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arxiv: 2606.22544 · v1 · pith:LURQCMKWnew · submitted 2026-06-21 · 📡 eess.SY · cs.SY

Towards an FMI Layered Standard for DAE: Applications for Simulation and Optimization

Elmir Nahodovic , Andreas Heuermann , Joel A. E. Andersson , Adwait Verulkar , Srikanth Sivaramakrishnan , Masoud Najafi , Linus Langenkamp , Christian Bertsch
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Erik Henningsson Hans Olsson Bernhard Bachmann
This is my paper

Pith reviewed 2026-06-26 09:38 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords FMIDAEFMUModel ExchangeOptimal ControlSimulationOptimizationIndex-1 DAE
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The pith

A proposed FMI layered standard for DAEs enables optimization convergence on an industrial model where the ODE version fails.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that FMI 3.0 forces FMUs to solve internal algebraic equations before returning derivatives, which can lower accuracy and cause robustness problems in simulation and optimization. It proposes a layered extension called fmi-ls-dae that instead exposes algebraic equations and variables as a semi-explicit index-1 DAE. Prototype generators in Dymola and CasADi and importers in CasADi, FMIOPT, Simcenter Twin Activate, and MOO demonstrate the approach. On a multilink suspension corner model, the DAE-FMU version lets an optimal control solver converge while the matching ODE-FMU version does not.

Core claim

Exposing algebraic equations and their variables directly in an FMI FMU as a semi-explicit index-1 DAE removes the need for hidden internal Newton iterations, improves numerical behavior, and allows downstream optimization routines to succeed on problems that fail under the equivalent ODE formulation.

What carries the argument

The fmi-ls-dae layered standard, an extension to the FMI XML schema that declares algebraic variables and equations alongside differential states in semi-explicit index-1 form.

If this is right

  • Dynamic optimization tools gain direct access to algebraic structure instead of relying on internal solver states.
  • Models generated from Modelica can avoid accuracy loss from hidden Newton iterations during export.
  • Simulation and optimization workflows become more robust for systems that contain significant algebraic constraints.
  • The same FMU can be used for both simulation and optimization without reformulation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Higher-index DAE support, consistent initialization, and event handling would extend the same benefit to a wider class of models.
  • Existing FMI importers would need targeted updates to read the new XML sections and treat algebraic residuals explicitly.
  • The approach could reduce the need for manual index reduction or reformulation steps before model export.

Load-bearing premise

Importers can accept the newly exposed algebraic variables and equations without creating fresh numerical problems or needing large changes to current FMI tools.

What would settle it

Run the same optimal control problem on the multilink suspension corner model once with the DAE-FMU and once with the ODE-FMU; convergence occurs only with the DAE version.

Figures

Figures reproduced from arXiv: 2606.22544 by Adwait Verulkar, Andreas Heuermann, Bernhard Bachmann, Christian Bertsch, Elmir Nahodovic, Erik Henningsson, Hans Olsson, Joel A. E. Andersson, Linus Langenkamp, Masoud Najafi, Srikanth Sivaramakrishnan.

Figure 1
Figure 1. Figure 1: Simplified State Machine for Model Exchange with FMI 3.0. The dashed and dotted lines indicate Super States of the FMU. The dashed line around Instantiated and Ini￾tialization Mode is FMU State Settable while the dotted line around Continuous-Time Mode and Event Mode is Initialized. The modes Configuration- and Reconfiguration mode allow the importer to set structuralParameters and tunable structuralParame… view at source ↗
Figure 3
Figure 3. Figure 3: presents a comparison of the simulation results from both the built-in block and the FMU, demonstrating a perfect match between the two implementations. 2GitHub repository: AMIT-HSBI/MOO branch fmi-ls-dae y1 −20 −10 0 Time [s] 0 5 10 15 20 25 30 y2 0.0 0.5 1.0 Simcenter Reference [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The fourbar1 FMU imported in Simcenter Twin Acti￾vate [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 2
Figure 2. Figure 2: , the internal DAE equations from the FMU were independently implemented in a built-in block to enable direct comparison and validation of the results [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Simcenter Twin Activate simulation results for Fourbar1.fmu compared to the Modelica reference solution: revolute joint angle ϕ1, angular velocity ϕ˙1, prismatic joint dis￾placement s2, and prismatic joint velocity ˙s2. pecially if the algebraics are not exposed to the optimizer, leading to a Newton-over-Newton solve that can produce noisy derivatives and poor Karush–Kuhn–Tucker (KKT) behavior. After symbo… view at source ↗
Figure 8
Figure 8. Figure 8: IPOPT convergence history (objective, primal and dual infeasibility, barrier parameter) for the multilink suspen￾sion corner OCP, comparing the fmi-ls-dae DAE-FMU with the standard ODE-FMU. The ODE-FMU run terminates in IPOPT’s restoration phase with a Restoration Failed! status, whereas the DAE-FMU run converges to the optimum. 4.3 MOO - Dynamic Optimization The DAE-FMU version of the multilink suspension… view at source ↗
Figure 9
Figure 9. Figure 9: Solution of the multilink suspension corner problem solved using MOO. The joint angle φ closely follows the refer￾ence φref and the actuator force fz agrees with the DAE-FMU solution of FMIOPT. and Biegler 2006) with first and second-order derivatives provided by CasADi. The same example also demon￾strates how an equivalent FMU can be exported from CasADi. 5 Outlook The handling of initialization and event… view at source ↗
read the original abstract

