Physics-informed Dynamic Emission Fields (PI-DEF)

Official code for the CVPR 2026 paper "Dynamic Black-hole Emission Tomography with Physics-informed Neural Fields."

@inproceedings{feng2026pidef,
  title={Dynamic Black-hole Emission Tomography with Physics-informed Neural Fields},
  author={Feng, Berthy T and Chael, Andrew A and Bromley, David and Levis, Aviad and Freeman, William T and Bouman, Katherine L},
  booktitle={Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  year={2026},
  organization={IEEE/CVF}
}

PI-DEF (Physics-informed Dynamic Emission Fields) infers the 4D emissivity field and 3D velocity field near a black hole given EHT measurements. The method involves two neural fields to represent the emissivity and velocity fields, which are jointly optimized according to a data-fit loss, dynamics loss, and light velocity regularization. So far, we have performed experiments on simulated EHT measurements of simulated emissivity fields.

Environment

Run the following commands to set up the Conda environment. The code was most recently tested with JAX v0.4.3 for CUDA 12.

conda update -n base -c defaults conda
conda create -y -n pidef python=3.9
conda activate pidef

Install the kgeo submodule in bhnerf:

git clone --recurse-submodules https://github.com/aviadlevis/bhnerf.git
pip install bhnerf/kgeo
rm -rf bhnerf

Install xarray and its dependencies:

conda install -y -c conda-forge xarray dask netCDF4 bottleneck

Install a forked version of ehtim v1.2.10 that resolves a bug and some warnings:

git clone https://github.com/berthyf96/eht-imaging
pip install eht-imaging/
rm -rf eht-imaging

Install remaining requirements:

conda install -y -c conda-forge ffmpeg
pip install ml-collections jupyterlab seaborn ipywidgets
pip install "jax[cuda12]"
pip install flax optax orbax-checkpoint diffrax

Running an experiment

The script run.py simulates data and fits PI-DEF to the simulated measurements. The following commands are provided to run experiments from the paper:

• scripts/eht.sh: fitting to noiseless EHT complex visibilities. You can try different EHT arrays by changing config.sim.array to one of the following: eht_arrays/EHT2017.txt, eht_arrays/EHT2025.txt, eht_arrays.ngEHT.txt.
• scripts/image.sh: fitting to noiseless full-image measurements (the highest-possible measurement resolution)
• scripts/eht_realistic_gaussian_noise.sh: fitting to EHT complex visibilities with realistic Gaussian noise
• scripts/eht_closure_phases_and_amps.sh: fitting to EHT closure phases and visbility amplitudes

The scripts will save experiment results to a folder of the form ./runs/{simulation_description}/{measurement_setting}/{hyperparameter_setting}.

Demo

The demo.ipynb notebook walks through how to simulate data, optimize PI-DEF, and evaluate PI-DEF. It basically guides you through all the steps in the script scripts/eht.sh, visualizing data along the way and visualizing the results after optimization. Since optimization can take a long time, you can download and use the checkpoints here.