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morgen logo morgen - Model Order Reduction for Gas and Energy Networks (1.2)

morgen is an open-source MATLAB and OCTAVE test platform to compare models, solvers, and model reduction methods (reductors) for gas networks and other energy network systems that are based on the (isothermal) Euler equations.


Current Version: morgen 1.2 (2022-10-07)



  • emgr == 5.99 (included, see reductors/private)


morgen is licensed under the BSD-2-Clause license, with copyright (c) 2020--2022: Christian Himpe, Sara Grundel; see LICENSE.


morgen is research software.


Please cite the morgen platform via its companion paper:

C. Himpe, S. Grundel, P. Benner: Model Order Reduction for Gas and Energy Networks; Journal of Mathematics in Industry 11: 13, 2021. doi:10.1186/s13362-021-00109-4

You can link to morgen via:

Getting Started

To setup simulation and reduction tests and demos:

> SETUP % adds the "tests" folder to the path and lists scripts

Tests can then be called directly as listed. To try morgen:

> DEMO  % runs a sample pipeline model reduction code


To reproduce the experiments from the companion paper, Model Order Reduction for Gas and Energy Networks, run:

> RUNME_HimpeGB21

To reproduce the experiments from the first add-on paper, Next-Gen Gas Network Simulation, run:

> RUNME_HimpeGB22

To reproduce the experiments from the second add-on paper, System Order Reduction for Gas and Energy Networks, run:

> RUNME_HimpeG22

Extending morgen

morgen's modules can be easily extended in the following ways:

  • to add a new model, see and modify: models/template_model.m
  • to add a new solver, see and modify: solvers/template_solver.m
  • to add a new reductor, see and modify: reductors/template_reductor.m
  • to add a new network, see and modify: networks/
  • to add a new scenario, see and modify: networks/template_network/training.ini
  • to add a new simulation test, see and modify: tests/sim_template.m
  • to add a new reduction test, see and modify: tests/mor_template.m


Main Function

(click to expand)

The morgen platform is called via the morgen.m function:

R = morgen(network_id,scenario_id,model_id,solver_id,reductor_ids,varargin)

and has four mandatory arguments:

  • network_id (string) The network identifier
  • scenario_id (string) The scenario identifier
  • model_id (string) The model identifier
  • solver_id (string) The solver identifier

as well as an optional argument and an additional variable length argument list:

  • reductor_ids (cell) An array of reductor identifiers (can be empty, too)
  • varargin Variable argument list each containing a string (see below)

All admissible additional (string) arguments are described below:

  • dt=X - Override time step in configuration with X (in seconds)
  • tf=X - Override tunable efficiency factor in configuration with X (positive real)
  • ys=X - Force minimum y-scale for error plots with 10^X (default: -16)
  • ord=X - Override maximum reduced order in configuration with X (natural number)
  • pid=X - Add custom string identifier to plot files (default: '')
  • notest - Do not test the reduced order models
  • compact - Display plots all in one figure

The morgen.m function returns a structure R with members depending on the arguments. If only reduced order models are computed:

  • .reductors (cell) Array of strings with names of the reductors
  • .offline (cell) Array of offline times for the reductors

If reduced order models are computed and tested:

  • .name (string) Output name of the experiment (as used by saved plots and scores)
  • .reductors (cell) Array of strings with names of the reductors
  • .orders (vector) The tested reduced orders
  • .l0error , .l1error , .l2error , .l8error (cell) Arrays of per reduced order average errors
  • .l0score , .l1score , .l2score , .l8score (cell) Arrays of per reduced order average MORscores
  • .offline (cell) Array of offline times for the reductors
  • .online (cell) Array of average relative online times for the reductors
  • .breven (cell) Array of average relative offline/online break even numbers

If only a simulation is run, R is a matrix, and contains the discrete output trajectory with dimensions outputs-times-time-steps.


(click to expand)

A network is described by a (directed) graph, given through an edgelist, which also specifies its edge type, and their physical dimensions and properties.

Network Topology Rules

  • A network must have at least one supply node!
  • All boundary nodes (supply or demand) must connect by exactly one edge!
    • Short pipes can be inserted to enforce this.
  • The edge from a supply node must be directed away from it!
    • Hence, no two supply nodes can be directly connected.
  • The edge to a demand node must be directed toward it!
    • Hence, no two demand nodes can be directly connected.

