Wolfram language modelica

System Modeling with Wolfram Language

This skill covers how to drive Modelica simulation from Wolfram Language using the built-in SystemModel* family. Use this when the downstream work lives in WL, for example, analysis of simulated data, calibration, optimization, surrogates, custom plots.

For pure command-line simulation / validation with no WL work afterward, prefer the simulate-modelica or validate-modelica skills — they are faster because they avoid kernel startup and WL context.

When to use which

Goal	Use
Does this .mo compile?	validate-modelica
Run a sim, get pass/fail + log	simulate-modelica
Debug torn systems, stiff init, blocks	diagnose-modelica
Pull time series into WL for Predict / AnomalyDetection / Fit	this skill
SystemModelCalibrate, SystemModelParametricSimulate	this skill
Requirement validation, uncertainty bands, surrogates	this skill
Live simulation you can pause / poke inputs & parameters mid-run	this skill (WSMRealTimeSimulate)

Official reference docs (LLM-friendly variant)

Every page of the official Wolfram documentation has an LLM-friendly Markdown variant — append .en.md to the page URL. Fetch these on demand when you need the full signature, all options, or more examples than this skill carries:

• Hub: https://reference.wolfram.com/language/guide/SystemModelingOverview.en.md
• Any SystemModel* function: https://reference.wolfram.com/language/ref/<Name>.en.md (e.g. SystemModelSimulate.en.md, SystemModelCalibrate.en.md, SystemModelValidate.en.md)
• WSMLink` (real-time) functions: https://reference.wolfram.com/system-modeler/WSMLink/ref/<Name>.en.md

The reference pages carry signatures and options but not the operational gotchas in this skill — those are verified against live kernels, and several (silent failures, headless-vs-notebook differences) are documented nowhere else. Where this skill and a doc example conflict in a headless/agent context, trust this skill.

Prerequisites — Wolfram Language + the Wolfram MCP server

Everything in this skill is Wolfram Language code (SystemModelSimulate, SystemModelPlot, SystemModelCalibrate, the requirement language, …). To run it the assistant needs a way to evaluate WL, which means two things:

1. Wolfram Language 14.3 or later — Mathematica or Wolfram|One (the SystemModel* simulation functions are not included in the free Wolfram Engine).
2. A C++ compiler. SystemModelSimulate compiles each model to a native executable before running it, so a working compiler toolchain must be available. Check (and fix) from within WL:

   SystemModel; (* Trigger loading of the system modeling functionality *)
   SystemModelConfiguration`VerifyCompiler[]    (* -> <|"Success" -> True|> when a working compiler is found *)
   SystemModelConfiguration`InstallCompiler[]   (* installs / configures a compiler if the check fails *)
   

3. The Wolfram MCP server connected to your agent, so the assistant can evaluate that WL on your machine.

Check before installing. First see whether Wolfram MCP tools (e.g. a WolframLanguageEvaluator) are already available in this session. If they are, skip setup and go straight to the workflow below.

Install — same on Windows, macOS, and Linux. In any Wolfram front end (a Mathematica notebook or wolframscript), evaluate:

PacletInstall["Wolfram/AgentTools"];
Needs["Wolfram`AgentTools`"];
InstallMCPServer["ClaudeCode"]   (* or "ClaudeDesktop", "Cursor", … for other clients *)

This writes the server entry into the MCP client's config and runs the kernel locally — no API key, nothing leaves the machine. Then fully restart the client (quit completely; closing the window often just minimizes it to the tray/menu bar).

If anything goes wrong — the paclet won't install, the server doesn't show up in the client after restart, or evaluations fail — point the user to the official setup and troubleshooting page: https://www.wolfram.com/artificial-intelligence/mcp/local/

If the user doesn't have Wolfram Language 14.3 or later (Mathematica or Wolfram|One), this skill can't run — point them to the page above and ask whether they want to install it. Meanwhile, the command-line skills (simulate-modelica, validate-modelica, diagnose-modelica) need only System Modeler, not WL, and can cover compile / run / debug in the interim.

