Learning Neural Differential Algebraic Equations via Operator Splitting
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911068345860096 |
|---|---|
| author | Koch, James Shapiro, Madelyn Sharma, Himanshu Vrabie, Draguna Drgona, Jan |
| author_facet | Koch, James Shapiro, Madelyn Sharma, Himanshu Vrabie, Draguna Drgona, Jan |
| contents | Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such as conservation laws. Here, we present an Operator Splitting (OS) numerical integration scheme for learning unknown components of DAEs from time-series data. In this work, we show that the proposed OS-based time-stepping scheme is suitable for relevant system-theoretic data-driven modeling tasks. Presented examples include (i) the inverse problem of tank-manifold dynamics and (ii) discrepancy modeling of a network of pumps, tanks, and pipes. Our experiments demonstrate the proposed method's robustness to noise and extrapolation ability to (i) learn the behaviors of the system components and their interaction physics and (ii) disambiguate between data trends and mechanistic relationships contained in the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Neural Differential Algebraic Equations via Operator Splitting Koch, James Shapiro, Madelyn Sharma, Himanshu Vrabie, Draguna Drgona, Jan Machine Learning Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such as conservation laws. Here, we present an Operator Splitting (OS) numerical integration scheme for learning unknown components of DAEs from time-series data. In this work, we show that the proposed OS-based time-stepping scheme is suitable for relevant system-theoretic data-driven modeling tasks. Presented examples include (i) the inverse problem of tank-manifold dynamics and (ii) discrepancy modeling of a network of pumps, tanks, and pipes. Our experiments demonstrate the proposed method's robustness to noise and extrapolation ability to (i) learn the behaviors of the system components and their interaction physics and (ii) disambiguate between data trends and mechanistic relationships contained in the system. |
| title | Learning Neural Differential Algebraic Equations via Operator Splitting |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2403.12938 |