Available Networks

All available network datasets are listed with the network's number of

  • internal junction nodes (n0),
  • supply boundary nodes (nS), and
  • demand boundary nodes (nD).
Test Networks
  • diamond - Diamond Network (n0=8, nS=1, nD=1, nC=0)
  • fork1 - Forked Pipeline (n0=12, nS=1, nD=2, nC=0)
  • fork2 - Forked Pipeline (n0=12, nS=2, nD=1, nC=0)
  • comptest - Compressor Test (n0=1, nS=1, nD=1, nC=1)
  • paratest - Parallel Pipes Test (n0=2, nS=1, nD=1, nC=0)
  • PamDB16 - Triangle Network (n0=0, nS=1, nD=2, nC=0)
Synthetic Networks
  • MORGEN - Small Network (n0=27, nS=2, nD=4, nC=1)
  • AzeJ07 - Small Network (n0=5, nS=1, nD=2, nC=1)
  • GruHKetal13 - Small Network (n0=11, nS=1, nD=8, nC=0)
  • Kiu94 - Small Network (n0=8, nS=1, nD=14, nC=0)
  • GruJHetal14 - Medium Network (n0=45, nS=4, nD=2, nC=0)
  • GasLib11 - Medium Network (n0=6, nS=3, nD=3, nC=2)
  • GasLib24 - Medium Network (n0=14, nS=3, nD=5, nC=3)
  • GasLib40 - Medium Network (n0=40, nS=3, nD=29, nC=6)
  • GasLib135 - Medium Network (n0=135, nS=3, nD=45, nC=29)
  • PelLL17a - Medium Network (n0=41, nS=1, nD=15, nC=5)
  • pipeline - Pipeline (n0=0, nS=1, nD=1, nC=0)
  • Cha09 - Pipeline (n0=0, nS=1, nD=1, nC=0)
  • RodS18 - Tree (n0=6, nS=1, nD=4, nC=0)
  • Guy67 - Tree (n0=8, nS=1, nD=8, nC=0)
  • LotH67a - Pipeline (n0=0, nS=1, nD=1, nC=0)
  • LotH67b - Pipeline (n0=0, nS=1, nD=1, nC=0)
  • LotH67c - Tree (n0=6, nS=2, nD=2, nC=2)
  • LotH67d - Tree (n0=4, nS=2, nD=2, nC=1)
Realistic Networks
  • AzePA19 - Portugal (n0=0, nS=1, nD=1, nC=0)
  • BerS19 - Spain (n0=6, nS=1, nD=5, nC=0)
  • DeWS00 - Belgium (n0=20, nS=6, nD=9, nC=0)
  • EkhDLetal19 - Ireland (n0=26, nS=3, nD=10, nC=0)
  • GasLib134 - Greece (n0=134, nS=3, nD=45, nC=1)
  • GasLib582 - Germany (n0=582, nS=31, nD=129, nC=5)
  • GasLib4197 - Germany (n0=4197, nS=11, nD=1009, nC=12)
  • SciGrid_NO - Norway (n0=44, nS=11, nD=9, nC=0)
  • JinW - China (n0=45, nS=5, nD=3, nC=38)

Data Origin

The GasLib network data-sets are derived from:

M. Schmidt, D. Aßmann, R. Burlacu, J. Humpola, I. Joormann, N. Kanelakis, T. Koch, D. Oucherif, M.E. Pfetsch, L. Schewe, R. Schwarz, M. Sirvent: GasLib - A Library of Gas Network Instances; Data 2(4): 40, 2017.

and licensed under CC-BY 3.0, see:

The SciGrid network data-sets are derived from:

J. Dasenbrock, J. Diettrich, A. Pluta, W. Medjroubi: SciGRID_gas NO_Raw; Zenodo: 10.5281/zenodo.3985268, 2020.

and licensed under CC-BY 4.0, see:

File Format

A network is encoded in a CSV file with the file extension .net. The first line is a comment header with a description of the columns, their meaning, and units.