Core workflow

1. Load the package

From a file / package directory:

sm = Import["/abs/path/to/package.mo", "MO"]   (* or "C:/..." on Windows *)
(* Returns SystemModel["PackageName", True] *)

From a Modelica source string (useful for inline models, templates, or LLM-generated models):

sm = ImportString[
"model Tiny
  Real x(start=0);
equation
  der(x) = 1 - x;
end Tiny;",
"MO"
]
(* Returns SystemModel["Tiny", True] *)

Notes:

• For multi-file packages, pass the top-level package.mo.
• The return value is a SystemModel[...] you can pass directly to SystemModelSimulate, SystemModelPlot, etc.
• You can also reference any loaded model by its full Modelica path as a string: "MyPackage.SubPackage.MyModel".
• Modelica source always goes through Import / ImportString — CreateSystemModel is for building models from WL equations and does not accept raw Modelica source (fails with SystemModel::nvr).

2. Simulate

sim = SystemModelSimulate["MyPackage.MyModel", {tmin, tmax}]              (* simulates over the simulation interval {tmin, tmax} *)

sim = SystemModelSimulate["MyPackage.MyModel", {"var1", "var2", "var3"}, {tmin, tmax}]     (* store results for specific variables, more efficient when only some results are of interest *)

Note: the list controls exactly what is stored — parameters you don't name in it are dropped too, so sim["ParameterNames"] returns {} unless the list includes them (e.g. {"var1", "k"}). Simulate without a variable list to keep everything.

sim = SystemModelSimulate["MyPackage.MyModel", {"var1", "var2", "var3"}, {tmin, tmax}, spec]     (* uses Association spec for initial values, parameters and inputs *)

Allowed spec keys:

Key	Purpose	Example
"ParameterValues"	Override tunable parameters	"ParameterValues" -> {"k" -> 2.5, "m" -> 10}
"InitialValues"	Override start values	"InitialValues" -> {"x" -> 0.1}
"Inputs"	Drive top-level inputs	"Inputs" -> {"u" -> (Sin[2 * #] &)}

sim = SystemModelSimulate["MyPackage.MyModel", {"var1", "var2", "var3"}, {tmin, tmax}, <|"ParameterValues" -> {"k" -> 2.5, "m" -> 10}|>]     (* uses the indicated parameter values *)

Pass ProgressReporting -> False — it drops the progress UI, which makes calls faster and keeps output clean. (Other options like Method for solver choice are rarely needed; see the SystemModelSimulate reference page if a model demands a specific solver.)

Parameter sweeps — pass a list for any parameter:

sweep = SystemModelSimulate["MyModel", {0, 10}, <|"ParameterValues" -> {"k" -> {1.0, 2.0, 5.0}}|>]
(* sweep is a list of SystemModelSimulationData objects *)

3. Extract numerical data

SystemModelSimulate returns a SystemModelSimulationData object. Several access patterns:

sim["Properties"]                (* list of properties this object supports *)
sim["VariableNames"]             (* list all time-dependent variables *)
sim["ParameterNames"]            (* list all parameters *)

(* An InterpolatingFunction or a Function over the simulation interval: *)
f = sim["var1"];
f[500.0]                         (* value of variable at t = 500.0 *)

(* Values at a single time: *)
sim[{"var1", "var2", "var3"}, t]                          (* list of variable values at t *)
sim[{"var1", "var2", "var3"}, 500.0]                      (* list of variable values at 500.0 *)

(* Values at a list of times: *)
sim[{"var1", "var2", "var3"}, {500.0, 700.0}]                      (* list of lists: values at 500.0 and 700.0 for each variable *)

(* Raw time/value pairs (faster than interpolation). Repeated times indicate events: *)
sim["RawData", {"var1", "var2"}]

(* All variables as a rules list, this is time consuming for large number of stored variables *)
sim["VariableValues"]

(* Association of parameter values, initial values and inputs used in the simulation call*)
sim["Configuration"]

4. Plot

SystemModelPlot[sim]                          (* default plots stored in the model — errors with SystemModelPlot::nov if the model has no stored plots; pass a variable list in that case *)
SystemModelPlot[sim, {"x", "y"}]              (* plot specific variables *)
SystemModelPlot[{simA, simB, simC}, {"x"}]    (* compare results for several simulations — auto legend *)
SystemModelPlot[model, ...]                   (* simulate + plot in one shot *)

Useful options: PlotLegends, PlotStyle, Filling, TargetUnits, ScalingFunctions.

