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System identification refers to estimation of process parameters and is a necessity in control theory. Physical systems usually have varying parameters. For such processes, accurate identification is particularly important. Online…
The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
The models of partially observed linear stochastic differential equations with unknown initial values of the non-observed component are considered in two situations. In the first problem, the initial value is deterministic, and in the…
This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…
Dynamical systems modeling is a core pillar of scientific inquiry across natural and life sciences. Increasingly, dynamical system models are learned from data, rendering identifiability a paramount concept. For systems that are not…
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…
Water treatment and liquid storage are the two plants implementing the hydraulic three-tank system. Maintaining certain levels is the critical scenario so that the systems run as desired. To deal with, the optimal linear control and the…
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…
This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…
Monitoring carbon dioxide (CO2) injected and stored in subsurface reservoirs is critical for avoiding failure scenarios and enables real-time optimization of CO2 injection rates. Sequential Bayesian data assimilation (DA) is a statistical…
Disentangled representation learning aims to uncover latent variables underlying the observed data, and generally speaking, rather strong assumptions are needed to ensure identifiability. Some approaches rely on sufficient changes on the…
System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of…
We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…
A crucial task in system identification problems is the selection of the most appropriate model class, and is classically addressed resorting to cross-validation or using asymptotic arguments. As recently suggested in the literature, this…
In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary…
Simulation-based inference (SBI) enables Bayesian analysis when the likelihood is intractable but model simulations are available. Recent advances in statistics and machine learning, including Approximate Bayesian Computation and deep…
High fidelity behavior prediction of human drivers is crucial for efficient and safe deployment of autonomous vehicles, which is challenging due to the stochasticity, heterogeneity, and time-varying nature of human behaviors. On one hand,…
Many signal processing applications such as acoustic echo cancellation and wireless channel estimation require identifying systems where only a small fraction of coefficients are actually active, i.e. sparse systems. Zero-attracting…
This paper investigates the adaptive identification and prediction problems for stochastic dynamical systems with saturated observations, which arise from various fields in engineering and social systems, but up to now still lack…