GeoSim Mantle Plume Simulation Dataset

Overview

GeoSim contains two-dimensional thermo-mechanical mantle plume simulations generated with I2VIS, a geodynamic solver based on Marker-in-Cell and finite-difference methods. The dataset supports spatiotemporal forecasting, surrogate modeling, operator learning, and related scientific machine-learning tasks.

The simulations are divided into two parameter-sampling groups:

• plume1: one model parameter is sampled.
• plume2: two model parameters are sampled.

Each group provides train and test splits at two resolutions:

• 401x309_physical: physical field values on the non-uniform I2VIS grid;
• 128x128_norm: normalized fields conservatively remapped to a 128 x 128 grid;

Files

Files follow the naming pattern:

geosim_<case>_<split>_<grid>_<values>.hdf5

Each field shape is (n_sample, n_time, H, W).

File	Field shape	Time unit
geosim_plume1_train_401x309_physical.hdf5	(97, 97, 401, 309)	yr
geosim_plume1_test_401x309_physical.hdf5	(12, 131, 401, 309)	yr
geosim_plume2_train_401x309_physical.hdf5	(103, 131, 401, 309)	yr
geosim_plume2_test_401x309_physical.hdf5	(25, 131, 401, 309)	yr
geosim_plume1_train_128x128_norm.hdf5	(97, 97, 128, 128)	Myr
geosim_plume1_test_128x128_norm.hdf5	(12, 131, 128, 128)	Myr
geosim_plume2_train_128x128_norm.hdf5	(103, 131, 128, 128)	Myr
geosim_plume2_test_128x128_norm.hdf5	(25, 131, 128, 128)	Myr

HDF5 Format

All files contain the same nine datasets:

<file>.hdf5
├── nu                 (n_sample, n_time, H, W)  float32
├── pr                 (n_sample, n_time, H, W)  float32
├── ro                 (n_sample, n_time, H, W)  float32
├── t-coordinate       (n_sample, n_time)        float32
├── tk                 (n_sample, n_time, H, W)  float32
├── vx                 (n_sample, n_time, H, W)  float32
├── vy                 (n_sample, n_time, H, W)  float32
├── x-coordinate       (H,)                      float32
└── y-coordinate       (W,)                      float32

Field axes are ordered as follows:

Axis	Meaning
0	sample
1	time
2	x
3	y

Access datasets by key rather than relying on HDF5 key order. For spatial meshes, use:

X, Y = np.meshgrid(x, y, indexing="ij")

Fields and Units

Key	Quantity	401x309_physical	128x128_norm
ro	density	kg/m³	normalized
pr	mechanical pressure	Pa	normalized
tk	temperature	K	normalized
nu	log10 viscosity	log10(Pa·s)	normalized
vx	horizontal velocity	m/s	normalized
vy	vertical velocity, positive upward	m/s	normalized
t-coordinate	physical time	yr	Myr

pr is the mechanical pressure unknown solved jointly with vx and vy in the Stokes-continuity system.

Coordinates and Time

The physical grid spans 1150 km × 660 km. It is non-uniform in both directions: horizontal spacing decreases from approximately 4 km near the lateral boundaries to 1 km in the central plume region, while the upper 220 km uses 1 km vertical spacing and the deeper domain gradually coarsens to approximately 9 km.

• x-coordinate: 0 to 1,150,000 m
• y-coordinate: 0 to 660,000 m

The 128 x 128 files contain their remapped coordinate arrays. Read x-coordinate and y-coordinate from each file instead of assuming a fixed normalized coordinate sequence.

For paired physical and normalized products,

t_myr = t_years / 1e6

This conversion applies only to t-coordinate. The unit is recorded in both metadata locations:

Product	Root attribute time_unit	t-coordinate attribute units
401x309_physical	yr	yr
128x128_norm	Myr	Myr

Normalization and Remapping

The 128 x 128 products use per-field max normalization:

field_norm = field_physical / max_value

Train and test files within each case use the same constants.

Field	plume1	plume2
ro	3828.61	3829.551
pr	2.18068e10	2.1789805e10
tk	2113.0	2260.3352
nu	24.0	24.000002
vx	7.59748e-09	1.9177052e-07
vy	4.59946e-09	9.3668184e-08

Normalized values are not guaranteed to lie within [-1, 1]. Signed velocity components may exceed this range because the constants are not maximum absolute values in both directions.

Spatial remapping uses separable first-order conservative interpolation:

F_target = w_x @ F_source @ w_y.T

The weights are source-target cell-overlap fractions on the non-uniform grid. This method preserves constant fields and area-weighted averages.

Physical Model

Numerical framework

The production simulations use a two-dimensional Marker-in-Cell formulation on a 401 x 309 non-uniform Eulerian grid. Lagrangian markers carry material identity and history, with an initial density of approximately 5 x 5 markers per cell. Finite-difference and interpolation weights on the non-uniform grid are generated with the Fornberg algorithm.