For a custom plot with Plot or ParametricPlot:

(* with Plot *)
Plot[Evaluate[sim[{"x", "y"}, t]], {t, tmin, tmax}, PlotLegends -> {"x", "y"}]

(* with ParametricPlot *)
ParametricPlot[Evaluate[sim[{"x", "y"}, t]], {t, tmin, tmax}]

(Note: using Evaluate is important so sim[...] is resolved once, not at every plot point.)

5. Resample onto a uniform grid (common for ML)

vars = {"var1", "var2", "var3"};
ts = Range[tmin, tmax, dt];
mat = Transpose[sim[vars, ts]];
(* mat has Dimensions {Length[ts], Length[vars]} — ready for AnomalyDetection etc. *)

Canonical end-to-end example

(* 1. Load *)
Import["/path/to/pkg/package.mo", "MO"];   (* use the OS-appropriate absolute path *)

(* 2. Simulate three scenarios *)
scenarios = {"pkg.Baseline", "pkg.Scenario1", "pkg.Scenario2"};
sims = SystemModelSimulate[#, {0, 1000}, ProgressReporting -> False] & /@ scenarios;

(* 3. Inspect what's in there *)
Take[First[sims]["VariableNames"], UpTo[10]]

(* 4. Extract a 3-variable time series from each scenario *)
variables = {"mIn.m_flow", "pTee.p", "mA.m_flow"};
ts = Range[0, 1000, 2.];
series = Through[sims[variables, ts]];
(* series is an array, has Dimensions {Length[scenarios], Length[variables], Length[ts]}, can be indexed with Part *)

(* 5. Compare with SystemModelPlot *)
SystemModelPlot[sims, variables]

(* 6. Downstream: anomaly detection trained on baseline *)
detector = AnomalyDetection[Transpose[series[[1]]]];
anomalyScores = detector[Transpose[series[[2]]], "RarerProbability"];

Gotchas

• Printing SystemModelSimulationData inside a List dumps every variable name. A raw sim object displays compactly, but wrapping it in a List (e.g. evaluating {sim1, sim2} as the output of a cell) strips the compact box form and you get the entire variable-name list printed inline — hundreds of kilobytes of output per simulation. Fix: end the assignment cell with ;, then either pass the list directly into consumers (SystemModelPlot[sims, ...], extractions) without displaying it, or produce a compact summary:

  KeyTake[sim1["Summary"], {"ModelName", "SimulationInterval", "VariableValues"}]         (* single simulation sim1 *)
  
  "NumberOfSimulations" -> Length[sims]                                                   (* list of simulations sims *)
  

• AnomalyDetection[...] has no "AnomalyProbability" property. The continuous score is called "RarerProbability", and its polarity is the opposite of what the name "anomaly probability" suggests: it is high (→ 1) for typical samples and low (→ 0) for anomalies. For an intuitive "higher = more anomalous" score, compute 1 - detector[x, "RarerProbability"]. For a hard yes/no, detector[x] (or "Decision") is already polarity-correct.

• SystemModelValidationData[...]["FirstFailureTime"] and other properties return a Dataset, not a number. On passing scenarios it is an empty Dataset; on failing scenarios it wraps the scalar in a row that also includes an empty Configuration column. Extract cleanly before displaying:

  prop = "FirstFailureTime";
  d = SystemModelValidationData[...][prop];
  With[{n = Normal[d, Dataset]},
    If[n === {}, "\[LongDash]", First[n][prop]]    (* "FirstFailureTime" for the first failure configuration, if there is one *)
  ];
  

• Variable name mismatches. Modelica uses dots: pipe1.port_a.p. Protected / mangled names can appear. Always run sim["VariableNames"] when in doubt instead of guessing.

