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Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…

Nonlinear model predictive control (NMPC) has gained widespread use in many applications. Its formulation traditionally involves repetitively solving a nonlinear constrained optimization problem online. In this paper, we investigate NMPC…

While sparse attention mitigates the computational bottleneck of long-context LLM training, its distributed training process exhibits extreme heterogeneity in both \textit{1)} sequence length and \textit{2)} sparsity sensitivity, leading to…

Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past…

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…

In this letter, a binary sparse Bayesian learning (BSBL) algorithm is proposed to slove the one-bit compressed sensing (CS) problem in both single measurement vector (SMV) and multiple measurement vectors (MMVs). By utilising the…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is…

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…

In this work, we introduce a generalized framework for multiscale state-space modeling that incorporates nested nonlinear dynamics, with a specific focus on Bayesian learning under switching regimes. Our framework captures the complex…

This work presents a novel framework for physically consistent model error characterization and operator learning for reduced-order models of non-equilibrium chemical kinetics. By leveraging the Bayesian framework, we identify and infer…

Despite rapid progress in live-imaging techniques, many complex biophysical and biochemical systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an…

A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…

An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…

The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the…

We develop a data-driven method, based on semi-supervised classification, to predict the asymptotic state of multistable systems when only sparse spatial measurements of the system are feasible. Our method predicts the asymptotic behavior…