Glossary#

A shared vocabulary across the three layers of the Microrobotics Simulation Framework. Terms link in from any page that uses the {term}`Name` MyST role; with sphinx-tippy enabled, hovering the link pops up the definition without leaving the page.

This page is single-source-of-truth in the MICROROBOTICA repo at docs/glossary.md. Identical mirrors live in MADDENING/docs/glossary.md and MIME/docs/glossary.md, kept in sync by MICROROBOTICA/scripts/sync_glossary.py.

Aitken acceleration#: A scalar relaxation factor (re-estimated each iteration from the residual sequence) that speeds up Gauss-Seidel / Jacobi convergence — cheap, no Jacobian needed.
Anatomical regime#: The set of physiological bounds (compartment, flow regime, pH, viscosity, temperature) under which a MIME asset has been validated. Enforced at load time before a simulation can run.
Anomaly registry#: MADDENING’s record of its known defects, docs/validation/known_anomalies.yaml: one entry per anomaly, with an ID (MADD-ANO-NNN), a severity, the versions it affects and its status. CI checks it with scripts/check_anomalies.py, and the known-anomaly tables of the SOUP package are generated from it.
ASME V&V 40#: Verification & Validation 40-2018 — the ASME standard that defines the COU framing and the credibility levels expected of medical-device computational models.
Boundary inputs#: The data a Node receives from its upstream neighbours on a given Graph step — the values flowing in along its incoming Edges.
Bouzidi scheme#: An interpolated bounce-back boundary condition for LBM that places curved walls accurately between lattice nodes, instead of stair-stepping them onto the grid. Improves confined-flow fidelity.
CFL number#: Courant–Friedrichs–Lewy number — a dimensionless stability limit for explicit time-stepping: information must not cross more than one grid cell per step. Exceeding it makes a solver blow up; it bounds the timestep of MIME’s fluid nodes.
Checkpoint#: A running graph saved to disk so the run can resume from it: every node’s state, the graph’s params and its internal bookkeeping (the multi-rate step counter, coupling warm starts) in one .npz archive. GraphManager.save_state writes one and load_state reads it back; the cloud entry point resumes from the one RESUME_FROM_URL names.
ComponentMeta#: The compile-time annotation MICROROBOTICA attaches to every interface, capturing intended use, verification status, and SOUP classification for IEC 62304 compliance.
COU#: Context Of Use — the FDA/ASME V&V40 framing of “what question is this simulation answering, and how much accuracy does that demand?” Drives per-node verification rigour.
Coupling#: The strategy by which mutually dependent nodes exchange data within a single graph step. MADDENING ships Gauss-Seidel and Jacobi coupling with Aitken acceleration and IQN-ILS.
Coupling group#: A set of nodes whose mutual dependence is solved by iteration inside each Graph step: the members run repeatedly, reading each other’s current-iteration values, until the change in a pass meets the group’s convergence norm or max_iterations is reached. Declared with GraphManager.add_coupling_group; one node with an edge to itself can form a group.
Cramér–Rao bound#: The smallest variance any unbiased estimator of a parameter can have, given the data: the diagonal of the inverse of the Fisher information matrix. maddening.sysid.fim reports it per parameter as crb, and reports inf for a parameter the data cannot identify.
CRBA#: Composite-Rigid-Body Algorithm — an O(n²) method for computing a robot’s joint-space mass matrix. Used by MIME’s RobotArmNode.
CSF#: Cerebrospinal fluid — the clear fluid in the brain ventricles and spinal canal. A primary target environment for the microrobots MIME models; its flow and viscosity define one Anatomical regime.
Cycle staggering#: How MADDENING handles feedback loops in the graph: a cyclic dependency is broken into an iterative Gauss-Seidel sweep rather than rejected, so strongly coupled subsystems still compile.
DeepONet#: Deep Operator Network — a neural architecture that learns function-to-function mappings (operators). MADDENING uses it as a Surrogate family for nodes that map fields to fields.
Defect correction#: An iterative scheme that solves a hard problem by repeatedly solving an easier approximate one and correcting with the residual (“defect”). MIME uses it to add fidelity to fast fluid nodes without paying the full solver cost every step.
DEPRECATED#: The Stability level of a surface scheduled for removal. Its docstring names the replacement, and using it warns (DeprecationWarning, or FutureWarning where the result will change).
Dipole response#: The force and torque a permanent-magnet or paramagnetic body experiences in an external field gradient. Modelled by MIME’s PermanentMagnetResponseNode.
