Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912522621157376 |
|---|---|
| author | Langenkamp, Linus Hannebohm, Philip Bachmann, Bernhard |
| author_facet | Langenkamp, Linus Hannebohm, Philip Bachmann, Bernhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03552 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming Langenkamp, Linus Hannebohm, Philip Bachmann, Bernhard Machine Learning Dynamical Systems Optimization and Control 90C30, 68T05 G.1.6; I.2.6 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. |
| title | Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming |
| topic | Machine Learning Dynamical Systems Optimization and Control 90C30, 68T05 G.1.6; I.2.6 |
| url | https://arxiv.org/abs/2505.03552 |