ReferenceAlpha
Weak Form PDE
Development scalar weak-form PDE interface for scripted custom scalar models.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | null | — |
| differentiable_runtime | {"certification":"WeakFormPDEScalarEllipticRuntime","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":["w.u"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["w.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["w.compliance"],"value_kind":"scalar-global"}],"residual_owner":"WeakFormPDE.supported_scalar_weak_forms","state_fields":["u"],"supported_objective_symbols":{"coordinate":["w.u","w.energy","w.compliance"],"material":["w.u","w.energy","w.compliance"],"topology":["w.u","w.energy","w.compliance"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | Supported scalar weak forms are assembled through the differentiable scalar elliptic runtime. | — |
| 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":"Supported scalar weak forms use the differentiable scalar elliptic adjoint path.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":null,"complexValued":false,"componentDescriptions":["Scalar state variable"],"componentNames":["u"],"componentSymbols":[],"components":1,"description":"Scalar weak-form state.","differentiability":"exact-ad","displayName":"State variable","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name":"u","namingPolicy":"model-authored","quantityId":"w.{name}:u","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"WeakFormPDE.supported_scalar_weak_forms"},"symbolPattern":"w.{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":"weak","name":"w.domain","test_field":"w.u"}] | — |
| category | Mathematics / PDE Interfaces | — |
| description | Development scalar weak-form PDE interface for scripted custom scalar models. | — |
| dimensions | [3] | — |
| display_name | Weak Form PDE | — |
| kind | Weak Form PDE | — |
| namespace | w | — |
| status | development | — |
| visible | false | — |
Development scalar weak-form PDE interface for scripted custom scalar models.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | null |
| differentiable_runtime | {"certification":"WeakFormPDEScalarEllipticRuntime","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_s... |
| dynamic_outputs | [] |
| equation_summary | Supported scalar weak forms are assembled through the differentiable scalar elliptic runtime. |
| 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":"Supported scalar weak forms use the differentiable scalar elliptic adjoint path.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":null,"complexValued":false,"componentDescriptions":["Scalar state variable"],"componentNames":["u"],"componentSymbols":[],"components":1,"description":"Scalar weak-form state.","differentiability":"exact-ad","displayName":"State variable","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name"... |
| 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":"weak","name":"w.domain","test_field":"w.u"}] |
| category | Mathematics / PDE Interfaces |
| description | Development scalar weak-form PDE interface for scripted custom scalar models. |
| dimensions | [3] |
| display_name | Weak Form PDE |
| kind | Weak Form PDE |
| namespace | w |
| status | development |
| visible | false |