Gravity is

$$g_x=0,g_y=9.80665\mathrm{m}{\mathrm{s}}^{-2}\mathrm{.}g\_x=0,\backslash qquad\; g\_y=9.80665\backslash \; \backslash mathrm\{m\backslash ,s^\{-2\}\}.$$

Mechanical equations

At each mechanical solve, pressure and velocity are obtained from the coupled Stokes-continuity system:

$$\frac{\mathrm{\partial }{\tau }_{xx}}{\mathrm{\partial }x}+\frac{\mathrm{\partial }{\tau }_{xy}}{\mathrm{\partial }y}-\frac{\mathrm{\partial }P}{\mathrm{\partial }x}=-\rho g_x,\backslash frac\{\backslash partial\; \backslash tau\_\{xx\}\}\{\backslash partial\; x\}\; +\backslash frac\{\backslash partial\; \backslash tau\_\{xy\}\}\{\backslash partial\; y\}\; -\backslash frac\{\backslash partial\; P\}\{\backslash partial\; x\}\; =-\backslash rho\; g\_x,$$

$$\frac{\mathrm{\partial }{\tau }_{yy}}{\mathrm{\partial }y}+\frac{\mathrm{\partial }{\tau }_{xy}}{\mathrm{\partial }x}-\frac{\mathrm{\partial }P}{\mathrm{\partial }y}=-\rho g_y\mathrm{.}\backslash frac\{\backslash partial\; \backslash tau\_\{yy\}\}\{\backslash partial\; y\}\; +\backslash frac\{\backslash partial\; \backslash tau\_\{xy\}\}\{\backslash partial\; x\}\; -\backslash frac\{\backslash partial\; P\}\{\backslash partial\; y\}\; =-\backslash rho\; g\_y.$$

The continuity residual includes volumetric and compressibility contributions:

$$R_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}}=\mathrm{\nabla }\cdot \mathbf{v}-d_v+{\beta }_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}\frac{P-P_0}{\mathrm{\Delta }t}\mathrm{.}R\_\{\backslash mathrm\{cont\}\}\; =\backslash nabla\backslash cdot\backslash mathbf\{v\}\; -d\_v\; +\backslash beta\_\{\backslash mathrm\{comp\}\}\backslash frac\{P-P\_0\}\{\backslash Delta\; t\}.$$

The global sparse system is solved with Intel MKL PARDISO. All velocity boundaries are free slip. Marker-to-grid viscosity uses arithmetic averaging, and the final viscosity is limited to

$${10}^{18}\le \eta \le {10}^{24}\mathrm{P}\mathrm{a}\mathrm{s}\mathrm{.}10^\{18\}\backslash leq\backslash eta\backslash leq10^\{24\}\backslash \; \backslash mathrm\{Pa\backslash ,s\}.$$

Rheology

The configured mantle, plume, and crustal materials use Ranalli-style visco-plastic parameterizations. Ductile deformation depends on pressure, temperature, and strain rate. Its general power-law form is

$${\eta }_{\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e}}\propto {[{\eta }_0\exp \left(\frac{E+PV}{RT}\right)]}^{1\mathrm{/}n}{\dot{\epsilon }}_{II}^{(1-n)\mathrm{/}n},\backslash eta\_\{\backslash mathrm\{ductile\}\}\; \backslash propto\; \backslash left[\; \backslash eta\_0\backslash exp\backslash left(\backslash frac\{E+PV\}\{RT\}\backslash right)\; \backslash right]^\{1/n\}\; \backslash dot\{\backslash varepsilon\}\_\{II\}^\{(1-n)/n\},$$

with material-dependent diffusion-dislocation transitions. Dry mantle materials use $n=3.5$, while plume material uses $n=4.0$.

Brittle yielding follows a Mohr-Coulomb-type relation:

$${\tau }_y=A({\epsilon }_{\mathrm{a}\mathrm{c}\mathrm{c}})+\lambda B({\epsilon }_{\mathrm{a}\mathrm{c}\mathrm{c}})P,\backslash tau\_y=A(\backslash varepsilon\_\{\backslash mathrm\{acc\}\})\; +\backslash lambda\; B(\backslash varepsilon\_\{\backslash mathrm\{acc\}\})P,$$

$${\eta }_{\mathrm{b}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{t}\mathrm{l}\mathrm{e}}=\frac{{\tau }_y}{2{\dot{\epsilon }}_{II}}\mathrm{.}\backslash eta\_\{\backslash mathrm\{brittle\}\}\; =\backslash frac\{\backslash tau\_y\}\{2\backslash dot\{\backslash varepsilon\}\_\{II\}\}.$$

