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Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify Framework

Yubo Ye, Sumeet Vadhavkar, Xiajun Jiang, Ryan Missel, Huafeng Liu, Linwei Wang

TL;DR

This paper combines the use of physics inductive bias specific to the data being modeled, and a learn-to-identify strategy that separates forecasting objectives from the data used for the identification, in a novel framework for unsupervised meta-learning of hybrid latent dynamics.

Abstract

Modern applications increasingly require unsupervised learning of latent dynamics from high-dimensional time-series. This presents a significant challenge of identifiability: many abstract latent representations may reconstruct observations, yet do they guarantee an adequate identification of the governing dynamics? This paper investigates this challenge from two angles: the use of physics inductive bias specific to the data being modeled, and a learn-to-identify strategy that separates forecasting objectives from the data used for the identification. We combine these two strategies in a novel framework for unsupervised meta-learning of hybrid latent dynamics (Meta-HyLaD) with: 1) a latent dynamic function that hybridize known mathematical expressions of prior physics with neural functions describing its unknown errors, and 2) a meta-learning formulation to learn to separately identify both components of the hybrid dynamics. Through extensive experiments on five physics and one biomedical systems, we provide strong evidence for the benefits of Meta-HyLaD to integrate rich prior knowledge while identifying their gap to observed data.

Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify Framework

TL;DR

This paper combines the use of physics inductive bias specific to the data being modeled, and a learn-to-identify strategy that separates forecasting objectives from the data used for the identification, in a novel framework for unsupervised meta-learning of hybrid latent dynamics.

Abstract

Modern applications increasingly require unsupervised learning of latent dynamics from high-dimensional time-series. This presents a significant challenge of identifiability: many abstract latent representations may reconstruct observations, yet do they guarantee an adequate identification of the governing dynamics? This paper investigates this challenge from two angles: the use of physics inductive bias specific to the data being modeled, and a learn-to-identify strategy that separates forecasting objectives from the data used for the identification. We combine these two strategies in a novel framework for unsupervised meta-learning of hybrid latent dynamics (Meta-HyLaD) with: 1) a latent dynamic function that hybridize known mathematical expressions of prior physics with neural functions describing its unknown errors, and 2) a meta-learning formulation to learn to separately identify both components of the hybrid dynamics. Through extensive experiments on five physics and one biomedical systems, we provide strong evidence for the benefits of Meta-HyLaD to integrate rich prior knowledge while identifying their gap to observed data.
Paper Structure (46 sections, 15 equations, 14 figures, 22 tables)

This paper contains 46 sections, 15 equations, 14 figures, 22 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Methods
  4. Hybrid Latent Dynamic Functions as a UDE
  5. Learn-to-Identify via Meta-Learning
  6. Identifying latent dynamics:
  7. Experiments and Results
  8. Data & Experimental Settings
  9. Identifiability of Physics. vs. Neural Dynamics
  10. Benefits of Hybrid Dynamic Functions
  11. Comparison with Existing Baselines
  12. Feasibility on Biomedical Systems: Dynamic PET
  13. Conclusions & Discussion
  14. Data Details and Experimental Settings of Physics Systems
  15. Data Details
  16. ...and 31 more sections

Figures (14)

  • Figure 1: Overview of Meta-HyLaD vs. existing frameworks for unsupervised learning of physics-based or neural latent dynamic functions.
  • Figure 2: HyLaD with alternative identification strategies
  • Figure 3: Comparison of alternative strategies for modeling the latent dynamic functions (purely physics, purely neural, Global-HyLaD, and Meta-HyLaD). MSE metrics are the lower the better, and VPT metrics are the higher the better.
  • Figure 4: Comparison of Meta-HyLAD and baselines with neural and physics-based (blue-shaded background) decoders.
  • Figure 5: A: Quantitative metrics and examples in dynamic PET. B: Ablation with context-size $k$.
  • ...and 9 more figures