# type, identifier-in, identifier-out, pipe-length [m], pipe diameter [m], height difference [m], pipe roughness [m]

Each line below the first holds one edge definition with the columns:

  • Edge type (P:pipe, S:shortpipe, C:compressor, V:valve)
  • Start node identifier (positive integer)
  • End node identifier (positive integer)
  • Pipe length [m] (positive real)
  • Pipe diameter [m] (positive real)
  • Pipe height difference [m] (positive real)
  • Pipe roughness [m] (positive real)

Thus, the gas network's directed graph is represented as an edge list, whereas the edge directions are not corresponding to flow directions except for boundary nodes. Note, currently only positive integers can be used as start and end identifiers.

Parsed Network Structure

A parsed network .net file is given as a network structure with members:

  • network (struct)
    • .length (vector) Pipe lengths
    • .incline (vector) Pipe inclines
    • .diameter (vector) Pipe diameters
    • .roughness (vector) Pipe roughnesses
    • .nomLen (vector) Per pipe length
    • .A0 (matrix) Incidence matrix reduced by supply nodes
    • .Ac (matrix) Incidence matrix of only compressor outlet nodes
    • .Bs (matrix) Incidence matrix of supply nodes
    • .Bd (matrix) Incidence matrix of demand nodes
    • .Fc (vector) Load vector of compressors
    • .nEdges (scalar) Number of edges
    • .nSupply (scalar) Number of supply nodes
    • .nDemand (scalar) Number of demand nodes
    • .nInternal (scalar) Number of internal nodes
    • .nCompressor (scalar) Number of compressors


(click to expand)

A scenario data set describes the boundary values and external inhomogeneities of the gas net. Transient behaviour of supply and demand functions is represented as step functions in compressed form by only marking changes. Each network has a training scenario (training.ini), which has constant boundary values for reduced order model assembly.

File Format

A scenario is encoded in an INI file, with the extension .ini. Each line holds a key-value pair, for the following keys:

  • T0 - Average ambient temperature [C]
  • Rs - Average specific gas constant [J/(kg*K)]
  • tH - Time horizon [s]
  • vs - Valve setting [1] (pipe separated list of {0,1}) {UNDER CONSTRUCTION, currently treated as short pipe}
  • cp - Compressor (output) pressure [bar] (pipe separated list)
  • up - Supply pressure changes [bar] (pipe separated list of semi-colon separated series)
  • uq - Demand flow changes [kg/s] (pipe separated list of semi-colon separated series)
  • ut - Time markers for changes in up and uq [s]

Parsed Scenario Structure

A parsed network .ini file is given as:

  • scenario (struct)
    • .T0 (scalar) Global mean temperature
    • .Rs (scalar) Global mean specific gas constant
    • .tH (scalar) Time horizon
    • .us (vector) Steady-state input
    • .ut (handle) Function handle with signature u_t = ut(t)
    • .cp (vector) Compressor outlet pressures


(click to expand)

A model encodes a spatially discrete input-output system of the form:

E(p) x'(t) = A x(t) + B u(t) + F c_p + f(x(t),u(t),p)

      y(t) = C x(t)

which consists of an implicit nonlinear ordinary differential equation, and an (uni-directionally coupled algebraic) output equation.


discrete = model(network,config)


  • network (struct) Parsed network structure
  • config (struct) Configuration structure


  • discrete (struct) (Semi-)Discrete model structure
    • .nP (scalar) Number of pressure states
    • .nQ (scalar) Number of mass-flux states
    • .nPorts (scalar) Number of ports
    • .E (handle) Mass matrix function handle E_rtz = E(rtz)
    • .A (matrix) System matrix
    • .B (matrix) Input matrix (models boundary nodes)
    • .F (matrix) Source matrix (models the compressor action)
    • .C (matrix) Output matrix (sensors at boundary nodes)
    • .f (handle) Nonlinear vector field x = f(xs,x,us,u,rtz)
    • .J (handle) Jacobian x = J(xs,x,u,rtz)
    • .dual (bool) This is only a member (of any value) if it is a dual model!

Available Models

  • ode_mid - ODE model using the mid-point discretization
  • ode_end - ODE model using the end-point discretization (port-Hamiltonian)


  • The argument xs is the steady state computed in the solver (wrapper).
  • The argument x in nonlinearity f and Jacobian J refers to the difference to the steady-state. This means xs + x yields the actual state.
  • Only the components E, f and J are parametrized. Particularly, A and B do not depend on the parameter.
  • Compressors can only be operated in discharge pressure control mode.
  • The argument rtz is the product Rs*T0*z0 formed in the solver.