Edge#: A typed, unit-aware connection between two nodes that carries a named field (e.g. magnetic_force, orientation). Edges encode the data-dependency graph the Graph step walks. An edge may also run from a node to itself: it then reads the node’s value from the previous step, or, with the node in a coupling group, is iterated with the group.
EU MDR#: EU Medical Device Regulation (2017/745). MDR Annex II.2 in particular asks for design rationale, V&V evidence, and traceability — the same evidence the framework’s regulatory docs are organised around.
EVOLVING#: The Stability level of a surface whose signature and wire format are settled, though additions are expected. An incompatible change needs a minor release and one minor release of DeprecationWarning first.
EXPERIMENTAL#: The Stability level of an opt-in surface that may change or disappear in any minor release, without a deprecation period. Each such change still gets a CHANGELOG entry.
External input#: A value fed into a node’s Boundary inputs from outside the graph (a controller, a sensor, a user command) rather than along an Edge. Declared with GraphManager.add_external_input and passed to each step or run call in external_inputs; a field takes an external input or edges, never both.
Fisher information matrix#
FIM#: F = JᵀJ, for J the Jacobian of a residual (model minus data) with respect to the parameters: how strongly the data constrain each combination of parameters. An eigenvalue near zero names a combination the data cannot distinguish; maddening.sysid.fim reports the eigenpairs, the rank and the Cramér–Rao bound.
Fixed point#: A state that one more pass of an iteration leaves unchanged: x* = F(x*). A Coupling group iterates towards the fixed point of its coupling pass in every step, and its default solver differentiates that fixed point with the IFT rather than through the iterations.
FMI#: Functional Mock-up Interface — the open standard for exchanging models between simulation tools as packaged FMUs and stepping them together (co-simulation). MADDENING exports to FMI 3.0.
FMU#: Functional Mock-up Unit — a .fmu zip holding a model description and a compiled binary that an FMI importer (FMPy, OpenModelica, …) loads and steps. A MADDENING FMU is a co-simulation FMU whose thin C wrapper forwards every call to a Python Sidecar holding the compiled graph.
FNO#: Fourier Neural Operator — a spectral-domain neural operator that is often dramatically more sample-efficient than MLPs on PDE surrogates. Another Surrogate option in MADDENING.
Gauss-Seidel#: Iterative coupling scheme where each node updates with the latest values from its neighbours within an iteration. Converges faster than Jacobi for many stiff systems but is sequential within a step.
Geometry-dependent mapping#: An Interface mapping that computes its weights at every step from positions held in the graph’s state, so the points it maps between may move (markers carried by a flow, a body crossing a grid). The edge names the positions with geometry=(anchor, field); multilinear_grid is the built-in kind.
GNN correction#: Graph Neural Network residual learnt on top of the analytical Stokeslet (or IBM-FVM) prediction to absorb modelling error. Optional in MIME; toggled via the asset schema.
Graph step#: One full traversal of a MADDENING node graph that advances simulation time by dt. Compiles into a single XLA op so the whole step is autodiff-able.
GraphManager#: The MADDENING object you add nodes and edges to. It validates the wiring, runs the Topological sort, applies Coupling, and compiles the whole Graph step into one XLA program.
Halo#: The ghost cells around a Shard, copied in from the neighbouring shards, so that a Stencil update near the shard’s border can read its neighbours. A node declares how many it needs per axis with halo_width(); at the edges of the global grid a boundary mode ("edge", "periodic" or "zero") fills them.
Helical UMR#: A UMR shaped as a helix and rotated by an external magnetic field, converting rotation into translation. See the de Jongh (2025) replication in MIME/docs/validation/umr_deboer2025/.
IB-LBM#: Immersed-Boundary Lattice Boltzmann Method — LBM with the microrobot represented as immersed-boundary forcing points rather than a body-fitted mesh. One of MIME’s confined-flow fluid nodes.
IBM-FVM#: Immersed Boundary Method on a Finite-Volume Mesh — MIME’s higher-fidelity option for confined low-Reynolds flow. The body is represented as forcing terms on a regular fluid grid rather than as a conforming mesh.
IEC 62304#: The international standard for medical device software lifecycle processes. MICROROBOTICA ships pre-wired traceability (ComponentMeta, anomaly registry, verification benchmarks) to keep audit overhead low.
IEC 62366-1#: The international standard for usability engineering of medical devices — the use-related risk and human-factors process that sits alongside IEC 62304 and ISO 14971.
IFT#
Implicit function theorem#: Implicit function theorem. A Coupling group’s default solver (solver="ift") uses it to differentiate the group’s converged Fixed point directly, by solving a linear system in I - dF/dx, instead of differentiating through every iteration. The derivative is exact only at a converged fixed point.
