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Meta-Learning for Physically-Constrained Neural System Identification

Ankush Chakrabarty, Gordon Wichern, Vedang M. Deshpande, Abraham P. Vinod, Karl Berntorp, Christopher R. Laughman

TL;DR

The paper develops a gradient-based meta-learning framework (MAML/ANIL) to rapidly adapt neural state-space models (NSSMs) for data-efficient, physics-informed system identification. By leveraging diverse source-system data, the approach enables fast adaptation to a new target with limited measurements, and it integrates these NSSMs into an EKF for improved state estimation. It introduces two physics constraints—polytopic state constraints and curl-free vector-field constraints—to guarantee physical plausibility in predictions and filters. Across Bouc-Wen hysteresis, chaotic oscillators, vapor-compression, and indoor magnetics case studies, the method demonstrates superior predictive and estimation performance compared to purely supervised or transfer-learning baselines, highlighting its potential for real-time estimation and control in engineering systems.

Abstract

We present a gradient-based meta-learning framework for rapid adaptation of neural state-space models (NSSMs) for black-box system identification. When applicable, we also incorporate domain-specific physical constraints to improve the accuracy of the NSSM. The major benefit of our approach is that instead of relying solely on data from a single target system, our framework utilizes data from a diverse set of source systems, enabling learning from limited target data, as well as with few online training iterations. Through benchmark examples, we demonstrate the potential of our approach, study the effect of fine-tuning subnetworks rather than full fine-tuning, and report real-world case studies to illustrate the practical application and generalizability of the approach to practical problems with physical-constraints. Specifically, we show that the meta-learned models result in improved downstream performance in model-based state estimation in indoor localization and energy systems.

Meta-Learning for Physically-Constrained Neural System Identification

TL;DR

The paper develops a gradient-based meta-learning framework (MAML/ANIL) to rapidly adapt neural state-space models (NSSMs) for data-efficient, physics-informed system identification. By leveraging diverse source-system data, the approach enables fast adaptation to a new target with limited measurements, and it integrates these NSSMs into an EKF for improved state estimation. It introduces two physics constraints—polytopic state constraints and curl-free vector-field constraints—to guarantee physical plausibility in predictions and filters. Across Bouc-Wen hysteresis, chaotic oscillators, vapor-compression, and indoor magnetics case studies, the method demonstrates superior predictive and estimation performance compared to purely supervised or transfer-learning baselines, highlighting its potential for real-time estimation and control in engineering systems.

Abstract

We present a gradient-based meta-learning framework for rapid adaptation of neural state-space models (NSSMs) for black-box system identification. When applicable, we also incorporate domain-specific physical constraints to improve the accuracy of the NSSM. The major benefit of our approach is that instead of relying solely on data from a single target system, our framework utilizes data from a diverse set of source systems, enabling learning from limited target data, as well as with few online training iterations. Through benchmark examples, we demonstrate the potential of our approach, study the effect of fine-tuning subnetworks rather than full fine-tuning, and report real-world case studies to illustrate the practical application and generalizability of the approach to practical problems with physical-constraints. Specifically, we show that the meta-learned models result in improved downstream performance in model-based state estimation in indoor localization and energy systems.
Paper Structure (28 sections, 3 theorems, 38 equations, 12 figures, 3 tables, 2 algorithms)

This paper contains 28 sections, 3 theorems, 38 equations, 12 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Neural System Identification
  3. Motivation
  4. Neural State-Space Modeling
  5. Extended Kalman filtering
  6. Problem Statement
  7. Model-Agnostic Meta-Learning (MAML) for Identification
  8. Physically-Constrained NSSMs
  9. Polytopic constraints
  10. Vector-field constraints
  11. Benchmarking and Ablations
  12. Example 1. The Bouc-Wen Hysteretic System Benchmark
  13. Example 2: Investigating Subnetwork Fine-Tuning with ANIL on Chaotic Oscillators
  14. Data collection and implementation details
  15. Meta-learning vs. supervised and transfer-learning
  16. ...and 13 more sections

Key Result

Theorem 1

Let $h$ be a vector field of class $\mathcal{C}^1$ whose domain is a simply connected region $\mathcal{R}\subset \mathbb{R}^3$. Then $h = \vv\nabla \varphi$ for some scalar-valued function $\varphi$ of class $\mathcal{C}^2$ on $\mathcal{R}$ if and only if $\vv\nabla\; \times\; h = 0$ at all points o

Figures (12)

  • Figure 1: Neural state-space models: general abstraction, and specific models for different target dataset composition.
  • Figure 2: Performance of meta-learning for Example 1.
  • Figure 3: Comparison of MAML-SSM with baselines. (upper, middle) State $x_1$ and $x_2$ of the oscillator. (lower) Comparison of sum-squared-error (SSE).
  • Figure 4: RMSE (averaged over 20 runs) heatmap produced by tuning subnetworks with ANIL.
  • Figure 5: Range of HVAC dynamics induced by variable refrigerant mass.
  • ...and 7 more figures

Theorems & Definitions (7)

  • Remark 1
  • Theorem 1
  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Remark 2