Functional Mock-up Interface (FMI)

A self-contained, compressed file (.fmu) that packages a dynamic simulation model along with its metadata, binaries, and documentation. An FMU is the atomic unit of exchange in the FMI ecosystem.

• Contents: An XML model description file, C code or compiled binaries for the target platform, and optional documentation
• Self-Describing: The XML header exposes all variables, parameters, and solver capabilities without requiring the original authoring tool
• Platform Portability: A single FMU can contain binaries for multiple operating systems (Windows, Linux, macOS) and architectures (x86, ARM)

The Model Exchange interface imports the dynamic equations of a model into a target simulator, where the importing tool's own solver integrates them. The FMU provides the mathematical model; the host provides the numerical integration.

• Solver Coupling: The FMU exposes continuous-time state derivatives and event indicators; the host solver calls these at each time step
• Computational Efficiency: Eliminates solver overhead by leveraging the importing tool's optimized integrator
• Use Case: Ideal when a high-fidelity engine model must run inside a vehicle dynamics simulator with a unified solver

The Co-Simulation interface allows each FMU to contain its own embedded solver, exchanging data only at discrete synchronization points. This decouples the internal numerics of each subsystem.

• Solver Independence: Each FMU can use a specialized solver tailored to its physics (e.g., stiff solvers for chemical kinetics, fixed-step for real-time hardware)
• Master Algorithm: An external orchestrator manages the communication time steps and data exchange between FMUs
• Use Case: Co-simulating a multi-physics system where a structural dynamics tool, a CFD solver, and a control system model run as independent FMUs

FMI defines a rigorous taxonomy of variable causality attributes that govern how signals flow between connected FMUs, preventing algebraic loops and ensuring well-defined system composition.

• Input / Output: Explicitly declared ports for signal flow; an output of one FMU connects to the input of another
• Parameter: Tunable constants that remain fixed during a simulation run but can be changed between runs
• CalculatedParameter: A parameter derived from other parameters at initialization time
• Local: Internal variables not exposed to the co-simulation bus, preserving proprietary model details

The master algorithm orchestrates the data exchange and time synchronization between multiple FMUs in a co-simulation. It defines the communication step size and the sequence of operations.

• Explicit Coupling: Jacobi-type schemes where FMUs exchange data only at the end of each macro-step
• Implicit Coupling: Gauss-Seidel iteration where FMUs are called sequentially within a step, using the latest available inputs
• Variable Step-Size: The master can adapt the communication interval based on event detection or error estimation
• Rollback Support: Advanced masters can request FMUs to revert to a previous state if an iteration fails to converge

Every FMU contains a mandatory modelDescription.xml file that serves as a machine-readable manifest. This schema is the contract between the exporting and importing tools.

• ModelVariables: Declares every scalar variable with its name, value reference, causality, variability, and unit
• ModelStructure: Defines the dependency graph—which outputs depend on which inputs—enabling the importing tool to compute execution order
• UnitDefinitions: Maps variables to physical units (SI and custom), ensuring dimensional consistency across multi-tool compositions
• Vendor Annotations: Extensible metadata for tool-specific information without breaking the standard

A middleware infrastructure that synchronizes and orchestrates data exchange between multiple independent simulation models running simultaneously. The co-simulation bus acts as the communication backbone, managing time synchronization and data marshaling between FMUs exported from different authoring tools.

• Handles step size negotiation between models with different solver rates
• Enables coupling of a mechanical FMU with a thermal FMU for multi-physics simulation
• Examples include open-source frameworks like HELICS and commercial platforms

A machine-to-machine communication protocol for industrial automation that provides a secure, platform-independent standard for data ingestion into a digital twin. OPC UA serves as the bridge between physical PLCs and FMI-based virtual models.

• Provides semantic information modeling beyond raw data transport
• Enables real-time telemetry from physical assets to drive FMU state updates
• Complements FMI by standardizing the interface between the physical world and the simulation layer

The dynamic adjustment of a simulation model's complexity and resolution to balance computational cost against required accuracy. FMUs can be exported at multiple fidelity levels—from high-fidelity 3D physics to reduced-order surrogate models.

• A high-fidelity FMU captures detailed dynamics but runs slowly
• A low-fidelity FMU uses lookup tables or linear approximations for real-time execution
• FMI supports this through co-simulation master algorithms that can switch between fidelity levels during runtime

A data-driven approximation of a complex, high-fidelity simulation that executes significantly faster. Surrogate models are often packaged as FMUs to replace computationally expensive physics-based components in system-level simulations.

• Trained using Design of Experiments (DOE) to sample the input space efficiently
• Common techniques include Gaussian Process Regression and neural networks
• Enables real-time what-if analysis where full-physics FMUs would be too slow

The rigorous three-phase process ensuring a simulation is built correctly, represents reality accurately, and is officially approved for a specific use case. FMUs must undergo VV&A before deployment in safety-critical applications.

• Verification: Is the FMU solving equations correctly?
• Validation: Does the FMU match physical test data?
• Accreditation: Is the FMU officially certified for a specific decision context (e.g., flight certification)?

A decentralized design pattern where multiple autonomous digital twins owned by different stakeholders are interconnected via standardized interfaces without centralizing proprietary data. FMI is the natural exchange format for federated twins.

• Each stakeholder exports a black-box FMU protecting their IP
• A co-simulation orchestrator couples FMUs across organizational boundaries
• Enables cross-enterprise supply chain simulation without exposing sensitive internal models