2D and 3D Maxwell modelling
Finite-difference time-domain forward modelling supports single and multiple excitation scenarios.
PyTorch × Maxwell FDTD
DeepGPR
Differentiable 2D and 3D electromagnetic modelling for ground-penetrating radar—built for forward simulation and full-waveform inversion with PyTorch.
pip install DeepGPR
2D + 3D
CPU + CUDA
Autograd
CPML
FDTD 2 / 4 / 8
Core capabilities
Physics operators that stay inside the PyTorch workflow.
Build GPR simulations from familiar tensors, preserve gradient flow, and move between local CPU work and CUDA execution through one public interface.
Differentiable parameters
Backpropagate to relative permittivity, conductivity, initial wavefields, and source amplitudes through PyTorch autograd.
CPU and CUDA backends
A native C CPU backend is selected for CPU tensors; CUDA libraries handle NVIDIA GPU execution where available.
Configurable CPML
Supply air and the target region. The solver adds external PML on each boundary and returns gradients at the input model size.
Selectable spatial order
Choose second-, fourth-, or eighth-order spatial finite differences, with material-aware CFL validation.
Large-model controls
Checkpointing, DDP, lower-precision wavefield storage, sampling, and optional CUDA-to-CPU offload support memory-aware workflows.
Differentiable workflow
From subsurface parameters to an inversion update.
01Model
εr + σ
εr + σ
02FDTD forward
modelling
modelling
03Receiver
waveforms
waveforms
04Data
misfit
misfit
05Adjoint /
autograd
autograd
06FWI model
update
update
Quick start
A forward model with a gradient.
Create material tensors, place a source and receiver, run DeepGPR.compute, then use standard PyTorch backpropagation.
import torch
import DeepGPR
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
eps_r = torch.full((64, 96, 1), 4.0, device=device, requires_grad=True)
sigma = torch.zeros_like(eps_r)
source = DeepGPR.wavelet.ricker(
2e8, 500, 3e-11, 5e-9, device=device
).reshape(1, 500, 1)
result = DeepGPR.compute(
device=device, dx=0.02, dt=3e-11,
source_amplitudes=source,
source_location=torch.tensor([[[16, 12, 0]]], device=device),
receiver_location=torch.tensor([[[48, 12, 0]]], device=device),
eps_r=eps_r, sigma=sigma,
)
receiver_data = result[-1]
receiver_data.square().sum().backward()
Project snapshot
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Repository results
Forward response and inversion outputs.
These figures are copied without modification from the DeepGPR repository and correspond to the documented forward-modelling and 2D FWI examples.
Forward modelling + gradient
Receiver data and the material gradient from the README's small modelling test.
2D dual-parameter FWI
Repository-provided inverted relative-permittivity and conductivity models.
Installation
Start with one package.
Python 3.8 or newer is required. Choose a PyTorch build appropriate for CPU or CUDA execution.
pip install DeepGPR
Citation
Research context
The repository asks users to cite: Liu, Lei; Song, Chao; He, Liangsheng; Wang, Silin; Feng, Xuan; and Liu, Cai. “Fast ground penetrating radar dual-parameter full waveform inversion method accelerated by hybrid compilation of CUDA kernel function and PyTorch.” Computers & Geosciences, 2026, 106101. Citation details →