contains 50 trajectories of length 6000.
References
Frank, D. statesim [Computer software]. https://github.com/Dany-L/statesim
Revay, M., Wang, R., & Manchester, I. R. (2020). A convex parameterization of robust recurrent neural networks. IEEE Control Systems Letters, 5(4), 1363-1368.
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Case1 - Single Fracture
No full textThis dataset contains results related to the benchmark case 1 as described in detail in the publication
I. Berre, W. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, and A. Tatomir.
Call for participation: Verification benchmarks for single-phase flow in three-dimensional fractured porous media,
arXiv e-prints, art. arXiv:1809.06926, 2018
The dataset is structured in sub-folders, namely "ustutt-mpfa" and "reference". The first contains the results obtained with the mpfa scheme available in the open-source simulator Dumux. These results are presented in the publication
Inga Berre, Wietse M. Boon, Bernd Flemisch, Alessio Fumagalli, Dennis Gläser, Eirik Keilegavlen, Anna Scotti, Ivar Stefansson, Alexandru Tatomir, Konstantin Brenner, Samuel Burbulla, Philippe Devloo, Omar Duran, Marco Favino, Julian Hennicker, I-Hsien Lee, Konstantin Lipnikov, Roland Masson, Klaus Mosthaf, Maria Giuseppina Chiara Nestola, Chuen-Fa Ni, Kirill Nikitin, Philipp Schädle, Daniil Svyatskiy, Ruslan Yanbarisov and Patrick Zulian.
Verification benchmarks for single-phase flow in three-dimensional fractured porous media,
arXiv e-prints, art. arXiv:2002.07005, 2020
The folder "reference" contains a reference solution, obtained from a simulation on a finer mesh as specified in the publication. The corresponding mesh can be found in the file "reference/single_500k.msh".
Both folders contain a sub-folder "vtk", which contains the results for each time step of the simulation in .vtu format, and which can be visualized with the open-source software ParaView. The .pvd files allow for visualization of sets of .vtu files together with time information. The .vtu files are organized as follows: the files with *_onep_* in the file names contain the pressure solution, while those with *_tracer_* contain the solution for the tracer concentration. In the folder "ustutt-mpfa", results are available for three refinements, indicated in the filenames by *_0*, *_1* and *_2*.
The files "dofs.csv" contain the number of degrees of freedom of a simulation as specified in Section 5.4, and the files "dataovertime_*" the concentration results over time as described in Section 4.1 of the Call for participation (reference above), respectively.
The results can be reproduced by getting the source code to the Dumux implementation of this test case from https://git.iws.uni-stuttgart.de/dumux-pub/berre2019a. Installation and execution instructions can be found therein
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