• .mat files from a kernel simulation aren't readable via sim[...] directly. Those come from the WSM kernel simulation. To read them in WL, load via SystemModelSimulationData[path] — and even then, the file path must still exist. Prefer going through SystemModelSimulate end-to-end when you need data in WL.

• Load WSMLink` in its own evaluation, before any code that uses it. WL binds symbols at parse time, so a single evaluation containing both Needs["WSMLink`"] and WSMRealTimeSimulate[...] creates Global`WSMRealTimeSimulate before the package loads, and the call returns unevaluated (Symbol::undefined). Evaluate the Needs on its own first, then the code. If loading itself emits messages (e.g. Set::write: Tag ... is Protected), the load went wrong — don't dismiss it; restart the kernel and load cleanly, and report it if it persists.

• Unit annotations. SystemModelPlot respects Modelica unit annotations; variables without units show raw numbers.

Requirements and validation

For anomaly detection, fault diagnosis, or safety-case work, Wolfram ships a requirement language plus SystemModelValidate that expresses assertions directly over the simulated trajectory — no scaffolding needed.

The requirement language

Temporal operators that wrap a predicate over a free time variable t:

Operator	Meaning
SystemModelAlways[t, texpr]	texpr holds for every t in the validation interval
SystemModelAlways[t, cond, texpr]	texpr holds whenever cond[t] is true (scoped "always")
SystemModelEventually[t, texpr]	texpr holds at some t
SystemModelUntil[...]	Hold until another condition fires
SystemModelSustain[...]	Hold continuously for at least a given duration
SystemModelDelay[...]	Shift a condition in time

Predicates compose with <, <=, >, >=, ==, &&, ||, !, etc., and reference any variable from the model by bracket syntax var[t], or parameter as par.

Calling SystemModelValidate

(* Against a live model *)
val = SystemModelValidate[model, req]
val = SystemModelValidate[model, req, spec]

(* Against an already-computed SystemModelSimulationData *)
val = SystemModelValidate[sim, req]

(* Direct property extraction *)
SystemModelValidate[sys, req, "FailureIntervals"]

Unlike SystemModelSimulate, SystemModelValidate does not accept a bare {tmin, tmax} as a positional argument — a simulation interval must be passed inside spec as "SimulationInterval" -> {tmin, tmax}. Passing {tmin, tmax} positionally leaves the call unevaluated.

Names in "ParameterValues" must match the model's parameters exactly, or the call fails with SystemModelValidate::pvf ("not among the expected ones"). When unsure, list them first with model["ParameterNames"].

Method -> {"InterpolationPoints" -> n} evaluates the requirement on an n-point time grid — reported failure times snap to grid points, and fewer points mean less post-processing on large sweeps.

spec is an Association with any of:

<|
  "InitialValues"      -> {v1 -> val1, ...},
  "ParameterValues"    -> {p1 -> val1, ...},     (* accepts lists / intervals / distributions *)
  "Inputs"             -> {in1 -> fun1, ...},
  "SimulationInterval" -> {tmin, tmax},
  "SimulationCount"    -> 200,                    (* for stochastic sweeps *)
  "MaxFailureIntervals"-> Automatic
|>

SystemModelValidationData properties

Property	Returns
"SuccessProbability"	Overall pass/fail or probability across a sweep
"FailureIntervals"	Time intervals where the requirement was violated
"FirstFailureTime"	First t where a failure occurred
"Configuration"	Parameter/initial-value/inputs that produced a failure
"FailurePlot"	Pass/fail step chart over time (index selects the failure configuration, e.g. val["FailurePlot", 1])
"FailureIntervalsPlot"	Time-window diagram of failure intervals

