ISEFlow is a hybrid flow-based neural network emulator for ice sheet sea-level projections with full uncertainty quantification. It supports both the Antarctic Ice Sheet (AIS) and the Greenland Ice Sheet (GrIS), producing IVAF (ice volume above flotation) change projections driven by ISMIP6 climate forcings for 2015–2100.

Developed at Brown University by Peter Van Katwyk.

GitHub: Brown-SciML/ise Documentation: ise.readthedocs.io PyPI: ise-py

Model Description

ISEFlow is a two-stage hybrid model trained sequentially:

NormalizingFlow — an autoregressive masked affine normalizing flow (via nflows) with a ConditionalDiagonalNormal base distribution. Trained first via maximum likelihood to capture aleatoric (data/structural) uncertainty.
DeepEnsemble — a heterogeneous ensemble of 10 single-layer LSTMs with varying hidden sizes (199–545 units) and sequence lengths (5–10). Each member is trained on [X, z] where z is the NF latent representation, capturing epistemic (model) uncertainty as ensemble disagreement.

Total uncertainty = epistemic + aleatoric (summed).

Architecture summary

Component	Type	Key parameters
NormalizingFlow	Autoregressive masked affine flow	`nflows`, ConditionalDiagonalNormal base
DeepEnsemble	10× LSTM members	Hidden: 199–545; Seq len: 5–10
Input features (AIS v1.1.0)	93 features	7 forcing vars + 5 lag steps + ISM one-hot configs
Input features (GrIS v1.1.0)	4 forcing vars + 5 lag steps + ISM one-hot configs
Output	IVAF change in mm SLE	Per timestep, 2015–2100 (86 steps)

Model Versions

Version	Ice Sheets	Notes
`v1.0.0`	AIS only	Includes `mrro_anomaly` (runoff) as a forcing variable
`v1.1.0` (current)	AIS + GrIS	`mrro_anomaly` removed from AIS; improved joint training

Repository Structure

v1.0.0/
  ISEFlow_AIS_v1-0-0/
    deep_ensemble.pth
    deep_ensemble_metadata.json
    normalizing_flow.pth
    normalizing_flow.pth_metadata.json
    ensemble_members/
      lstm1.pth ... lstm10.pth
v1.1.0/
  ISEFlow_AIS_v1-1-0/
    deep_ensemble.pth
    deep_ensemble_metadata.json
    normalizing_flow.pth
    normalizing_flow.pth_metadata.json
    scaler_X.pkl
    scaler_y.pkl
    ensemble_members/
      member_1.pth ... member_10.pth
  ISEFlow_GrIS_v1-1-0/
    (same structure as AIS)

Usage

Install the ise-py package:

pip install ise-py

Weights are downloaded automatically on first use:

python

from ise.models.iseflow import ISEFlow_AIS
from ise.data.inputs import ISEFlowAISInputs
import numpy as np

year = np.arange(2015, 2101)

# Option A: pre-computed anomaly inputs
inputs = ISEFlowAISInputs(
    year=year,
    sector=10,
    pr_anomaly=np.zeros(86),
    evspsbl_anomaly=np.zeros(86),
    smb_anomaly=np.zeros(86),
    ts_anomaly=np.zeros(86),
    ocean_thermal_forcing=np.linspace(1.5, 2.5, 86),
    ocean_salinity=np.full(86, 34.5),
    ocean_temperature=np.zeros(86),
    numerics="fd",
    stress_balance="hybrid",
    resolution="8",
    init_method="eq",
    initial_year=2005,
    melt_in_floating_cells="sub-grid",
    icefront_migration="str",
    ocean_forcing_type="open",
    ocean_sensitivity="medium",
    ice_shelf_fracture=False,
    open_melt_type="quad",
    standard_melt_type="nonlocal",
)

# Option B: raw absolute forcing values (anomaly conversion is automatic)
inputs = ISEFlowAISInputs.from_absolute_forcings(
    year=year,
    sector=10,
    pr=np.full(86, 1.3e-5),
    evspsbl=np.full(86, 4e-6),
    smb=np.full(86, 9e-6),
    ts=np.full(86, 255.0),
    ocean_thermal_forcing=np.linspace(1.5, 2.5, 86),
    ocean_salinity=np.full(86, 34.5),
    ocean_temperature=np.zeros(86),
    aogcm="noresm1-m_rcp85",
    numerics="fd",
    stress_balance="hybrid",
    resolution="8",
    init_method="eq",
    initial_year=2005,
    melt_in_floating_cells="sub-grid",
    icefront_migration="str",
    ocean_forcing_type="open",
    ocean_sensitivity="medium",
    ice_shelf_fracture=False,
    open_melt_type="quad",
    standard_melt_type="nonlocal",
)