(click to expand)

A solver is a time stepper that simulates a trajectory of a model and a scenario. The prerequisite steady-state initial value is computed from the scenario's boundary values.


solution = solver(discrete,scenario,config)


  • discrete (struct) Discrete model structure
  • scenario (struct) Scenario structure
  • config (struct) Configuration structure


  • solution (struct)
    • t (vector) Time-steps vector
    • u (matrix) Discrete inputs-times-steps trajectory
    • y (matrix) Discrete outputs-times-steps trajectory
    • steady_z0 (scalar) Global average compressibility
    • steady_error (scalar) Steady-state error
    • steady_iter1 (scalar) Algebraic steady-state iterations
    • steady_iter2 (scalar) Differential steady-state iterations
    • runtime (scalar) Transient solver runtime

Available Solvers

  • imex1 - First-order implicit-explicit solver

  • imex2 - Second-order implicit-explicit Runge-Kutta solver

  • cnab2 - Second-order Crank-Nicolson-Adams-Bashforth solver

  • rk4 - Fourth-order "classic" explicit Runge-Kutta solver (unstable, use only for testing)

  • rk2hyp - Second-order explicit Runge-Kutta solver (increased hyperbolic stability)

  • rk4hyp - Fourth-order explicit Runge-Kutta solver (increased hyperbolic stability)

  • generic - Second-order implicit adaptive ode23s Rosenbrock solver

  • linear_export - Linearize and export state-space model (wraps imex1 solver)

Model Export

The linear_export "solver" is not an actual solver, but exports a linearization with fixed parametrization:

E x'(t) = A x(t) + B u(t) + F,

   y(t) = C x(t),

of the selected network-scenario as a (E,A,B,C,F) state-space model, with the load vector F jointly describing the compressors, steady-state, and steady-state effects:

F := F * c_p + A * xs + B * us.

These sparse system matrices are stored in a .mat file and named network_id--scenario_id--IySxOy.mat, where y is the number of boundary ports (inputs and outputs), and x is the discretized state-space dimension.

  • Internally, linear_export calls the imex1 solver to return a solution.

  • For the linear_export "solver", the model_gravity configuration should be set to none.

  • To obtain a (E,A,B,C) system, the load vector F can be concatenated to the input matrix B, i.e.: B' := [B, F], incrementing the number of inputs.


(click to expand)

A reductor computes a reduced order discrete model, aiming to approximate the input-output (boundary-quantity-of-interest) behavior.


[proj,name] = reductor(solver,discrete,scenario,config)


  • solver (handle) Solver procedure handle
  • discrete (struct) Discrete model structure
  • scenario (struct) Scenario structure
  • config (struct) Configuration structure


  • proj (cell) Array of projectors {LP,RP;LQ,RQ} (Bi-Orthogonal / Oblique) or {LP;LQ} (Orthogonal)
  • name (string) Detailed name of reductor

Available Reductors

These structured reductors approximate pressure and mass-flux components separately ("Structured" is abbreviated as "Struct."):

  • pod_r Struct. Proper Orthogonal Decomposition
  • eds_ro / eds_ro_l Struct. Empirical Dominant Subspaces
  • eds_wx / eds_wx_l Struct. Empirical Cross-Gramian-Based Dominant Subspaces
  • eds_wz / eds_wz_l Struct. Empirical Non-Symmetric-Cross-Gramian-Based Dominant Subspaces
  • mpod_ro / mpod_ro_l Struct. Modified Proper Orthogonal Decomposition
  • mpod_wx / mpod_wx_l Struct. Modified Proper Orthogonal Decomposition
  • mpod_wz / mpod_wz_l Struct. Modified Proper Orthogonal Decomposition
  • bpod_ro / bpod_ro_l Struct. Empirical Balanced Proper Orthogonal Decomposition
  • ebt_ro / ebt_ro_l Struct. Empirical Balanced Truncation
  • ebt_wx / ebt_wx_l Struct. Empirical Cross-Gramian-Based Balanced Truncation
  • ebt_wz / ebt_wz_l Struct. Empirical Non-Symmetric-Cross-Gramian-Based Balanced Truncation
  • gopod_r Struct. Goal-Oriented Proper Orthogonal Decomposition
  • ebg_ro / ebg_ro_l Struct. Empirical Balanced Gains
  • ebg_wx / ebg_wx_l Struct. Empirical Cross-Gramian-Based Balanced Gains
  • ebg_wz /ebg_wz_l Struct. Empirical Non-Symmetric-Cross-Gramian-Based Balanced Gains
  • dmd_r Struct. Dynamic Mode Decomposition Galerkin