Cohesion $A$ and friction coefficient $B$ weaken with accumulated strain. When plastic yielding is active, marker strain history evolves as

$${\epsilon }_{\mathrm{a}\mathrm{c}\mathrm{c}}^{n+1}={\epsilon }_{\mathrm{a}\mathrm{c}\mathrm{c}}^n+\mathrm{\Delta }t{\dot{\epsilon }}_{II}\mathrm{.}\backslash varepsilon\_\{\backslash mathrm\{acc\}\}^\{n+1\}\; =\backslash varepsilon\_\{\backslash mathrm\{acc\}\}^n\; +\backslash Delta\; t\backslash ,\backslash dot\{\backslash varepsilon\}\_\{II\}.$$

The weakest active ductile or brittle mechanism controls the effective viscosity. A conditional Peierls mechanism is also included for eligible materials when

Thermal model

Temperature is advanced with an implicit thermal solve:

$$\rho C_p\frac{DT}{Dt}=\mathrm{\nabla }\cdot (k\mathrm{\nabla }T)+H_r+H_a+H_s\mathrm{.}\backslash rho\; C\_p\backslash frac\{DT\}\{Dt\}\; =\backslash nabla\backslash cdot(k\backslash nabla\; T)+H\_r+H\_a+H\_s.$$

The configured source terms are radiogenic heating, viscous or shear heating, and simplified adiabatic heating. The latter uses

$$\frac{{\alpha }_{T}T}{C_p}(g_x{v}_x+g_y{v}_y)\mathrm{.}\backslash frac\{\backslash alpha\_T\; T\}\{C\_p\}\; \backslash left(g\_xv\_x+g\_yv\_y\backslash right).$$

The top and bottom temperatures are fixed at 273 K and 2113 K, respectively. Both lateral thermal boundaries are symmetric.

Material properties and conditional processes

Material properties are evaluated from the configured material laws, including enabled material and melt corrections. With densimod=3, the final density, heat capacity, and thermal conductivity used for marker-to-grid reconstruction are the material-law values. The thermodynamic database participates in the water, hydration, and material-state calculations but does not provide the final reconstructed density field.

The partial-melting routine is evaluated during marker updates and includes pressure- and water-dependent mantle melting. A conditional hydration and material-water subsystem is also enabled and contains an antigorite-stability criterion. These branches depend on the evolving marker state; their activation frequency and spatial extent are not encoded in the released fields.

Marker transport and time stepping

Markers are advected through the Eulerian velocity field with a four-stage Runge-Kutta scheme. After advection, density, viscosity, heat capacity, thermal conductivity, and related material properties are reconstructed on the Eulerian grid. Consequently, ro and nu reflect material identity, marker history, constitutive laws, and marker-to-grid reconstruction rather than independent scalar evolution alone.

The solver timestep is adaptive. It is bounded by the configured maximum timestep and by the allowed marker displacement:

$$\mathrm{\Delta }t\le \min (\frac{f_{\mathrm{m}\mathrm{o}\mathrm{v}\mathrm{e}}\mathrm{\Delta }{x}_{\mathrm{r}\mathrm{e}\mathrm{f}}}{\mathrm{\mid }{v}_x{\mathrm{\mid }}_{\max }},\frac{f_{\mathrm{m}\mathrm{o}\mathrm{v}\mathrm{e}}\mathrm{\Delta }{y}_{\mathrm{r}\mathrm{e}\mathrm{f}}}{\mathrm{\mid }{v}_y{\mathrm{\mid }}_{\max }})\mathrm{.}\backslash Delta\; t\backslash leq\; \backslash min\backslash left(\; \backslash frac\{f\_\{\backslash mathrm\{move\}\}\backslash Delta\; x\_\{\backslash mathrm\{ref\}\}\}\{|v\_x|\_\{\backslash max\}\},\; \backslash frac\{f\_\{\backslash mathrm\{move\}\}\backslash Delta\; y\_\{\backslash mathrm\{ref\}\}\}\{|v\_y|\_\{\backslash max\}\}\; \backslash right).$$

The thermal solver can reduce it further using

$$\mathrm{\Delta }{t}_T=\frac{\mathrm{\Delta }{T}_{\max }}{\max \mathrm{\mid }dT\mathrm{/}dt\mathrm{\mid }}\mathrm{.}\backslash Delta\; t\_T=\backslash frac\{\backslash Delta\; T\_\{\backslash max\}\}\{\backslash max|dT/dt|\}.$$

The internal solver timestep is distinct from both the saved output interval and any time normalization used by machine-learning pipelines.

Usage

import h5py
import numpy as np

path = "geosim_plume2_train_128x128_norm.hdf5"
fields = ["ro", "pr", "tk", "nu", "vx", "vy"]

with h5py.File(path, "r") as f:
    # Read one simulation while keeping the full time axis.
    sample = np.stack([f[key][0] for key in fields], axis=-1)
    time = f["t-coordinate"][0]
    time_unit = f["t-coordinate"].attrs["units"]
    x = f["x-coordinate"][:]
    y = f["y-coordinate"][:]

X, Y = np.meshgrid(x, y, indexing="ij")

print(sample.shape)  # (n_time, H, W, 6)
print(time.shape)    # (n_time,)
print(time_unit)     # Myr