Eqiora

Define mathematical models, run them from Python, and inspect their results. Eqiora provides equation authoring, synchronous and asynchronous execution, NumPy and DLPack arrays, first-order differentiation with PyTorch and JAX, and optional Matplotlib plots and notebook views.

Alpha — 0.1.0a9. See Capabilities for available models, methods, and platforms.

Install

Eqiora 0.1.0a9 supports ordinary-GIL CPython 3.11–3.14 on manylinux x86-64:

uv venv --python 3.13 .venv
uv pip install --python .venv/bin/python eqiora==0.1.0a9

Automatic exact-cylinder meshing requires Gmsh 4.15.2. The conventional Linux installation is:

sudo apt-get install libglu1-mesa
uv pip install --python .venv/bin/python "eqiora[gmsh]==0.1.0a9"

The Gmsh extra is separate so the base manylinux_2_17 package keeps its compatibility floor; the current Gmsh wheel has a newer Linux floor.

Install plotting, notebook viewing, or first-order framework adapters as needed:

uv pip install --python .venv/bin/python "eqiora[torch]==0.1.0a9"
uv pip install --python .venv/bin/python "eqiora[jax]==0.1.0a9"
uv pip install --python .venv/bin/python "eqiora[matplotlib]==0.1.0a9"
uv pip install --python .venv/bin/python "eqiora[viewer]==0.1.0a9"

The exact-cylinder pressure example combines the mesher and plot adapter: uv pip install --python .venv/bin/python "eqiora[gmsh,matplotlib]==0.1.0a9".

Run scripts with uv run --no-project --python .venv/bin/python your_script.py to use this environment explicitly. Current-source features described in the development guides may not yet be included in this published release.

The base package imports none of these optional libraries. The viewer extra pins anywidget==0.11.0; its JavaScript and CSS are already carried inside the Eqiora wheel, so the host does not fetch renderer assets at display time. The PyTorch extra declares torch>=2.13,<2.14; the tested version is PyTorch 2.13.0. JAX/JAXLIB 0.11.0 and Matplotlib 3.11.1 were also tested on CPython 3.13. The JAX extra requires Python 3.12 or newer.

Run a model

Start with Get started for a complete decay example. The guides follow the current source revision; use their source-install instructions when trying features newer than 0.1.0a9.

A spatial workflow has five steps:

1. Define geometry and name its regions and boundaries.
2. Choose a mesher and generate the mesh.
3. Compile the equations with that geometry and the model parameters.
4. Resolve the model, mesh, elements, and solver settings into a Plan.
5. Run the Plan and select the fields to inspect.

The modeling guide contains complete examples for steady cylinder flow, mixed-boundary linear elasticity, and fixed-reference fluid–structure interaction. It also explains how to compile and inspect locked model packages.

For cylinder flow, GeometryGraph subtracts a circle from a rectangle. Coordinates and radii use metres. Gmsh generates linear triangles for this 2D geometry; missing Gmsh, an incompatible version, or invalid output raises an error. The mesh target size controls meshing and does not guarantee every edge length.

Read and plot results

Select fields from the Result using the field handles supplied by the Plan. Field values and mesh coordinates use matching order. Check the units and compare the values with a prediction before interpreting a plot.

For example, after running the steady cylinder model:

import eqiora.matplotlib as eqplot

pressure = result.snapshots[0]
figure = eqplot.plot_scalar_field(result, field=pressure.field)
figure.savefig("exact-cylinder-pressure.png")

The pressure scale is in pascals. The plotting helper supports scalar vertex and cell fields. The Gallery explains how to read pressure, displacement, and transient vorticity plots from worked examples.

In a notebook with the viewer extra, display geometry, mesh, and a scalar field:

view = eqiora.View().add(geometry).add(mesh).add(pressure)
view.show()
view.close()  # Release the widget when finished.

The viewer supports planar geometry, 2D triangular or quadrilateral meshes, named edge/face selections, and scalar vertex/cell fields. A field must use the same mesh displayed in the view. Without the viewer extra or a rich notebook host, the view provides a text representation.

Structured diagnostics

Failures expose stable categories and structured diagnostics:

try:
    eqiora.run(
        plan,
        state=eqiora.State.initial(plan),
        until_s=-1.0,
        output_times_s=(-1.0,),
    )
except eqiora.EqioraError as error:
    print(error.category)
    for diagnostic in error.diagnostics:
        print(diagnostic.code, diagnostic.severity, diagnostic.message)

Validation, compatibility, capability, execution, cancellation, and internal failures have distinct subclasses. Ordinary Python call-shape errors remain TypeError.

NumPy arrays and copies

Eqiora Array values own dense, rank-one CPU float64 storage:

array = result["state"].values
view = array.numpy(copy=False)
writable = array.numpy(copy=True)

assert not view.flags.writeable
assert writable.flags.writeable

copy=False and copy=None return the same lifetime-safe, read-only NumPy projection. If that contract cannot be honored, Eqiora fails instead of copying silently. copy=True returns an independent writable allocation. DLPack exports copy data into independent versioned CPU snapshots. Differentiable-program DLPack inputs are checked for dtype, shape, alignment, byte order, and contiguity, then copied before execution. Read the details in Execution, diagnostics, and arrays.

Await, progress, and cancellation

Use eqiora.run(plan) to wait synchronously, or submit a run and await it:

async def simulate(plan):
    run = eqiora.submit(
        plan,
        state=eqiora.State.initial(plan),
        until_s=10.0,
        output_times_s=(10.0,),
    )
    try:
        print(run.status, run.progress)
        return await run
    finally:
        if not run.done:
            run.cancel()

Cancelling the surrounding asyncio task or dropping a Run does not implicitly cancel native work. Call run.cancel() explicitly. Cancellation is cooperative: it takes effect when execution reaches a cancellation point. A cancelled run does not publish a partial Result.

Pass profile=True to run or submit when investigating runtime cost. The returned result.profile provides a hierarchical timing summary and structured phase/solver events. Profiling is process-local telemetry and is omitted from persisted Result artifacts.

PyTorch and JAX

Compile a differentiable program by selecting the parameters and output field of a Plan, then bind it with eqiora.torch.bind(program) or eqiora.jax.bind(program). PyTorch uses the vector–Jacobian product during backpropagation; JAX provides primal evaluation and first-order JVP/VJP.

These adapters use real, rank-one CPU float64 inputs and rectangular 2D Cartesian meshes with scalar-elliptic Q1 FEM or TPFA FVM. Enable JAX 64-bit mode with jax.config.update("jax_enable_x64", True). Device transfers must be explicit, and differentiation is first order.

Follow Differentiation and framework adapters for complete setup, input shapes, and framework examples.

Compatibility

0.1.0a9 is an alpha prerelease. Python APIs and saved-file formats may change before 1.0; release notes describe changes and migrations. Corrections to a published package receive a new version.

Links

• Documentation
• Guides
• Reference
• Source
• Issue tracker
• Security policy
• Apache-2.0 license