For a plot of the variable itself against its requirement bound with the failure intervals shaded, validate an existing simulation and combine trajectory, bound and intervals:

requirementFailurePlot[sim_, var_, bound_, val_] :=
 Module[{ints, ymin, ymax, pad, tspan},
  ints = Join @@ (#FailureIntervals & /@ Normal[val["FailureIntervals"]]);
  {ymin, ymax} = MinMax[Join[sim[var]["ValuesOnGrid"], {bound}]];
  pad = 0.08 (ymax - ymin);
  tspan = sim["SimulationInterval"];
  SystemModelPlot[sim, var,
   Prolog -> {Opacity[0.12], Red,
     Rectangle[{Min[#], ymin - pad}, {Max[#], ymax + pad}] & /@ ints},
   Epilog -> {Dashed, Red, Line[{{tspan[[1]], bound}, {tspan[[2]], bound}}]},
   PlotRange -> {ymin - pad, ymax + pad}]]

sim = SystemModelSimulate[model, 1000];
val = SystemModelValidate[sim, SystemModelAlways[t, "tank1.level"[t] < 0.45]];
requirementFailurePlot[sim, "tank1.level", 0.45, val]

This is the single-run form (validate the sim you plot); for a sweep, pick one configuration's intervals instead of joining all rows.

Uncertainty bands

SystemModelUncertaintyPlot[sys, spec] plots median and quantile bands over a stochastic sweep. It takes the same uncertainty spec as SystemModelValidate ("ParameterValues", "SimulationCount", ...), with the plotted variables under "Outputs":

SystemModelUncertaintyPlot[model, <|
  "Outputs" -> {"tank1.level"},
  "ParameterValues" -> {"inflow.qFlow" -> NormalDistribution[0.001, 0.0001]},
  "SimulationCount" -> 200|>,
  Method -> <|"SimulationMethod" -> {"InterpolationPoints" -> 25}|>]

It is a two-argument form: passing variables positionally leaves the call unevaluated. Its interpolation-points setting nests under the "SimulationMethod" key (unlike SystemModelValidate's flat Method list).

Surrogate models for fast repeated evaluation

When a workflow needs many evaluations across a parameter range (optimization, Pareto sweeps, interactive exploration), train a surrogate once and evaluate it in milliseconds instead of resimulating:

sur = SystemModelSurrogateTrain[model, <|
  "Outputs" -> {"tank1.level", "tank2.level"},
  "ParameterValues" -> {"inflow.qFlow" -> CenteredInterval[0.001, 0.0002]},
  "SimulationCount" -> 200, "SimulationInterval" -> {0, 1000},
  "ReservoirNeuronsCount" -> 100, "InterpolationPoints" -> 100|>];

{level1Fun, level2Fun} = sur["ParametricFunction"];   (* one function per output *)
(level1Fun @@ {0.0011})[500]                          (* trajectory value at t = 500 *)

• Same spec family as SystemModelValidate / SystemModelUncertaintyPlot, plus training hyperparameters as spec keys: "ReservoirNeuronsCount", "InterpolationPoints", "CentroidsCount", "CholeskyFactorDensity". Bigger reservoirs are not automatically better — sweep reservoir size × sample count and pick the knee of sur["MeanLoss"] (a per-output table).
• For multi-parameter design spaces, pass an explicit joint-sample matrix: "ParameterValues" -> {{"p1", "p2"} -> samples} (n×d rows, e.g. Latin Hypercube). Training then runs exactly those n samples — omit "SimulationCount".
• With one output, "ParametricFunction" is a single function; with several, a list in "Outputs" order. Call as fun @@ point; the result is a trajectory InterpolatingFunction of time.
• Surrogates serialize: Export["sur.wxf", sur, "WXF"], Import back — train once, reuse across sessions.
• If the downstream use is scalar objectives (cycle time, integrated losses, peaks), compute them as variables inside the Modelica model and include them in "Outputs" — applying quadrature or root-finding to surrogate-predicted trajectories compounds error.
• Other properties: "SystemModel" (use like any model), "Net", "SimulationCount", error plots "RMSEPlot" / "MAEPlot" / "RRMSEPlot". Check an error plot (or spot-check against a real simulation) before trusting a surrogate.

Why this matters for anomaly detection

A physics-based requirement is already a detector. Two patterns worth knowing:

1. Mass / energy balance as a hard requirement. In a pipe network:

leakFree = SystemModelAlways[t, Abs["mIn.m_flow"[t] - "mA.m_flow"[t] - "mB.m_flow"[t]] < 0.5];

val = SystemModelValidate[sim, leakFree];

val["ValidationSucceeded"]
(* True / False - flags a leak instantly *)

val["FailureIntervals"]
(* Dataset with failure intervals *)

A detector you can explain to a CIO in one sentence, derived from first principles, with zero training data.

