Synthetic Data Generation for System Identification: Leveraging Knowledge Transfer

Centrala begrepp

The author introduces a novel approach to generating synthetic data for system identification by leveraging knowledge transfer from similar systems. This method aims to enhance model generalization and robustness in scenarios with data scarcity.

Sammanfattning

The paper addresses the challenge of overfitting in learning dynamical systems by introducing a new approach to synthetic data generation. It emphasizes the importance of knowledge transfer from similar systems and demonstrates the effectiveness through a numerical example. The use of synthetic data is shown to improve model performance and generalization capabilities, especially in scenarios with limited training datasets.

Statistik

Synthetic data is generated through a pre-trained meta-model that describes a broad class of systems.
A validation dataset is used to tune a scalar hyper-parameter balancing the relative importance of training and synthetic data.
The Transformer architecture used for synthetic data generation has nlayers = 12, dmodel = 128 units per layer, nheads = 4 attention heads, and an encoder's context window length of m = T = 400.

Citat

"The efficacy of the approach is shown through a numerical example that highlights the advantages of integrating synthetic data into the system identification process."
"Synthetic data goes beyond simply modifying existing data, providing a method to generate large and diverse datasets."
"The pre-trained Transformer serves as an extensive meta-model for the class, enabling it to infer the behavior of specific query systems directly."

Viktiga insikter från

Synthetic data generation for system identification

by Dario Piga,M... på arxiv.org 03-11-2024

https://arxiv.org/pdf/2403.05164.pdf

Djupare frågor

How can this approach be adapted for different classes of dynamical systems?

The approach outlined in the context can be adapted for various classes of dynamical systems by customizing the pre-trained meta-model to suit the specific characteristics and dynamics of each class. This adaptation involves training the Transformer on data generated from systems within a particular class, allowing it to learn the underlying patterns and behaviors common to that group of systems. By adjusting the parameters, structure, and training data used for the meta-model, it can effectively capture the nuances and complexities unique to different classes of dynamical systems. Additionally, incorporating domain-specific knowledge during pre-training can enhance the meta-model's ability to generate synthetic data accurately across diverse system classes.

What are the potential drawbacks or limitations of relying heavily on synthetic data in model estimation?

While leveraging synthetic data offers significant advantages in scenarios with limited real-world data, there are several drawbacks and limitations associated with relying heavily on synthetic data in model estimation:

Quality Concerns: The reliability and accuracy of synthetic data may not always match that of real-world observations, leading to potential biases or inaccuracies in model predictions.
Generalization Issues: Models trained extensively on synthetic data may struggle to generalize well beyond the specific scenarios represented in the synthetic datasets.
Epistemic Uncertainty: Synthetic data generation processes introduce uncertainty that may not fully capture all variations present in actual system behavior.
Overfitting Risks: Depending too much on synthesized samples without proper regularization mechanisms could result in overfitting models that do not generalize effectively.
Domain Complexity: Complex dynamical systems may have intricate interactions and nonlinearities that are challenging to replicate accurately through synthetic means alone.

How can Bayesian estimation algorithms be enhanced by incorporating outputs from meta-models?

Incorporating outputs from meta-models into Bayesian estimation algorithms presents opportunities for enhancing inference processes:

Prior Knowledge Integration: Meta-model outputs serve as informative priors for Bayesian estimators, enabling them to leverage insights gained from similar systems within a class.
Uncertainty Quantification: Meta-model predictions contain inherent uncertainties which can enrich Bayesian frameworks by providing probabilistic distributions over model parameters or predictions.
Regularization Mechanisms: By treating meta-model outputs as prior distributions within a Bayesian framework, regularization techniques naturally emerge, preventing overfitting while balancing between observed training data and synthesized information.
Improved Inference Accuracy: Combining information from both real-world observations and synthetically generated datasets through Bayesian methods enhances inference accuracy by capturing a broader range of system behaviors.

These enhancements empower Bayesian algorithms with richer contextual information derived from meta-models' outputs, leading to more robust estimations under uncertainty while improving generalization capabilities across diverse dynamical system classes