Linus Langenkamp | Searcharxiv

arXiv2026

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

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,

eess.SY↗

arXiv2025

Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming

We propose a novel approach for training Physics-enhanced Neural ODEs (PeN-ODEs) by expressing the training process as a dynamic optimization problem. The full model, including neural components, is discretized using a high-order implicit Runge-Kutta method with flipped Legendre-Gauss-Radau points, resulting in a large-scale nonlinear program (NLP) efficiently solved by state-of-the-art NLP solvers such as Ipopt. This formulation enables simultaneous optimization of network parameters and state trajectories, addressing key limitations of ODE solver-based training in terms of stability, runtime, and accuracy. Extending on a recent direct collocation-based method for Neural ODEs, we generalize to PeN-ODEs, incorporate physical constraints, and present a custom, parallelized, open-source implementation. Benchmarks on a Quarter Vehicle Model and a Van-der-Pol oscillator demonstrate superior accuracy, speed, generalization with smaller networks compared to other training techniques. We also outline a planned integration into OpenModelica to enable accessible training of Neural DAEs.

cs.LG↗