Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Learning Hybrid Dynamics Models With Simulator-Informed Latent States (2309.02873v2)

Published 6 Sep 2023 in cs.LG

Abstract: Dynamics model learning deals with the task of inferring unknown dynamics from measurement data and predicting the future behavior of the system. A typical approach to address this problem is to train recurrent models. However, predictions with these models are often not physically meaningful. Further, they suffer from deteriorated behavior over time due to accumulating errors. Often, simulators building on first principles are available being physically meaningful by design. However, modeling simplifications typically cause inaccuracies in these models. Consequently, hybrid modeling is an emerging trend that aims to combine the best of both worlds. In this paper, we propose a new approach to hybrid modeling, where we inform the latent states of a learned model via a black-box simulator. This allows to control the predictions via the simulator preventing them from accumulating errors. This is especially challenging since, in contrast to previous approaches, access to the simulator's latent states is not available. We tackle the task by leveraging observers, a well-known concept from control theory, inferring unknown latent states from observations and dynamics over time. In our learning-based setting, we jointly learn the dynamics and an observer that infers the latent states via the simulator. Thus, the simulator constantly corrects the latent states, compensating for modeling mismatch caused by learning. To maintain flexibility, we train an RNN-based residuum for the latent states that cannot be informed by the simulator.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (43)
  1. Torsional vibrations with bit off bottom: Modeling, characterization and field data validation. Journal of Petroleum Science and Engineering, 163.
  2. Bernard, P. 2019. Observer Design for Nonlinear Systems. In Lecture Notes in Control and Information Sciences, volume 479. Springer International Publishing.
  3. Luenberger Observers for Nonautonomous Nonlinear Systems. IEEE Transactions on Automatic Control, 64(1): 270–281.
  4. Observer design for continuous-time dynamical systems. Annual Reviews in Control, 53: 224–248.
  5. On the stability properties of Gated Recurrent Units neural networks. Systems And Control Letters, 157: 105049.
  6. Luenberger observers for discrete-time nonlinear systems. In 58th IEEE Conference on Decision and Control, (CDC).
  7. Towards Gain Tuning for Numerical KKL Observers. IFAC-PapersOnLine, 56(2): 4061–4067. 22nd IFAC World Congress.
  8. Recognition Models to Learn Dynamics from Partial Observations with Neural ODEs. Transactions on Machine Learning Research.
  9. Symplectic Recurrent Neural Networks. In International Conference on Learning Representations.
  10. Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing, EMNLP 2014, October 25-29, 2014, Doha, Qatar, A meeting of SIGDAT, a Special Interest Group of the ACL, 1724–1734.
  11. Density estimation using Real NVP. In 5th International Conference on Learning Representations, ICLR.
  12. Combining Slow and Fast: Complementary Filtering for Dynamics Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 37(6): 7476–7484.
  13. Combining Semi-Physical and Neural Network Modeling: An Example of Its Usefulness. In the 11th IFAC Symposium on System Identification (SYSID’97), 795–798.
  14. Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes. In Proceedings of the 2nd Conference on Learning for Dynamics and Control, volume 120 of Proceedings of Machine Learning Research (PMLR), 225–234.
  15. Hamiltonian Neural Networks. In Advances in Neural Information Processing Systems, volume 32.
  16. Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models. Journal of Machine Learning Research, 17(125): 1–47.
  17. Long Short-Term Memory. Neural Computation, 9(8): 1735–1780.
  18. Deep KKL: Data-driven Output Prediction for Non-Linear Systems. In 2021 60th IEEE Conference on Decision and Control (CDC), 4376–4381.
  19. Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles. ACM/IMS Trans. Data Sci., 2(3).
  20. Generative ODE modeling with known unknowns. Proceedings of the Conference on Health, Inference, and Learning.
  21. Semiempirical identification of nonlinear dynamics of a two-degree-of-freedom real torsion pendulum with a nonuniform planar stick–slip friction and elastic barriers. Nonlinear Dynamics, 100: 3215–3234.
  22. Stable Recurrent Models. In International Conference on Learning Representations.
  23. Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems. Preprint arXiv:2210.01476.
  24. Ogata, K. 1997. Modern Control Engineering. Number Bd. 1 in Prentice Hall International Editions.
  25. The Statistical Recurrent Unit. In Proceedings of the 34th International Conference on Machine Learning - Volume 70, 2671–2680.
  26. Deep Learning-based Luenberger observer design for discrete-time nonlinear systems. In 2021 60th IEEE Conference on Decision and Control (CDC), 4370–4375.
  27. Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression. In Advances in Neural Information Processing Systems, volume 34.
  28. Incorporating Unmodeled Dynamics Into First-Principles Models Through Machine Learning. IEEE Access, 9: 22014–22022.
  29. Universal Differential Equations for Scientific Machine Learning. Preprint arXiv:2001.04385.
  30. Numerical design of Luenberger observers for nonlinear systems. In 2020 59th IEEE Conference on Decision and Control (CDC), 5435–5442.
  31. Using Physics Knowledge for Learning Rigid-Body Forward Dynamics with Gaussian Process Force Priors. In Proceedings of the 5th Conference on Robot Learning, volume 164 of Proceedings of Machine Learning Research, 101–111.
  32. Observer design using a partial nonlinear observer canonical form. International Journal of Applied Mathematics and Computer Science, 16(3): 333–343.
  33. Learning To Simulate. In 7th International Conference on Learning Representations, ICLR 2019.
  34. Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems. In Neural Information Processing Systems.
  35. Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems. IFAC-PapersOnLine, 55(12): 19–24. 14th IFAC Workshop on Adaptive and Learning Control Systems ALCOS 2022.
  36. Integrating Neural Networks with First Principles Models for Dynamic Modeling. IFAC Proceedings Volumes, 25(5): 327–332.
  37. Hybrid model for forecasting time series with trend, seasonal and salendar variation patterns. Journal of Physics: Conference Series, 890: 012160.
  38. Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling. In Advances in Neural Information Processing Systems.
  39. Partial observer normal form for nonlinear system. Automatica, 64: 54–62.
  40. Robust Hybrid Learning With Expert Augmentation. Transactions on Machine Learning Research.
  41. Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems. ACM Comput. Surv., 55(4).
  42. Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting. In 9th International Conference on Learning Representations, ICLR 2021.
  43. Auto-Conditioned Recurrent Networks for Extended Complex Human Motion Synthesis. In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now