ReferenceAlpha
Thermal Dynamics
Conductive transient thermal physics with exact density-heat-capacity BDF1/BDF2 evolution and differentiable optimization support.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | null | — |
| differentiable_runtime | {"certification":"ThermalDynamicsScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["thermalConductivity"],"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","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maximum","smooth-minimum"],"supports_selection":true,"symbols":["td.T"],"value_kind":"field"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["td.energy"],"value_kind":"scalar-global"},{"entity_dimensions":["global"],"modes":["stationary"],"operators":["value"],"supports_selection":false,"symbols":["td.compliance"],"value_kind":"scalar-global"}],"residual_owner":"ThermalDynamics.element_residual","state_fields":["T"],"supported_objective_symbols":{"coordinate":["td.T","td.energy","td.compliance"],"material":["td.T","td.energy","td.compliance"],"topology":["td.T","td.energy","td.compliance"]},"topology_expression_gradient":true} | — |
| dynamic_outputs | [] | — |
| equation_summary | rho*Cp*dT/dt - div(k*grad(T)) = Q | — |
| 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 thermal adjoint solve supports expression objectives and topology material sensitivities for temperature.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"td.T","complexValued":false,"componentDescriptions":["Temperature"],"componentNames":["T"],"componentSymbols":["td.T"],"components":1,"description":"Absolute temperature field.","differentiability":"exact-ad","displayName":"Temperature","finiteElementSpace":"H1-P1","initialValue":"0","location":"node","name":"T","namingPolicy":"fixed","quantityId":"td.T","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"ThermalDynamics.element_residual"},"symbolPattern":null,"unit":"K"}] | — |
| studies | [{"certified":false,"differentiability":"exact-ad","kind":"stationary","reason":"Stationary is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"transient","reason":"Transient 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."}] | — |
| transient_runtime | {"capacity_properties":["density","heatCapacity"],"certification":"ThermalDynamicsScalarCapacityBdfRuntime","checkpointing":true,"design_properties":["thermalConductivity","density","heatCapacity"],"design_property_conditions":{},"design_vjp_owner":"ThermalDynamicsTransientRuntime","expression_objectives":true,"gradient_channels":["coordinates","parameter","material","input","capacity","initial"],"gradient_vjp_owner":"ThermalDynamicsTransientRuntime","history_depth":2,"input_gradient":true,"input_vjp_owner":"ThermalDynamicsTransientRuntime","observation_vjp_owner":"ThermalDynamicsTransientRuntime","residual_linearization_owner":"ThermalDynamicsTransientRuntime","runtime":"thermal-dynamics-scalar-capacity-bdf","state_fields":["T"],"state_reconstruction_owner":"ThermalDynamicsTransientRuntime","supported_integrators":["BDF1","BDF2"],"supported_observation_symbols":["td.T"],"time_derivative_orders":{"T":1},"topology_gradient":true,"transpose_solve_owner":"ThermalDynamicsTransientRuntime"} | — |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(td.T)), thermalConductivity*grad(td.T)) - test(td.T)*heatSource","name":"td.conduction","test_field":"td.T"}] | — |
| category | Heat Transfer | — |
| description | Conductive transient thermal physics with exact density-heat-capacity BDF1/BDF2 evolution and differentiable optimization support. | — |
| dimensions | [3] | — |
| display_name | Thermal Dynamics | — |
| kind | Thermal Dynamics | — |
| namespace | td | — |
| status | development | — |
| visible | false | — |
Conductive transient thermal physics with exact density-heat-capacity BDF1/BDF2 evolution and differentiable optimization support.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | null |
| differentiable_runtime | {"certification":"ThermalDynamicsScalarEllipticRuntime","coordinate_expression_gradient":true,"coordinate_gradient":true,"design_properties":["thermalConductivity"],"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","transient"],"operators":["integral","average","minimum","maximum","rms","norm","smooth-maxi... |
| dynamic_outputs | [] |
| equation_summary | rho*Cp*dT/dt - div(k*grad(T)) = Q |
| 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 thermal adjoint solve supports expression objectives and topology material sensitivities for temperature.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":"td.T","complexValued":false,"componentDescriptions":["Temperature"],"componentNames":["T"],"componentSymbols":["td.T"],"components":1,"description":"Absolute temperature field.","differentiability":"exact-ad","displayName":"Temperature","finiteElementSpace":"H1-P1","initialValu... |
| studies | [{"certified":false,"differentiability":"exact-ad","kind":"stationary","reason":"Stationary is unavailable for this physics interface."},{"certified":false,"differentiability":"exact-ad","kind":"transient","reason":"Transient 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":"Optimi... |
| transient_runtime | {"capacity_properties":["density","heatCapacity"],"certification":"ThermalDynamicsScalarCapacityBdfRuntime","checkpointing":true,"design_properties":["thermalConductivity","density","heatCapacity"],"design_property_conditions":{},"design_vjp_owner":"ThermalDynamicsTransientRuntime","expression_objectives":true,"gradient_channels":["coordinates","parameter","material","input","capacity","initial"],"gradient_vjp_owner":"ThermalDynamicsTransientRuntime","history_depth":2,"input_gradient":true,"i... |
| weak_contributions | [{"differentiability":"exact-ad","entity_dimension":"domain","expression":"dot(grad(test(td.T)), thermalConductivity*grad(td.T)) - test(td.T)*heatSource","name":"td.conduction","test_field":"td.T"}] |
| category | Heat Transfer |
| description | Conductive transient thermal physics with exact density-heat-capacity BDF1/BDF2 evolution and differentiable optimization support. |
| dimensions | [3] |
| display_name | Thermal Dynamics |
| kind | Thermal Dynamics |
| namespace | td |
| status | development |
| visible | false |