The Functional Mock-up Interface (FMI) 3.0 standard for Model Exchange is restricted to hybrid ordinary differential equations, requiring any internal algebraic equations to be solved inside the Functional Mock-up Unit (FMU) before derivatives are returned to the importer. For models originating from, e.g. Modelica, this means that nonlinear algebraic equations must be solved through internal Newton iterations, which can reduce accuracy, increase computational cost, introduce hidden solver states, and cause robustness issues in downstream simulation and optimization workflows. In this article, we present a proposal for a layered standard, fmi-ls-dae, that exposes algebraic equations and their associated algebraic variables as part of a semi-explicit index-1 differential-algebraic equation. We describe the proposed extensions to the FMI XML schema and demonstrate the approach through prototype implementations: Dymola and CasADi generate FMUs that expose this semi-explicit index-1 formulation, while CasADi, FMIOPT, Simcenter Twin Activate, and MOO (the dynamic optimization tool of OpenModelica) import them for simulation and dynamic optimization. On an industrially relevant multilink suspension corner model, the proposed DAE-FMU formulation enables the optimization routine to converge on an optimal control problem on which the equivalent ODE-FMU fails to converge. We outline ongoing work towards supporting higher-index DAEs, consistent initialization, and event handling,

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a layered standard fmi-ls-dae extending FMI 3.0 Model Exchange to expose semi-explicit index-1 DAEs (algebraic equations and variables) rather than requiring internal solution inside the FMU. It describes XML schema extensions and presents prototype generators (Dymola, CasADi) and importers (CasADi, FMIOPT, Simcenter Twin Activate, MOO) for simulation and dynamic optimization. The central empirical claim is that, on an industrially relevant multilink suspension corner model, the DAE-FMU formulation enables convergence of an optimal control problem on which the equivalent ODE-FMU fails to converge. Ongoing work on higher-index DAEs, initialization, and events is outlined.

Significance. If the approach can be shown to work with standard FMI importers, exposing algebraic structure could improve numerical robustness and accuracy for Modelica-derived models in simulation and optimization pipelines. The concrete industrial example and multiple prototype implementations constitute a useful existence proof and are strengths of the work.

major comments (2)
  1. [Abstract] Abstract: the claim that the DAE-FMU formulation enables convergence on the multilink suspension OCP where the ODE-FMU fails is demonstrated exclusively inside custom-extended importers (CasADi/FMIOPT/MOO) that were modified to consume the new algebraic variables and residuals; no evidence is supplied that a stock FMI 3.0 importer (or even a minimally modified one) can ingest the exposed algebraic equations without introducing its own Newton iterations, step-size restrictions, or accuracy loss.
  2. [Abstract] Abstract: the manuscript provides neither error analysis, tabulated convergence metrics, nor verification that the observed improvement is due to DAE exposure rather than other differences between the prototype importers.
minor comments (1)
  1. The distinction between the proposed layered standard and the specific prototype modifications should be stated more explicitly when discussing applicability to existing FMI infrastructure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the industrial relevance of the multilink suspension example along with the multiple prototype implementations. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the DAE-FMU formulation enables convergence on the multilink suspension OCP where the ODE-FMU fails is demonstrated exclusively inside custom-extended importers (CasADi/FMIOPT/MOO) that were modified to consume the new algebraic variables and residuals; no evidence is supplied that a stock FMI 3.0 importer (or even a minimally modified one) can ingest the exposed algebraic equations without introducing its own Newton iterations, step-size restrictions, or accuracy loss.

    Authors: We agree that the reported convergence result is obtained with prototype importers that were extended to directly consume the exposed algebraic variables and residuals. The manuscript does not provide evidence that unmodified stock FMI 3.0 importers would automatically benefit without their own internal algebraic handling. The core contribution is the definition of the layered standard that makes such direct access possible; the prototypes serve as an existence proof of the benefit when importers exploit the exposed structure. We will revise the abstract to state explicitly that the convergence improvement is observed in the extended prototype importers. revision: partial

  2. Referee: [Abstract] Abstract: the manuscript provides neither error analysis, tabulated convergence metrics, nor verification that the observed improvement is due to DAE exposure rather than other differences between the prototype importers.

    Authors: The empirical claim is presented as a binary outcome (convergence versus failure) on an otherwise comparable optimal-control formulation. We acknowledge that tabulated metrics (e.g., iteration counts, residual histories) and a more explicit isolation of the DAE-exposure effect would strengthen the evidence. We will add a table of key optimization metrics and a short discussion of the controlled differences between the ODE-FMU and DAE-FMU setups in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

Proposal paper with prototype demonstration; no derivation chain reduces to inputs by construction

full rationale

The manuscript is a standards proposal for exposing semi-explicit index-1 DAEs via FMI layered extensions, accompanied by prototype generators and importers. No mathematical derivation, uniqueness theorem, fitted parameter, or prediction is presented whose result is equivalent to its inputs by definition or self-citation. The empirical convergence result on the multilink suspension model is produced inside the described prototypes; this is an implementation demonstration rather than a self-referential reduction of any claimed first-principles result. No instances of the six enumerated circularity patterns appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The proposal rests on standard DAE theory and FMI XML extensions, with the new layered standard as the primary addition.

axioms (1)
  • domain assumption Physical models from tools like Modelica can be represented as semi-explicit index-1 DAEs without loss of fidelity.
    Invoked as the basis for the FMI extension in the abstract.
invented entities (1)
  • fmi-ls-dae layered standard no independent evidence
    purpose: To expose algebraic equations and variables in FMI for external solving
    New entity proposed by the paper with no independent evidence outside this work.

pith-pipeline@v0.9.1-grok · 5828 in / 1149 out tokens · 24521 ms · 2026-06-26T09:38:35.924770+00:00 · methodology

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Reference graph

Works this paper leans on

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