All reductors utilizing observability information are available in two variants. By default the nonlinear variant (no suffix) is used. The _l suffix signifies a "linear" variant of the reductor, which assumes a dual system is available. While either method can be applied to both, ode_mid and ode_end, models, theory suggest to use the linear variant only with the port-Hamiltonian ode_end.


(click to expand)

A test defines an experiment, which is implemented as a script whose filename consists of a prefix and the tested network's name. Two types of experiments are currently implemented:

  • A simulation experiment is prefixed with sim_ and executes the morgen.m function for combinations of models and solvers against a fixed network and scenario.

  • A model order reduction experiment is prefixed with mor_ and executes the morgen.m function for combinations of models, solvers and reductors against a network and scenario while using the training.ini scenario for computing the reduced order model.

Note that tests can only be called from the morgen base directory, after running the SETUP script, or manually adding the tests folder to the path:


Available Tests

The available experiments are listed by running the SETUP script, which lists the contents of the tests folder.

Reduced Order Models

Reduced order models are saved in the z_roms folder (or the folder specified by the morgen_roms configuration entry).

A reduced order model is saved by storing the projectors and encoding the associated: network, model, and reductor in the filename as follows:


with pid being custom identifier configurable via optional arguments.

To load a reduced order model provide a filename of a saved reduced order model instead of the reductor identifier.


Plots and MORscores computed by morgen.m are stored in the z_plots folder (or the folder specified by the morgen_plots configuration entry).


The MORscore is a benchmark index measuring the area above the model reduction error graph, which is also plotted. This score jointly assesses the model reduction goals of minimum size and maximum accuracy. Unstable reduced order models are counted as evaluated with relative error of 1.0.


(click to expand)

The morgen platform assumes a configuration INI-file in the base folder named morgen.ini, if not found hard-coded default values are used.

  • morgen_plots (String) Folder to store plots, default: z_plots

  • morgen_roms (String) Folder to store reduced order models, defaut: z_roms

  • network_dt (Positive float) Requested time step width in seconds, default: 60.0

  • network_vmax (Positive float) Maximum velocity of gas in meters per second, default: 20.0

  • network_cfl (Positive float) Target CFL constant of spatial discretization, default: 0.5

  • model_tuning (Positive float) Tunable efficiency factor scaling the friction term, default: 1.0

  • model_reynolds (Positive float) Estimated Reynolds number, default: 1000000.0

  • model_friction (String) Friction factor model, select from hofer, nikuradse, altshul, schifrinson, pmt1025, igt, default: schifrinson

  • model_compressibility (String) Compressibility factor model, select from: ideal, dvgw, aga88, papay, default: aga88

  • model_compref (String) Reference for compressibility: steady, normal, default: steady

  • model_gravity (String) Gravity computation: none, static, dynamic, default: static

  • steady_maxiter_lin (Positive Integer) Number of least-norm iterations to refine steady-state estimation, default: 20

  • steady_maxiter_non (Positive Integer) Number of time-step iterations to refine steady-state estimation, default: 1000

  • steady_maxerror (Positive Float) Maximal error of refined steady-state, default: 1e-6

  • steady_Tc (Float) Critical temperature in Celsius, default: -82.595

  • steady_pc (Float) Critical pressure in Bar, default: 45.988

  • steady_pn (Float) Normal pressure in Bar, default: 1.01325

  • solver_relax (Float in (0,1]) IMEX solver relaxation, default: 1.0

  • solver_rk2type (Positive Integer) Number of 2nd order hyperbolic Runge-Kutta stages 5, 6, 7, 8, 9, 10, 11, 12, default: 11

