ReferenceAvailable
Global ODEs and DAEs
Dimensioned global differential and algebraic states assembled into Telion's monolithic coupled transient runtime.
Reference
| Field | Value | Description |
|---|---|---|
| constraints | [] | — |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.global_ode","adjoint_vjp_owner":"GlobalOdeDaeAdapter","certification":"AST-whitelisted JAX residuals and output expressions with monolithic sparse Newton solves, exact affine ZOH stepping, and checkpointed discrete adjoints.","checkpointing":true,"dynamic_state_schema":true,"execution_backend":"telion-v2-shared-execution","gradient_channels":["ode:<label>.parameters","ode:<label>.inputs"],"history_depth":2,"history_jacobian_owner":"GlobalOdeDaeAdapter","jacobian_owner":"GlobalOdeDaeAdapter","nonlinear_solver":"CoupledNewtonSession","output_vjp_owner":"GlobalOdeDaeAdapter","requires_spatial_mesh":false,"residual_owner":"GlobalOdeDaeAdapter","runtime":"telion-coupled-graph","state_fields":["ode.{name}"],"supported_integrators":["BDF1","BDF2"]} | — |
| differentiable_runtime | null | — |
| dynamic_outputs | [{"components":1,"differentiability":"exact-ad","display_name":"Authored expression output","location":"global","name_pattern":"ode.{name}","plottable":true,"quantity_id_pattern":"ode.{name}","rank":"scalar","role":"functional","studies":["transient"],"unit_source":"Expression Output.Unit"}] | — |
| equation_summary | Dimensioned first-order differential states f(t,q,qdot,p,u)=0 and algebraic constraints g(t,q,p,u)=0; affine differential systems may use exact zero-order-hold matrix-exponential steps. | — |
| frequency_domain_runtime | null | — |
| metadata | {"releaseSupport":{"certifiedStudies":["transient"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} | — |
| preferred_material | null | — |
| schema_version | 0.1.0 | — |
| stateVariables | [{"adjointDescription":"The graph runtime publishes exact residual, history, parameter, input, and output VJPs for every state row.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":null,"complexValued":false,"componentDescriptions":["Dimensioned global state value"],"componentNames":["q"],"componentSymbols":[],"components":1,"description":"Template global state; runtime state rows define concrete names, units, equations, and initial values.","differentiability":"exact-ad","displayName":"Global state","finiteElementSpace":"Global-Scalar","initialValue":"0","location":"global","name":"q","namingPolicy":"model-authored","quantityId":"ode.{name}:q","rank":"scalar","role":"state","runtimeEvidence":{"certificationFixture":"tests/python_backend/test_differentiable_physics_contract.py::test_builtin_physics_optimization_contract_gate","provider":"GlobalOdeDaeAdapter"},"symbolPattern":"ode.{name}","unit":"1"}] | — |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"transient","reason":"september-2026-classroom verified contract: dimension-preserving BDF residuals for differential and algebraic states, exact affine zero-order-hold propagation, and state/input/parameter adjoints checked against analytical or centered finite-difference references"}] | — |
| transient_runtime | {"capacity_properties":[],"certification":"GlobalOdeDaeAdapter","checkpointing":true,"design_properties":[],"design_property_conditions":{},"design_vjp_owner":"GlobalOdeDaeAdapter","expression_objectives":true,"gradient_channels":["ode:<label>.parameters","ode:<label>.inputs"],"gradient_vjp_owner":"GlobalOdeDaeAdapter","history_depth":2,"input_gradient":true,"input_vjp_owner":"GlobalOdeDaeAdapter","observation_vjp_owner":"GlobalOdeDaeAdapter","residual_linearization_owner":"GlobalOdeDaeAdapter","runtime":"coupled-global-ode-dae","state_fields":["q"],"state_reconstruction_owner":"GlobalOdeDaeAdapter","supported_integrators":["BDF1","BDF2"],"supported_observation_symbols":["*"],"time_derivative_orders":{"q":1},"topology_gradient":false,"transpose_solve_owner":"CoupledNewtonSession"} | — |
| weak_contributions | [] | — |
| category | Mathematics / ODE and DAE Interfaces | — |
| description | Dimensioned global differential and algebraic states assembled into Telion's monolithic coupled transient runtime. | — |
| dimensions | [3] | — |
| display_name | Global ODEs and DAEs | — |
| kind | Global ODEs and DAEs | — |
| namespace | ode | — |
| status | certified | — |
| visible | true | — |
Dimensioned global differential and algebraic states assembled into Telion's monolithic coupled transient runtime.