2. Physics-based baseline envelope. For signatures that don't come from a conservation law, run the healthy model once, build a tolerance band around each channel, and validate future runs against it.

Do not splice a raw InterpolatingFunction (i.e. simBaseline["pTee.p", t] or simBaseline["pTee.p"]) directly into the requirement — the validator walks the requirement expression looking for model variables, descends into the InterpolatingFunction's packed-array internals, and fails with SystemModel::nvr ("Developer\PackedArrayForm" is not a valid identifier) / SystemModelValidate::bms. Instead, capture the baseline trajectory in a NumericQ`-guarded wrapper function so the validator treats it as opaque and only ever evaluates it at numeric sample times:

simBaseline = SystemModelSimulate["pkg.Baseline", {0, T}];
simScenario1 = SystemModelSimulate["pkg.Scenario1", {0, T}];

ref = simBaseline["pTee.p"];              (* the InterpolatingFunction *)
gref[tt_?NumericQ] := ref[tt];            (* opaque numeric-guarded reference *)
req = SystemModelAlways[t, Abs["pTee.p"[t] - gref[t]] < 0.05 * Abs[gref[t]]];

val = SystemModelValidate[simScenario1, req];

val["ValidationSucceeded"]

When to use what

Situation	Use
A conservation law or a clean inequality defines "healthy"	Requirement + SystemModelValidate
Signature is multivariate / subtle / data-driven	AnomalyDetection on extracted channels
Need both a yes/no certificate AND continuous anomaly scoring	Layer them — requirement for the hard gate, AnomalyDetection for early warning
Hardware-in-the-loop, formal safety case	Requirement language — it's the proof artifact you hand to auditors

The combination is the Wolfram story: physics-aware requirements set the floor (no false negatives for known faults), statistical anomaly detection catches the unknown ones.

Parameter calibration (fitting a model to measured data)

SystemModelCalibrate takes measured data, a model, and a list of parameters to tune, and returns a model with calibrated parameter values, or, if specified a CalibratedSystemModel object with information on the fitted values, residuals, and prediction bands.

Signature

SystemModelCalibrate[data, model, params]
SystemModelCalibrate[data, model, params, spec]
SystemModelCalibrate[..., "prop"]     (* direct property extraction *)

The bare SystemModelCalibrate[data, model, params] form returns a calibrated SystemModel (ready to simulate), not an information object — so cal["CalibratedParameters"] / cal["RMSE"] on it will not resolve. To get the fitted values, residuals, or bands, either use the direct property form SystemModelCalibrate[..., "CalibratedParameters"] or grab the info object once with SystemModelCalibrate[..., "CalibratedSystemModel"] and query that.

The measured data's time span must be consistent with the model's simulation interval, otherwise calibration fails with SystemModelCalibrate::bvs. Pass spec with "SimulationInterval" -> {tmin, tmax} (or supply data only within the model's interval).

• data is an Association mapping the measured variable name to a list of {t_i, y_i} pairs: <|"sensor.p" -> {{0., 1.2e5}, {0.1, 1.4e5}, ...}|>. Multiple variables can be calibrated against simultaneously by adding more entries to the association.
• model is a SystemModel[...] or model-name string.
• params is a list of parameter names or {name, initial_guess} pairs: {{"compressor.a0", 100000.}, {"compressor.a1", 1000.}}. Initial guesses far from the truth slow convergence but don't prevent it.

Key properties of the result

Property	What it gives you
"CalibratedParameters"	The fitted values as a rules list, ready to pass into SystemModelSimulate via "ParameterValues".
"CalibratedSystemModel"	Information object with properties.
"ParameterConfidence"	Uncertainty on each fitted parameter.
"RMSE"	Root-mean-square residual between measured and predicted output.
"SinglePredictionBandsPlot"	Visual diagnostic: measured vs. predicted with 95% bands.