Interface mapping#: The transfer of a field between two nodes that discretise a shared interface differently (a coarse and a fine rod, a mesh and a point cloud), applied on the Edge before its transform. A "consistent" mapping interpolates a value field; a "conservative" one transfers an integral quantity, such as a force, so that its total is preserved.
Interface norm#: The convergence norm convergence_norm="interface" of a Coupling group: the RMS change, relative to rtol times each value’s magnitude, of only the fields the group’s internal edges carry between members. It often needs fewer iterations than "l2", but it cannot see a member’s other fields, so a group can stop while the rest of its state is still moving.
IQN-ILS#: Interface Quasi-Newton with Inverse Least-Squares. A vector-valued acceleration scheme that builds a low-rank approximation of the Jacobian from past iterations — usually much faster than Aitken acceleration for strongly coupled multiphysics.
ISO 13485#: The international standard for a medical-device quality management system. Governs the processes around the software, complementary to the product-focused IEC 62304.
ISO 14971#: The international standard for risk management of medical devices. The framework’s hazard-hint metadata is structured to feed an ISO 14971 risk file.
Jacobi#: Iterative coupling scheme where every node updates from the previous iteration’s values, so all nodes can update in parallel. Slower convergence than Gauss-Seidel but trivially parallelisable.
JAX#: The Python array library MADDENING is built on: NumPy-style code with composable transforms — grad (autodiff), jit (JIT compilation to XLA), vmap (vmap), and scan.
JAX-traceable#: Code that JAX can trace into its IR: no Python-level side effects, no data-dependent Python control flow, no in-place mutation. Node update methods must be JAX-traceable — use jnp.where instead of if/else.
JIT compilation#: Just-In-Time compilation. Each MADDENING Graph step is jax.jit-compiled into a single XLA op the first time it is called; subsequent calls reuse the cached binary.
LBM#: Lattice Boltzmann Method — a fluid solver that evolves particle distribution functions on a regular lattice rather than solving the Navier-Stokes equations directly. Well suited to confined, complex-geometry flow.
Low-Re#: Low Reynolds number (Re ≪ 1). The regime where viscous forces dominate inertia — i.e. the regime nearly all microrobots in biological fluids operate in.
Lubrication correction#: A near-wall force correction added on top of bulk drag in confined flows. MIME’s LubricationCorrectionNode adds this to MLP-predicted resistance.
MDCG 2019-11#: EU Medical Device Coordination Group guidance on qualification and classification of software under the EU MDR. Determines whether and at what class a piece of software is regulated.
MDCG 2019-16#: EU Medical Device Coordination Group guidance on cybersecurity for medical devices under the EU MDR.
MimeNode#: MIME’s base node class — a SimulationNode whose NodeMeta is extended with domain metadata (biocompatibility, Anatomical regime, SOUP classification).
MLP#: Multi-Layer Perceptron — a stack of dense layers. The default Surrogate architecture for short-range physics nodes such as MLPResistanceNode.
Momentum exchange#: The standard way to read the hydrodynamic force on an immersed body out of an LBM simulation: sum the momentum transferred as distribution functions bounce off the body’s boundary links.
Multi-rate#: A scheduling mode where different nodes advance at different dts, reconciled by a GCD-based scheduler. Used for stiff subsystems that need a smaller step than the rest of the graph. Between the base steps a slower node fires on, its readers see what it holds: its held state, and the flux (compute_boundary_fluxes) of that held state.
Node#: The fundamental unit of computation in a MADDENING graph: a pure function (state, dt, boundary_inputs) -> new_state. Subclassed in MIME to add physics- and biology-specific metadata.
NodeMeta#: The compliance-metadata record attached to every MADDENING SimulationNode: stability level, validated regimes, references. MIME’s MimeNode extends it with biomedical fields; MICROROBOTICA’s ComponentMeta is the IDE-side analogue.
Notified Body#: The independent organisation that audits a manufacturer and its technical documentation before a medical device may be CE-marked under the EU MDR.
OpenUSD#: Open Universal Scene Description — Pixar’s open scene-graph format and composition engine. The framework’s interchange format: MADDENING serialises graphs to USD, MICROROBOTICA composes and renders them via USD layers.
ParamSpec#: The metadata for one leaf of a graph’s parameter Pytree (maddening.core.params.ParamSpec): whether an optimiser may change it (trainable), its physical bounds, and the transform ("log", "logit") that keeps an unconstrained optimiser inside them. Nodes declare specs for their own constants, and a graph can override them with GraphManager.set_param_spec.