  • solver_rk4type (String) 4th order hyperbolic Runge-Kutta type MeaR99a, MeaR99b, TseS05, default: MeaR99a

  • T0_min (Float) Minimum ambient temperature in Celsius, default: 0.0

  • T0_max (Float) Maximum ambient temperature in Celsius, default: 20.0

  • Rs_min (Float) Minimum specific gas constant in [J/(kg*K)], default: 500.0

  • Rs_max (Float) Maximum specific gas constant in [J/(kg*K)], default: 600.0

  • mor_excitation (String) Generic training input type, select from: impulse, step, random-binary, white-noise, default: step

  • mor_max (Positive Integer) Maximum reduced order, default: 200

  • mor_parametric (Boolean) Use parametric model order reduction, select from true, false, default: true

  • mor_pgrid (Positive Integer) Sparse parameter grid refinement level, default: 1

  • eval_pnorm (Float) Parameter norm: 1, 2, Inf, default: 2

  • eval_skip (Positive Integer) Evaluate every n-th reduced order model, default: 3

  • eval_max (Positive Integer) Maximum reduced order to evaluate, default: 200 (use Inf for maximum possible)

  • eval_parametric (Boolean) Parametric reduced order model evaluation: true, false, default: true

  • eval_ptest (Positive Integer) Number of test parameters, default: 5

  • eval_gain (Boolean) Use gain correction: true, false, default: true

Internal Configuration Structure

Internally, the configuration is stored in a structure of structures as follows:

  • config (struct)
    • .network (struct) Members: .dt, .vmax, .cfl
    • .model (struct) Members: .tuning, .reynolds, .friction, .gravity
    • .steady (struct) Members: .dt, .maxiter_lin, .maxiter_non, .maxerror, .Tc, .pc, .pn, .compressibility
    • .solver (struct) Members: .dt, .relax, .rk2type, .rk4type
    • .mor (struct) Members: .rom_max, .parametric, .solver, .excitation, .T0_min, .T0_max, .Rs_min, .Rs_max, .pgrid
    • .eval (struct) Members: .parametric, .ptest, .T0_min, .T0_max, .Rs_min, .Rs_max, .skip, .max, .pnorm, .gain

Temperature Units

All input temperatures, i.e., in:

  • morgen.ini configuration
  • XXXXXX.ini scenario

and all output temperatures are in Celsius. Internally, all temperatures are in Kelvin.


(click to expand)
  • xml2net.xsl Converts gaslib .net XML network definitions into MORGEN-compatible .net CSV network definitions via XSLTproc:
xsltproc -o GasLib-X.csv xml2net.xsl GasLib-X.xml
  • csv2net.m Converts SciGRID_Gas .csv CSV network definitions into MORGEN-compatible .net CSV network definitions:
  • json2net.m Converts MathEnergy .json network definitions into MORGEN-compatible .net CSV network definitions:
  • vf2kgs.m Converts volume flow to kg/s (default gas density is 0.7)
  • psi2bar.m Converts psi to bar
b = psi2bar(p)
  • randscen.m Generates a random scenario given a network, implicitly defining training scenario
  • cmp_friction.m Compare friction factors
  • cmp_compressibility.m Compare compressibility factors


Based on numerous numerical experiments we currently recommend the following model-solver-reductor ensemble(s):

  • Model: ode_end (Port-Hamiltonian Endpoint Discretization)
  • Solver: imex1 (First-Order Implicit-Explicit)
  • Reductor: eds_ro_l (Structured Linear Empirical Dominant Subspaces)


  • 1.2 (2022-10-07): doi:10.5281/zenodo.7157808

    • ADDED Modified POD mpod reductor in six variants
    • ADDED configurable number of stages for rk2hyp solver
    • ADDED configurable coefficient sets for rk4hyp solver
    • ADDED Crank-Nicolson/Adams-Bashforth cnab2 solver
    • ADDED total elapsed time
    • ADDED MORscore horizontal bar plot
    • ADDED optional argument cfl
    • ADDED networks and tests
    • FIXED randscen tool
    • IMPROVED formulation of model nonlinearities
    • IMPROVED model reduction backend emgr via 5.99 update
    • IMPROVED memory footprint of rk2hyp solver
    • IMPROVED steady-state extra steps
    • IMPROVED plot labels and legends
    • CHANGED reductor full names
  • 1.1 (2021-08-08): doi:10.5281/zenodo.5168949

