Equations¶

This page summarizes the available equation classes and the model parameters they expect. The goal is to make it easy to answer three practical questions:

Which physical system does this equation represent?
Which model tensors must be provided, and in what order?
Which dimensions/backends does it support?

Summary Table¶

Equation	Models	Notes	PyTorch Binding
`Acoustic/Acoustic3D`	`['vp']`	Second-order acoustic wave equation	✅
`Acoustic1st`	`['vp', 'rho']`	First-order acoustic wave equation	❌
`Elastic/Elastic3D`	`['vp', 'vs', 'rho']`	2D Elastic wave propagation (Velocity-Stress)	✅

Acoustic¶

What It Represents¶

Acoustic implements the second-order acoustic wave equation with CPML absorbing boundaries. In the PyTorch path it is usually the default choice for scalar wave propagation, forward modeling, and acoustic FWI examples.

Implementation:

acoustic.py

Constructor¶

from sweep.equations import Acoustic

eq = Acoustic(
    spatial_order=4,
    device="cuda",
    backend="torch",
)

Main constructor arguments:

spatial_order: finite-difference order. Must be even. Common values are 4 and 8.
device: target device for operator/kernel tensors, such as "cpu" or "cuda".
backend: usually "torch" or "jax".
dim: defaults to 2 for Acoustic.

Required Models¶

Acoustic.models returns:

['vp']

You must therefore provide one model tensor, in this order:

vp: P-wave velocity model

Wavefields¶

Acoustic.wavefields returns:

['h1', 'h2', 'psix', 'psiz', 'zetax', 'zetaz']

Roughly:

h1, h2: main second-order wavefield states
psix, psiz, zetax, zetaz: CPML auxiliary states

Dimensions and Variants¶

Acoustic: 2D acoustic equation
Acoustic3D: 3D counterpart
AcousticVRZ: acoustic variant with impedance-like parameterization
AcousticLSRTM: acoustic LSRTM-oriented variant

Supported Backends¶

Acoustic is commonly used with:

backend="torch": pure PyTorch propagation and autograd
backend="jax": JAX propagation and differentiation

Torch Binding Support¶

Acoustic supports the compiled PyTorch CUDA binding through sweep._C.

That means:

equation-level torch binding support: yes
runtime availability still depends on whether your environment can import sweep._C

You can inspect this from the CLI:

sweep list equations

Or from Python:

import sweep

print(sweep.backend.torch.binding.is_available())

Notes¶

In the current PyTorch implementation, the acoustic path uses separable Laplace operators and, on CUDA, fixed-stencil gradient kernels where available.

Next¶

If this template looks good, the next equation sections should follow the same pattern:

What it represents
Constructor
Required models
Wavefields
Dimensions and variants
Supported backends
Torch binding support
Notes