PI controller#: A Proportional–Integral feedback controller. In MADDENING’s adaptive timestepper it shrinks/grows dt based on the current Richardson extrapolation error and its trend across recent steps — gentler than a pure proportional rule.
PISO#: Pressure-Implicit with Splitting of Operators — a segregated pressure–velocity solver for incompressible flow, used by MIME’s finite-volume (IBM-FVM) fluid node.
Precision floor#: The size below which a computed difference is float rounding rather than signal, set by the working precision (the eps of the dtype). A Coupling group’s diagnostics report the residual’s floor as residual_precision_floor and flag a residual at or below it as precision_limited; maddening.sysid.fim warns when its rank verdict lands near the cutoff the precision sets.
Pure function#: A function whose output depends only on its inputs and which has no side effects. MADDENING nodes are pure functions of (state, boundary_inputs, dt); this is what makes them JAX-traceable and safe to vmap.
pybind11#: Header-only C++ ↔ Python binding generator. MICROROBOTICA ships one microrobotica C++ library and exposes it both to the Qt app and to the embedded scripting console via pybind11.
Pytree#: JAX’s name for a nested structure of Python containers (dicts, lists, tuples) whose leaves are arrays; jax.jit, jax.grad and jax.vmap work leaf by leaf. A MADDENING graph’s parameters are one pytree, GraphManager.params, so the same object flows into a run, an optimiser and the System identification tools.
Quasi-Newton#: A family of iterative solvers that approximate the Jacobian from past iterates instead of computing it directly. IQN-ILS is the quasi-Newton scheme MADDENING uses to accelerate Coupling.
Reason code#: A short string in a Coupling group’s diagnostics report that says why a flag such as spectral_usable is False (maddening.core.coupling.reason_codes), so that code can branch on the cause instead of parsing the sentence in not_usable_reason. Every cause that holds is listed; a flag that is True has none.
Reynolds number#: The dimensionless ratio of inertial to viscous forces in a flow. Microrobots operate at Low-Re (Re ≪ 1), where viscosity dominates and motion is effectively time-reversible.
RFT#: Resistance-Force Theory — a fast analytical model for slender-body propulsion in Low-Re flow: drag is decomposed into components parallel and perpendicular to the body. Used as a cheap baseline against the full hydrodynamic nodes.
Richardson extrapolation#: Run a step at two different dts and combine the results to estimate the truncation error and a higher-order solution. MADDENING uses it to drive an adaptive timestepper.
RNEA#: Recursive Newton–Euler Algorithm — an O(n) method for robot inverse dynamics (joint torques from motion). Paired with CRBA in MIME’s robot-arm nodes.
ROS#: Robot Operating System. The hardware-integration bridge: the MICROROBOTICA IDE can publish or subscribe to ROS topics so a simulation can drive (or be driven by) a real robotic platform.
SaMD#: Software as a Medical Device — software that is itself a medical device, rather than software embedded in hardware. The regulatory category the simulation framework’s downstream uses fall under.
SBOM#: Software Bill of Materials — a machine-readable inventory of every dependency in a build. MADDENING commits one per covered install (CycloneDX format, docs/validation/sbom/) so downstream SOUP analysis has a complete component list.
Schwarz coupling#: A domain-decomposition method: two solvers covering overlapping sub-regions exchange boundary values and iterate to agreement. MIME uses it to couple a boundary-element near field to an LBM or FVM far field.
Shard#
Sharding#
Sharded#: One device’s slice of a node’s state when the state is split across devices along the axes of a JAX device mesh; sharding is the splitting. ShardedPointwiseNode and ShardedStencilNode wrap a node so that each device updates its own shard, the stencil wrapper exchanging a Halo between neighbours.
Sidecar#: The long-running Python process behind a MADDENING FMU: it holds the compiled graph and answers the FMU’s calls, forwarded over TCP, so that XLA’s compile cost is paid once rather than on every instantiation (maddening.fmi.sidecar.FmuSidecar).
SimulationNode#: The MADDENING base class every physics block subclasses. It declares an initial_state and an update(state, boundary_inputs, dt) method — see Node.
SkyPilot#: Open-source multi-cloud orchestration framework. MADDENING uses it to provision GPU VMs (RunPod, Lambda, AWS, GCP) for distributed graph execution and surrogate training.
SOUP#: Software Of Unknown Provenance — an IEC 62304 term for any third-party software included in a medical device. Each SOUP needs a documented classification and risk analysis.
