ReferenceAlpha
Coefficient Form PDE
Development scalar coefficient-form PDE interface for custom scripted elliptic models.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | null | — |
| differentiable_runtime | {"certification":"CoefficientFormPDEScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["c"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["cfpde.u"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["cfpde.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["cfpde.compliance"],"value_kind":"scalar-global"}],"residual_owner":"CoefficientFormPDE.element_residual","state_fields":["u"],"supported_objective_symbols":{"coordinate":["cfpde.u","cfpde.energy","cfpde.compliance"],"material":["cfpde.u","cfpde.energy","cfpde.compliance"],"topology":["cfpde.u","cfpde.energy","cfpde.compliance"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | -div(c grad(u)) = f | — |
| frequency_domain_runtime | null | — |
| metadata | {"releaseSupport":{"certifiedStudies":[],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Unavailable.","selectable":false}} | — |
| preferred_material | null | — |
| schema_version | 0.1.0 | — |
| stateVariables | [{"adjointDescription":"Scalar elliptic adjoint solve supports expression objectives and coefficient sensitivities.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":null,"complexValued":false,"componentDescriptions":["Scalar state variable"],"componentNames":["u"],"componentSymbols":[],"components":1,"description":"Scalar coefficient-form PDE state.","differentiability":"exact-ad","displayName":"State variable","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name":"u","namingPolicy":"model-authored","quantityId":"cfpde.{name}:u","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"CoefficientFormPDE.element_residual"},"symbolPattern":"cfpde.{name}","unit":"1"}] | — |
| studies | [{"certified":false,"differentiability":"exact-ad","kind":"stationary","reason":"Stationary is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Optimization is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"eigenvalue","reason":"Eigenvalue is unavailable for this physics interface."}] | — |
| transient_runtime | null | — |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(cfpde.u)), c*grad(cfpde.u)) + test(cfpde.u)*a*cfpde.u - test(cfpde.u)*f","name":"cfpde.coefficient","test_field":"cfpde.u"}] | — |
| category | Mathematics / PDE Interfaces | — |
| description | Development scalar coefficient-form PDE interface for custom scripted elliptic models. | — |
| dimensions | [3] | — |
| display_name | Coefficient Form PDE | — |
| kind | Coefficient Form PDE | — |
| namespace | cfpde | — |
| status | development | — |
| visible | false | — |
Development scalar coefficient-form PDE interface for custom scripted elliptic models.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | null |
| differentiable_runtime | {"certification":"CoefficientFormPDEScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["c"],"execution_backend":"telion-v2-shared-execution","expression_objectives":true,"material_expression_gradient":true,"material_gradient":true,"objective_rules":[{"entity_dimensions":["global","domain","boundary","point"],"modes":["stationary"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"sup... |
| dynamic_outputs | [] |
| equation_summary | -div(c grad(u)) = f |
| frequency_domain_runtime | null |
| metadata | {"releaseSupport":{"certifiedStudies":[],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Unavailable.","selectable":false}} |
| preferred_material | null |
| schema_version | 0.1.0 |
| stateVariables | [{"adjointDescription":"Scalar elliptic adjoint solve supports expression objectives and coefficient sensitivities.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":null,"complexValued":false,"componentDescriptions":["Scalar state variable"],"componentNames":["u"],"componentSymbols":[],"components":1,"description":"Scalar coefficient-form PDE state.","differentiability":"exact-ad","displayName":"State variable","finiteElementSpace":"H1-P1","initialValue":"0","l... |
| studies | [{"certified":false,"differentiability":"exact-ad","kind":"stationary","reason":"Stationary is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"sensitivity","reason":"Sensitivity is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"optimization","reason":"Optimization is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"eigenvalue","reason":"Ei... |
| transient_runtime | null |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(cfpde.u)), c*grad(cfpde.u)) + test(cfpde.u)*a*cfpde.u - test(cfpde.u)*f","name":"cfpde.coefficient","test_field":"cfpde.u"}] |
| category | Mathematics / PDE Interfaces |
| description | Development scalar coefficient-form PDE interface for custom scripted elliptic models. |
| dimensions | [3] |
| display_name | Coefficient Form PDE |
| kind | Coefficient Form PDE |
| namespace | cfpde |
| status | development |
| visible | false |