Physics-Informed Neural ODE (PINODE): Embedding Physics into Models using Collocation Points

    •  Sholokhov, A., Liu, Y., Mansour, H., Nabi, S., "Physics-Informed Neural ODE (PINODE): Embedding Physics into Models using Collocation Points", Nature Scientific Reports, DOI: 10.1038/​s41598-023-36799-6, Vol. 13, No. 1, pp. 10166, October 2023.
      BibTeX TR2023-136 PDF
      • @article{Sholokhov2023oct,
      • author = {Sholokhov, Aleksei and Liu, Yuying and Mansour, Hassan and Nabi, Saleh},
      • title = {Physics-Informed Neural ODE (PINODE): Embedding Physics into Models using Collocation Points},
      • journal = {Nature Scientific Reports},
      • year = 2023,
      • volume = 13,
      • number = 1,
      • pages = 10166,
      • month = oct,
      • doi = {10.1038/s41598-023-36799-6},
      • url = {}
      • }
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  • Research Areas:

    Dynamical Systems, Optimization


Building reduced-order models (ROMs) is essential for efficient forecasting and control of complex dynamical systems. Recently, auto encoder-based methods for building such models have gained significant traction, but their demand for data limits their use when the data is scarce and expensive. We propose aiding a model’s training with the knowledge of physics using a collocation-based physics-informed loss term. Our innovation builds on ideas from classical collocation methods of numerical analysis to embed knowledge from a known equation into the latent-space dynamics of a ROM. We show that the addition of our physics-informed loss allows for exceptional data supply strategies that improves the performance of ROMs in data-scarce settings, where training high-quality data-driven models is impossible. Namely, for a problem of modeling a high-dimensional nonlinear PDE, our experiments show x5 performance gains, measured by prediction error, in a low-data regime, x10 performance gains in tasks of high-noise learning, x100 gains in the efficiency of utilizing the latent-space dimension, and x200 gains in tasks of far-out out-of-distribution forecasting relative to purely data-driven models. These improvements pave the way for broader adoption of network-based physics-informed ROMs in compressive sensing and control applications.