Practical tips

• Parameters live on the component, not the testbench. Reference them with their full Modelica path: "compressor.a0", not "a0".
• Starting guesses matter for robustness. Order-of-magnitude right is fine; being off by a sign will usually still converge but slowly. Bad starting guesses with narrow parameter bounds is where calibrations get stuck.

Interactive exploration with sliders (SystemModelManipulate)

For a notebook Manipulate over model parameters and initial values — sliders that re-simulate and re-plot on release — use the Function Repository resource:

ResourceFunction["SystemModelManipulate"][model, {"inflow.qFlow", 0.0005, 0.0015}]

With no control spec it exposes all top-level parameters and initial values; controls follow Manipulate syntax ({u, umin, umax}, {{u, uinit}, ...}, discrete value lists). Its defaults are pre-tuned so slow models stay stable (ContinuousAction -> False, SynchronousUpdating -> False — simulate on slider release, not on every drag tick). Prefer this over hand-rolling Manipulate[SystemModelPlot[SystemModelSimulate[...]], ...], which with default Manipulate settings re-simulates on every drag tick. First use fetches the resource from the cloud.

Real-time interactive simulation (WSMRealTimeSimulate)

For a live simulation you interact with while it runs — pause/resume, change inputs or parameters mid-run, read variable values at the current sim time — use WSMRealTimeSimulate from the WSMLink` package instead of the batch SystemModelSimulate. This is the right tool for turn-based / agent-in-the-loop setups (an LLM or optimizer making sequential decisions against a running model), hardware-style demos, and injecting disturbances mid-run. It avoids the extract-final-state / re-initialize plumbing that chunked batch simulation would need: hidden states carry over automatically because the simulation never stops.

Works in standalone Wolfram Language — no separate System Modeler installation is needed. The model must already be loaded (e.g. via Import[..., "MO"]).

Recipe

Needs["WSMLink`"];

conn = WSMRealTimeSimulate["MyModel", stopTime,
  Method -> {"WriteSimulationData" -> True,   (* log the trajectory for later retrieval *)
             "SimulationRate" -> 10}]         (* 10 sim-seconds per wall-second *)
(* conn is a WSMSimulationConnection; the simulator runs as a separate local process *)

conn["Start"];                                       (* run *)
WSMLink`Simulate`SetInputs[conn, "u" -> 2];          (* change a top-level input, effective immediately *)
Pause[3];                                            (* let it run 3 wall-seconds = 30 sim-seconds *)
conn["Pause"];                                       (* freeze sim time *)

conn[{"y", "x"}]                                     (* read live values at current sim time *)

WSMLink`Simulate`SetParameters[conn, "k" -> 5];      (* parameters can change mid-run too *)
conn["Start"];                                       (* resume — states carried over *)
...
conn["Stop"];
sd = Quiet@Check[conn["SimulationData"], $Failed];   (* best-effort — unreliable headless, see gotchas *)
If[sd =!= $Failed, WSMPlot[sd, {"y"}]];
conn["Close"];                                       (* kill the simulator process when done *)

Other useful pieces: WSMLink`Simulate`SetInputs[conn, "u" -> Function[...], RefreshRate -> 0.5] (input driven by a WL function evaluated periodically), WSMLink`Simulate`AddDataMonitor[conn, f, vars] (callback when variables update — event triggers like "cash < 0 → stop"), and WSMRealTimePlot for a continuously updating plot in a notebook front end.

Turn-based agent loop (the pattern that works)

(* one turn: run a fixed chunk of sim time, then hand control to the agent *)
conn["Start"]; Pause[turnWallSeconds]; conn["Pause"]; Pause[0.3];  (* let pause settle *)
now  = First[conn[{"clk"}]];        (* ACTUAL sim time — see gotchas: never assume it *)
obs  = conn[{"revenue", "cash"}];   (* observables for the agent *)
(* ... agent decides ... *)
WSMLink`Simulate`SetInputs[conn, {"price" -> p, "adBudget" -> a}];
(* next turn *)

The connection object persists in the kernel session, so an agent driving the loop through separate evaluator calls (e.g. over MCP) works — create conn once, keep using it across calls.

