femx

Verification-first, differentiable electrothermal FEM for silicon photonics.

femx connects electrical conduction, Joule heating, thermal transport, thermo-optic material updates, waveguide modes, and FDTDX optical objectives through explicit numerical contracts.

• JAX provides native differentiable finite-element operators and implicit adjoints.
• Elmer provides an independently executed open-source FEM reference.
• FDTDX consumes explicit material, mode, source, detector, and result contracts.

Research preview: APIs, evidence schemas, and experimental distributed interfaces may change before the first stable release.

3D silicon-photonics ring heater

Native JAX and locked external Elmer independently solve the same coarse Gmsh Tet4 problem at 5 mA. No displayed temperature or parity field is rescaled from the retained 15 mA result.

Direct 5 mA reference	Value
Mesh	12,761 nodes; 71,808 Tet4 cells
Voltage	0.229573 V
Joule power	1.14786 mW
Peak temperature rise	18.2608 K
Maximum JAX-Elmer temperature difference	$2.12\times10^{-8}\ \mathrm{K}$
Relative $L_2$ temperature-rise difference	$2.31\times10^{-10}$
Maximum conductor-potential difference	$7.72\times10^{-11}\ \mathrm{V}$

This 3D same-discretization parity result is solver evidence for an uncalibrated, constant-property benchmark. The modeled thermal domain is 20 um by 20 um, contains only 0.5 um of silicon below the 2 um BOX, fixes the bottom at 300 K, uses adiabatic sides, and applies top convection to 300 K with $h=10\ \mathrm{W,m^{-2},K^{-1}}$. In the retained coarse result, 99.997 percent of the heat exits through the fixed bottom. The result is not a fabricated-device prediction.

The original 15 mA source-reproduction reaches a 164.348 K peak rise and is retained for source traceability, not as a recommended operating point. See the direct 5 mA method and open fields, thermal-scope note, original 15 mA bundle, and earlier 2D adjoint reference.

Thermal-envelope sensitivity

A separate CPU float64 study crosses 20, 40, and 80 um square domains with 0.5, 5, and 50 um modeled silicon depths while holding material values and the mesh-size policy fixed. The widest, deepest case differs from the source envelope by -1.41 percent in peak K/mW and -3.23 percent in ring-mean K/mW. Width and depth interact; this bounded study is not formal domain convergence or device calibration. The complete case evidence is public.

What femx provides

• Solver-neutral problem, mesh, material, artifact, and validation contracts.
• JAX-native steady heat, current, Joule-heating, and electrothermal paths.
• Independent same-mesh checks against separately installed Elmer.
• Residual-defined differentiation with finite-difference or independent-adjoint checks.
• Explicit FEM-to-Yee mode transfer and FDTDX interoperability.
• Experimental distributed JAX paths with bounded physical TPU evidence.

Process success, numerical convergence, and scientific validation are reported separately. A test or completed executable does not by itself establish a physical claim.

Current public scope

Capability	Status
2D steady heat and current FEM	Available and cross-validated
2D electrothermal coupling and implicit adjoint	Available for the documented subset
3D Tet4 current, Joule heating, and steady heat	Available for the constant-property forward subset
3D ring-heater JAX-Elmer field parity	Available on the public coarse mesh
Three-level 3D ring-heater mesh sensitivity	Available through 3,179,879 Tet4 cells
2D waveguide port modes and documented eigen-adjoints	Available for the lossless PEC subset
FEM-to-Yee transfer and FDTDX consumers	Available for the documented contracts
Distributed scalar and electrothermal JAX paths	Experimental; bounded TPU evidence retained
3D ring-heater FDTDX resonance response	In development

Transient thermal analysis, foundry-calibrated prediction, and a continuum-converged ring-heater value are not currently claimed.

Installation

femx supports Python 3.11 to 3.14. Install the published development release from PyPI with:

pip install "femx==0.1.0.dev0"
femx doctor

For an editable source checkout, install uv and run:

git clone https://github.com/yspkm/femx.git
cd femx
uv sync --locked --extra jax --extra artifacts --extra meshing
uv run femx doctor

The optional jax, artifacts, and meshing extras may be selected for workflows that need them. Gmsh, Elmer, and FDTDX remain separately installed external tools.

Run the portable public CI selection with:

uv run pytest -m "unit or architecture"

Elmer comparison requires JAX float64. Set JAX_ENABLE_X64=1 before importing JAX.

Runtime model

prepared = femx.prepare(problem, backend, request=prepare_request)
solution = femx.solve(prepared, backend, request=solve_request)

Problem contains solver-neutral physics. PreparedProblem binds one exact backend payload, and Solution records fields, observables, convergence, and validation state. femx does not silently change the backend, precision, mesh, element family, or scalar type.

Documentation

• Roadmap
• Materials and provenance
• FDTDX interoperability
• Tet4 scalar H1 formulation
• Steady heat formulation
• Steady current formulation
• Electrothermal coupling
• Port eigenmode formulation
• Contributing

For reproducible work, record the exact femx version or source commit together with external solver revisions, mesh and material identities, numerical policy, and the relevant evidence artifact.

License

femx is distributed under the MIT License. Elmer, FDTDX, JAX, and Gmsh are separate projects with their own licenses; femx does not vendor their implementations.

Acknowledgements

We gratefully acknowledge Google's TPU Research Cloud (TRC) program for providing access to Cloud TPU resources that supported the development and distributed validation of femx.