Spectral radius#: The largest modulus among a matrix’s eigenvalues. For a fixed-point iteration it is the factor by which the error shrinks per pass in the long run, so the iteration converges locally when it is below 1. A Coupling group built with diagnostics=True reports an estimate for its Jacobian dF/dx as rho_spectral.
Stability level#: The promise a public MADDENING surface makes about change, set with @stability(StabilityLevel.X): STABLE, EVOLVING, EXPERIMENTAL or DEPRECATED. The level decides in which release an incompatible change may land and how much notice it needs (MADDENING’s deprecation policy).
STABLE#: The Stability level whose signature and documented behaviour hold for the life of the major version. An incompatible change needs a major release and two minor releases of DeprecationWarning first; MADDENING’s STABLE set is first frozen at 1.0.
Stencil#: The neighbouring grid points a computation reads to produce one value: the five points of a 2-D diffusion step, or the lattice cells a multilinear interpolation weights. A node whose update reads neighbours declares how far its stencil reaches per axis with halo_width(), which sizes the Halo when the node is sharded.
Step-out frequency#: The rotation rate above which a magnetically driven UMR can no longer keep up with the rotating field and desynchronises — its propulsion speed collapses past this point. A key validation metric for Helical UMR experiments.
Stokeslet#: The fundamental Green’s function of the Stokes equations: the flow field produced by a point force in a viscous, low-Reynolds fluid. MIME uses regularised Stokeslets for confined low-Re hydrodynamics.
Sub-cycling#
Sub-cycled#: Letting the faster members of a Coupling group take several smaller steps inside one step of the group (subcycling=True): a member with timestep node_dt takes macro_dt / node_dt sub-steps, where macro_dt, the group’s largest timestep, must be a whole multiple of every member’s. It is the in-group counterpart of Multi-rate scheduling.
Surrogate#: A neural network (MLP / DeepONet / FNO) trained to mimic a slow physics node so it can be hot-swapped in at runtime. See surrogates/ in MADDENING.
System identification#
sysid#: Estimating a model’s parameters from measured data. maddening.sysid does it on a graph’s parameter Pytree: a windowed trajectory loss (windowed_loss), a fitter (fit) that keeps to each leaf’s ParamSpec, and the Fisher information matrix (fim), which says which parameter combinations the data cannot identify.
Topological sort#: The ordering of graph nodes such that every edge points from earlier to later. MADDENING’s GraphManager topologically sorts each step; cycles are broken by cycle staggering (run them iteratively under Coupling).
UMR#: Untethered Microrobot — a microscale device propelled and steered by external fields rather than wires. The framework’s reference workload.
USD layer#: One of the three Pixar OpenUSD layers MICROROBOTICA uses to compose a scene: the immutable anatomy base, the simulator-written results layer, and the user override layer. Output never overwrites anatomy.
Verification benchmark#: A reproducible test that checks a node or graph against a known analytical solution or reference dataset. Every MADDENING / MIME node ships verification benchmarks; their results feed the audit trail.
vmap#: jax.vmap — automatic vectorisation. Lets you run the same Graph step across a batch of initial conditions (or parameters) with no manual loop and no per-instance compilation.
WebRTC#: The browser-native real-time streaming protocol. MADDENING uses it to push rendered viewport frames from a remote GPU VM to a local browser or to the MICROROBOTICA IDE (SelkiesSession, with the browser client api/static/webrtc_client.html). The stream encodes in software (x264enc) on every host. What is tested: a GStreamer WebRTC peer that signals as the browser client does gets the answer, completes ICE, and decodes the frames pushed, on CPU in a network-less container (tests/cloud/test_webrtc_loopback.py, CI job test-streaming); the cloud container’s entry point, run as the container runs it, streams the simulation built and run over its REST API to that peer (tests/cloud/test_entrypoint_streams.py). On 2026-10-12 the stream was also tested from a GPU host with the simulation on CUDA, and over the internet through a TURN relay. By default the media travels over UDP, which a cloud provider may not expose; StreamConfig.ice_servers is where a STUN or TURN server is set.
Womersley number#: A dimensionless number for pulsatile flow, comparing the oscillation frequency to viscous diffusion. It characterises time-varying physiological flows such as pulsing CSF.
XLA#: Accelerated Linear Algebra — the optimising tensor-program compiler JAX targets. XLA emits CPU / GPU / TPU code from JAX’s tracing IR.
ZMQ#: ZeroMQ — the message-passing library MADDENING uses to wire distributed graph fragments together and to stream graph state to visualisation clients.