    • ADDED optional static gravity term
    • ADDED optional gain correction
    • ADDED explicit RK2 solver rk2hyp with increased stability
    • ADDED explicit RK4 solver rk4hyp with increased stability
    • ADDED linearized model export pseudo-solver
    • ADDED networks and tests
    • CHANGED nonlinear vector field model-interface
    • IMPROVED ROM test logging
    • IMPROVED steady state solver stopping criteria
    • IMPROVED plot presentation
    • FIXED generic path separators
    • FIXED solver caching
    • FIXED rk4 solver
    • FIXED compact plot labels
  • 1.0 (2021-06-22): doi:10.5281/zenodo.5012357

    • ADDED configurable CFL constant
    • ADDED psi2bar converter tool
    • ADDED tunable efficiency factor
    • ADDED networks and tests
    • IMPROVED steady-state interface
    • IMPROVED model-solver interface
    • IMPROVED reductor interface
    • IMPROVED rk4 solver
    • IMPROVED logging
    • IMPROVED vf2kgs tool
  • 0.99 (2021-04-12): doi:10.5281/zenodo.4680265

    • ADDED gopod_r reductor
    • ADDED linear reductor variants
    • ADDED SciGRID_gas CSV converter
    • ADDED DEMO code
    • IMPROVED model structure
  • 0.9 (2020-11-24): doi:10.5281/zenodo.4288510

    • Initial release


  • C. Himpe, S. Grundel: System Order Reduction for Gas and Energy Networks; in: Proceedings in Applied Mathematics and Mechanics, 22: e202200201, 2023. doi:10.1002/pamm.202200201

    • See also the references listed herein.
  • C. Himpe, S. Grundel, P. Benner: Next-Gen Gas Network Simulation; in: Progress in Industrial Mathematics at ECMI 2021: 107--113, 2022. doi:10.1007/978-3-031-11818-0_15

    • See also the references listed herein.
  • C. Himpe, S. Grundel, P. Benner: Model Order Reduction for Gas and Energy Networks; Journal of Mathematics in Industry 11: 13, 2021. doi:10.1186/s13362-021-00109-4

    • See also the references listed herein.
  • P. Benner, S. Grundel, C. Himpe, C. Huck, T. Streubel, C. Tischendorf: Gas Network Benchmark Models; in: Applications of Differential-Algebraic Equations: Examples and Benchmarks: 171--197, 2019. doi:10.1007/11221_2018_5

  • C. Himpe: Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms; in: Model Reduction of Complex Dynamical Systems: 141--164, 2021. doi:10.1007/978-3-030-72983-7_7

  • C. Himpe, S. Grundel, P. Benner: Efficient Gas Network Simulations; in: German Success Stories in Industrial Mathematics: 17--22, 2022. doi:10.1007/978-3-030-81455-7_4

  • T. Clees, A. Baldin, P. Benner, S. Grundel, C. Himpe, B. Klaassen, F. Küsters, N. Marheineke, L. Nikitina, I. Nikitin, J. Pade, N. Stahl, C. Strohm, C. Tischendorf, A. Wirsen: MathEnergy – Mathematical Key Technologies for Evolving Energy Grids; in: Mathematical Modeling, Simulation and Optimization for Power Engineering and Management: 233--262, 2021. doi:10.1007/978-3-030-62732-4_11

For references see also: GasMOR



  • [Model] ADD variable supply-demand input-output boundaries
  • [Model] ADD scenario valve handling
  • [Model] ADD generic compressors as input-output combination
  • [Reductor] ADD hyper-reductor module (DMD, DEIM, Q-DEIM, Numerical linearization)
  • [Octave] FIX slow convergence of ode23s in generic solver
  • [Octave] FIX incompatibilities in format_network (textscan)

Development Guidelines

  • The main branch must complete reproducibility (RUNME_xxx) system tests successfully !
  • All source code headers must include: project, version, authors, license, summary !
  • Understand closures in Matlab !
  • This project uses Readme-Driven Development !



The morgen gas network simulation, testing and benchmarking platform was developed as part of the MathEnergy project.