# Load model and predict
model = ISEFlow_AIS(version="v1.1.0")
predictions, uncertainties = model.predict(inputs)

print(predictions.shape)            # (86, 1) — mm SLE, 2015-2100
print(uncertainties["epistemic"])   # epistemic uncertainty per timestep
print(uncertainties["aleatoric"])   # aleatoric uncertainty per timestep
print(uncertainties["total"])       # total = epistemic + aleatoric

Greenland Ice Sheet (GrIS)

python

from ise.models.iseflow import ISEFlow_GrIS
from ise.data.inputs import ISEFlowGrISInputs
import numpy as np

year = np.arange(2015, 2101)

inputs = ISEFlowGrISInputs.from_absolute_forcings(
    year=year,
    sector=1,
    smb=np.full(86, -200.0),
    st=np.full(86, -20.0),
    ocean_thermal_forcing=np.linspace(2.2, 3.5, 86),
    basin_runoff=np.linspace(0.01, 0.10, 86),
    aogcm="hadgem2-es_rcp85",
    initial_year=1990,
    numerics="fe",
    ice_flow_model="ho",
    initialization="dav",
    initial_smb="ra3",
    velocity="joughin",
    bedrock_topography="morlighem",
    surface_thickness="None",
    geothermal_heat_flux="g",
    res_min=1.0,
    res_max=7.5,
    standard_ocean_forcing=True,
    ocean_sensitivity="medium",
    ice_shelf_fracture=False,
)

model = ISEFlow_GrIS(version="v1.1.0")
predictions, uncertainties = model.predict(inputs)

Input Variables

AIS v1.1.0 Forcings

Variable	Description	Units
`pr_anomaly`	Precipitation anomaly (vs. 1995–2014 baseline)	kg m⁻² s⁻¹
`evspsbl_anomaly`	Evaporation/sublimation anomaly	kg m⁻² s⁻¹
`smb_anomaly`	Surface mass balance anomaly	kg m⁻² s⁻¹
`ts_anomaly`	Surface temperature anomaly	K
`ocean_thermal_forcing`	Ocean thermal forcing (absolute)	°C
`ocean_salinity`	Ocean salinity (absolute)	PSU
`ocean_temperature`	Ocean temperature (absolute)	°C

Atmospheric anomalies are computed relative to the ISMIP6 1995–2014 sector-averaged climatology. Use from_absolute_forcings() + aogcm= to convert raw values automatically.

GrIS v1.1.0 Forcings

Variable	Description
`aSMB`	SMB anomaly vs. 1960–1989 MAR baseline
`aST`	Surface temperature anomaly
`ocean_thermal_forcing`	Ocean thermal forcing (absolute)
`basin_runoff`	Basin-integrated runoff (absolute)

Training Data

Trained on ISMIP6 projections:

AIS: 18 drainage sectors, 8 km resolution
GrIS: 6 drainage basins, 5 km resolution
Period: 2015–2100 (86 annual timesteps)
Split: 70% train / 15% val / 15% test (random_state=42)

Performance

Model performance is evaluated on held-out ISMIP6 test projections. See the associated paper for quantitative metrics (RMSE, CRPS, coverage).

Citation

If you use ISEFlow in your research, please cite:

bibtex

@software{vankatwyk2026ise,
  author       = {Van Katwyk, Peter},
  title        = {{ISE}: {Ice Sheet Emulator}},
  year         = {2026},
  version      = {2.0.0},
  publisher    = {GitHub},
  url          = {https://github.com/Brown-SciML/ise},
}

And the associated paper:

bibtex

@article{vankatwyk_iseflow,
  title   = {ISEFlow: A Flow-Based Neural Network Emulator for Improved Sea Level Projections and Uncertainty Quantification},
  author  = {Van Katwyk, Peter},
  year    = {2025},
}

License

MIT License. See LICENSE.md.

Contact

Peter Van Katwyk — pvankatwyk@gmail.com Brown University, Department of Earth, Environmental and Planetary Sciences

pvankatwyk/iseflow

ISEFlow — Ice Sheet Emulator (AIS + GrIS)