Driving the connection headless — do it this way

The notebook front end papers over several connection behaviors that surface when WSMLink is driven headless (e.g. over MCP). These rules keep the loop solid:

• Read everything through live variable reads. conn[{"y", ...}] is reliable headless. Don't branch on conn["Time"] or conn["State"] — they return stale values ("Time" stuck near 0; "State" reporting "Running" after a successful Pause/Stop, or "NotStarted" while the simulation is demonstrably running).
• For sim time, put a clock state in the model and live-read it. Plain time, or an alias like tclock = time, is alias-eliminated and reads back as 0. over the connection. A genuine state works:

  Real clk(start = 0, fixed = true);
  equation
    der(clk) = 1;   // clk == sim time, live-readable via conn[{"clk"}]
  

• Timestamp each turn from clk, never by arithmetic. Each Start→Pause window overshoots by roughly 10–50 ms of wall-clock command latency, which becomes latency × SimulationRate of extra sim time (measured: +0.03–0.05 sim-s per window at rate 1; up to +4 sim-s at rate 100). The error is always positive, per-window jitter, and does not accumulate beyond that — but it means nTurns × Pause × rate drifts from the truth. Read clk back after each pause instead.
• Collect the trajectory yourself while the simulation runs — log the observables you need at each turn with live reads, or accumulate them with WSMLink`Simulate`AddDataMonitor. conn["SimulationData"] is unreliable headless: it always fails while paused mid-run, and often fails with WSMSimulationConnection::nos even after conn["Stop"] or natural completion, regardless of "WriteSimulationData" -> True or a stored-vars list at creation. Treat a successful retrieval as a bonus, not a plan.
• Expose every decision knob as a top-level input. SetInputs targets only declared top-level input variables; knobs buried inside components (time tables, ramp/pulse sources) must first be promoted to top-level inputs in a model variant.

Common follow-on tools

Once data is in WL, the useful downstream functions are:

Tool	Use
SystemModelValidate + SystemModelAlways / SystemModelEventually	Requirement-based validation (mass balance, envelopes, safety bounds)
SystemModelUncertaintyPlot	Median/quantile uncertainty bands from stochastic parameter sweeps
SystemModelSurrogateTrain	Fast trained surrogate for repeated evaluation across a parameter range
ResourceFunction["SystemModelManipulate"]	Slider-driven interactive exploration of parameters/initial values
AnomalyDetection	Statistical detector trained on baseline residuals
Predict / Classify	Supervised models trained on simulated scenarios
FindFit / NonlinearModelFit	Parameter identification from data
ModelFit	Fit/select empirical models on extracted data, with cross-validation
SystemModelCalibrate	Direct Modelica-aware calibration against measurements
SystemModelParametricSimulate	Pre-compiled parametric simulator (fast sweeps)
SystemModelLinearize	Extract a linear model around an operating point
PredictorMeasurements	Evaluate model performance

ModelFit usage notes

ModelFit distills sweep or trajectory data into an empirical formula — e.g. fitting steady-state level vs. flow recovers the valve's quadratic law:

ModelFit[data, {PolynomialModel[1], PolynomialModel[2], PowerModel[]},
  {"Name", "Expression", "RSquared"}]

Two traps:

• ModelFit[data, model] returns the fitted model as a callable function. Request properties in the third argument — fit["Expression"] does not query a property, it silently evaluates the model at the string.
• For model selection, pass model objects (PolynomialModel[2], PowerModel[], ...). A list of string names ({"Linear", "Quadratic"}) fails with ModelFit::nofit even on clean data; string names work only in the single-model form.

Writing results to disk

(* Native WL — fast round-trip, keeps InterpolatingFunctions *)
DumpSave["sim.mx", sim];
Get["sim.mx"];      (* restores the symbol `sim` in place — do NOT write `sim = Get[...]` *)

(* Portable / CSV — for handoff to Python etc. *)
Export["sim.csv", sim[variables, times]];

Do not write sim = Get["sim.mx"]. Get on a DumpSave file restores the saved symbol (sim) in place and itself returns Null, so the assignment would immediately clobber the just-restored value with Null. Just evaluate Get["sim.mx"] (or << "sim.mx") on its own — sim is valid afterward.