Model order reduction of deep structured state-space models: A system-theoretic approach

With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. The recently introduced deep structured state-space models (SSM), which feature linear dynamical blocks as key constituent components, offer high predictive performance. However, the learned representations often suffer from excessively large model orders, which render them unsuitable for control design purposes. The current paper addresses this challenge by means of system-theoretic model order reduction techniques that target the linear dynamical blocks of SSMs. We introduce two regularization terms which can be incorporated into the training loss for improved model order reduction. In particular, we consider modal $\ell_1$ and Hankel nuclear norm regularization to promote sparsity, allowing one to retain only the relevant states without sacrificing accuracy. The presented regularizers lead to advantages in terms of parsimonious representations and faster inference resulting from the reduced order models. The effectiveness of the proposed methodology is demonstrated using real-world ground vibration data from an aircraft.

Synthetic data generation for system identification: leveraging knowledge transfer from similar systems

This paper addresses the challenge of overfitting in the learning of dynamical systems by introducing a novel approach for the generation of synthetic data, aimed at enhancing model generalization and robustness in scenarios characterized by data scarcity. Central to the proposed methodology is the concept of knowledge transfer from systems within the same class. Specifically, synthetic data is generated through a pre-trained meta-model that describes a broad class of systems to which the system of interest is assumed to belong. Training data serves a dual purpose: firstly, as input to the pre-trained meta model to discern the system's dynamics, enabling the prediction of its behavior and thereby generating synthetic output sequences for new input sequences; secondly, in conjunction with synthetic data, to define the loss function used for model estimation. A validation dataset is used to tune a scalar hyper-parameter balancing the relative importance of training and synthetic data in the definition of the loss function. The same validation set can be also used for other purposes, such as early stopping during the training, fundamental to avoid overfitting in case of small-size training datasets. The efficacy of the approach is shown through a numerical example that highlights the advantages of integrating synthetic data into the system identification process.

BenchCloudVision: A Benchmark Analysis of Deep Learning Approaches for Cloud Detection and Segmentation in Remote Sensing Imagery

Satellites equipped with optical sensors capture high-resolution imagery, providing valuable insights into various environmental phenomena. In recent years, there has been a surge of research focused on addressing some challenges in remote sensing, ranging from water detection in diverse landscapes to the segmentation of mountainous and terrains. Ongoing investigations goals to enhance the precision and efficiency of satellite imagery analysis. Especially, there is a growing emphasis on developing methodologies for accurate water body detection, snow and clouds, important for environmental monitoring, resource management, and disaster response. Within this context, this paper focus on the cloud segmentation from remote sensing imagery. Accurate remote sensing data analysis can be challenging due to the presence of clouds in optical sensor-based applications. The quality of resulting products such as applications and research is directly impacted by cloud detection, which plays a key role in the remote sensing data processing pipeline. This paper examines seven cutting-edge semantic segmentation and detection algorithms applied to clouds identification, conducting a benchmark analysis to evaluate their architectural approaches and identify the most performing ones. To increase the model's adaptability, critical elements including the type of imagery and the amount of spectral bands used during training are analyzed. Additionally, this research tries to produce machine learning algorithms that can perform cloud segmentation using only a few spectral bands, including RGB and RGBN-IR combinations. The model's flexibility for a variety of applications and user scenarios is assessed by using imagery from Sentinel-2 and Landsat-8 as datasets. This benchmark can be reproduced using the material from this github link: https://github.com/toelt-llc/cloud_segmentation_comparative.

On the adaptation of in-context learners for system identification

In-context system identification aims at constructing meta-models to describe classes of systems, differently from traditional approaches that model single systems. This paradigm facilitates the leveraging of knowledge acquired from observing the behaviour of different, yet related dynamics. This paper discusses the role of meta-model adaptation. Through numerical examples, we demonstrate how meta-model adaptation can enhance predictive performance in three realistic scenarios: tailoring the meta-model to describe a specific system rather than a class; extending the meta-model to capture the behaviour of systems beyond the initial training class; and recalibrating the model for new prediction tasks. Results highlight the effectiveness of meta-model adaptation to achieve a more robust and versatile meta-learning framework for system identification.

Gradient-based bilevel optimization for multi-penalty Ridge regression through matrix differential calculus

Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm's flexibility and potential for better generalization. In this paper, we address the problem of linear regression with l2-regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that our multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.

Shedding Light on the Ageing of Extra Virgin Olive Oil: Probing the Impact of Temperature with Fluorescence Spectroscopy and Machine Learning Techniques

This work systematically investigates the oxidation of extra virgin olive oil (EVOO) under accelerated storage conditions with UV absorption and total fluorescence spectroscopy. With the large amount of data collected, it proposes a method to monitor the oil's quality based on machine learning applied to highly-aggregated data. EVOO is a high-quality vegetable oil that has earned worldwide reputation for its numerous health benefits and excellent taste. Despite its outstanding quality, EVOO degrades over time owing to oxidation, which can affect both its health qualities and flavour. Therefore, it is highly relevant to quantify the effects of oxidation on EVOO and develop methods to assess it that can be easily implemented under field conditions, rather than in specialized laboratories. The following study demonstrates that fluorescence spectroscopy has the capability to monitor the effect of oxidation and assess the quality of EVOO, even when the data are highly aggregated. It shows that complex laboratory equipment is not necessary to exploit fluorescence spectroscopy using the proposed method and that cost-effective solutions, which can be used in-field by non-scientists, could provide an easily-accessible assessment of the quality of EVOO.

Split-Boost Neural Networks

The calibration and training of a neural network is a complex and time-consuming procedure that requires significant computational resources to achieve satisfactory results. Key obstacles are a large number of hyperparameters to select and the onset of overfitting in the face of a small amount of data. In this framework, we propose an innovative training strategy for feed-forward architectures - called split-boost - that improves performance and automatically includes a regularizing behaviour without modeling it explicitly. Such a novel approach ultimately allows us to avoid explicitly modeling the regularization term, decreasing the total number of hyperparameters and speeding up the tuning phase. The proposed strategy is tested on a real-world (anonymized) dataset within a benchmark medical insurance design problem.

In-context learning for model-free system identification

In traditional system identification, we estimate a model of an unknown dynamical system based on given input/output sequences and available physical knowledge. Yet, is it also possible to understand the intricacies of dynamical systems not solely from their input/output patterns, but by observing the behavior of other systems within the same class? This central question drives the study presented in this paper. In response to this query, we introduce a novel paradigm for system identification, addressing two primary tasks: one-step-ahead prediction and multi-step simulation. Unlike conventional methods, we do not directly estimate a model for the specific system. Instead, we pretrain a meta model that represents a class of dynamical systems. This meta model is trained from a potentially infinite stream of synthetic data, generated by systems randomly extracted from a certain distribution. At its core, the meta model serves as an implicit representation of the main characteristics of a class of dynamical systems. When provided with a brief context from a new system - specifically, a short input/output sequence - the meta model implicitly discerns its dynamics, enabling predictions of its behavior. The proposed approach harnesses the power of Transformer architectures, renowned for their in-context learning capabilities in Natural Language Processing tasks. For one-step prediction, a GPT-like decoder-only architecture is utilized, whereas the simulation problem employs an encoder-decoder structure. Initial experimental results affirmatively answer our foundational question, opening doors to fresh research avenues in system identification.

Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the predictive uncertainty of deep-learning models describing non-linear dynamical systems are very limited to date. This paper is aimed at filling this gap and presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs through approximate inference techniques. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime, where predictions cannot be trusted.