Contract
| Property | Value |
|---|---|
| constraints | [] |
| coupled_runtime | {"adapter_module":"telion_backend.v2.runtimes.global_ode","adjoint_vjp_owner":"GlobalOdeDaeAdapter","certification":"AST-whitelisted JAX residuals and output expressions with monolithic sparse Newton solves, exact affine ZOH stepping, and checkpointed discrete adjoints.","checkpointing":true,"dynamic_state_schema":true,"execution_backend":"telion-v2-shared-execution","gradient_channels":["ode:<label>.parameters","ode:<label>.inputs"],"history_depth":2,"history_jacobian_owner":"GlobalOdeDaeAda... |
| differentiable_runtime | null |
| dynamic_outputs | [{"components":1,"differentiability":"exact-ad","display_name":"Authored expression output","location":"global","name_pattern":"ode.{name}","plottable":true,"quantity_id_pattern":"ode.{name}","rank":"scalar","role":"functional","studies":["transient"],"unit_source":"Expression Output.Unit"}] |
| equation_summary | Dimensioned first-order differential states f(t,q,qdot,p,u)=0 and algebraic constraints g(t,q,p,u)=0; affine differential systems may use exact zero-order-hold matrix-exponential steps. |
| frequency_domain_runtime | null |
| metadata | {"releaseSupport":{"certifiedStudies":["transient"],"manifest":"docs/september-2026-classroom-physics-matrix.json","manifestSha256":"0a819976ac943e9eedf5bc7f9c80880dd9103cb62bb4c5a915b98c452b135a5c","profile":"september-2026-classroom","reason":"Available.","selectable":true}} |
| preferred_material | null |
| schema_version | 0.1.0 |
| stateVariables | [{"adjointDescription":"The graph runtime publishes exact residual, history, parameter, input, and output VJPs for every state row.","adjointSupported":true,"availability":{"topologyMethods":[]},"canonicalSymbol":null,"complexValued":false,"componentDescriptions":["Dimensioned global state value"],"componentNames":["q"],"componentSymbols":[],"components":1,"description":"Template global state; runtime state rows define concrete names, units, equations, and initial values.","differentiability"... |
| studies | [{"certified":true,"differentiability":"exact-ad","kind":"transient","reason":"september-2026-classroom verified contract: dimension-preserving BDF residuals for differential and algebraic states, exact affine zero-order-hold propagation, and state/input/parameter adjoints checked against analytical or centered finite-difference references"}] |
| transient_runtime | {"capacity_properties":[],"certification":"GlobalOdeDaeAdapter","checkpointing":true,"design_properties":[],"design_property_conditions":{},"design_vjp_owner":"GlobalOdeDaeAdapter","expression_objectives":true,"gradient_channels":["ode:<label>.parameters","ode:<label>.inputs"],"gradient_vjp_owner":"GlobalOdeDaeAdapter","history_depth":2,"input_gradient":true,"input_vjp_owner":"GlobalOdeDaeAdapter","observation_vjp_owner":"GlobalOdeDaeAdapter","residual_linearization_owner":"GlobalOdeDaeAdapte... |
| weak_contributions | [] |
| category | Mathematics / ODE and DAE Interfaces |
| description | Dimensioned global differential and algebraic states assembled into Telion's monolithic coupled transient runtime. |
| dimensions | [3] |
| display_name | Global ODEs and DAEs |
| kind | Global ODEs and DAEs |
| namespace | ode |
| status | certified |
| visible | true |