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Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

In this work, we introduce a novel data-driven model-reference control design approach for unknown linear systems with fully measurable state. The proposed control action is composed by a static feedback term and a reference tracking block,…

We prove that a denoising diffusion sampler equipped with a sequential bias across the batch dimension is exactly an Euler-Maruyama integrator for overdamped Langevin dynamics. Each reverse denoising step, with its associated spring…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

This paper presents a Finite Element Model Updating framework for identifying heterogeneous material distributions in planar Bernoulli-Euler beams based on a rotation-free isogeometric formulation. The procedure follows two steps: First,…

This research presents a dynamic modeling framework and parameter identification methods for describing the highly nonlinear behaviors of flexibly connected dual-AUV systems. The modeling framework is established based on the lumped mass…

We introduce a Toeplitz-based framework for data-driven spectral estimation of linear evolution operators in dynamical systems. Focusing on transfer and Koopman operators from equilibrium trajectories without access to the underlying…

In the field of Structural Dynamics, modal analysis is the foundation of System Identification and vibration-based inspection. However, despite their widespread use, current state-of-the-art methods for extracting modal parameters from…

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…

We present an efficient and validated method for approximating the stationary measures of random dynamical systems with smooth additive noise. The approach leverages the strong regularizing properties of the associated transfer operator…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

This paper addresses the challenges of the Euler-Bernoulli beam theory regarding shortening and stretching assumptions. Certain boundary conditions, such as a cantilever with a horizontal spring attached to its end, result in beams that…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Laminated glass structures are formed by stiff layers of glass connected with a compliant plastic interlayer. Due to their slenderness and heterogeneity, they exhibit a complex mechanical response that is difficult to capture by…

Accurately modeling power distribution grids is crucial for designing effective monitoring and decision making algorithms. This paper addresses the partial observability issue of data-driven distribution modeling in order to improve the…

Discovering the governing equations of a physical system and designing an effective feedback controller remains one of the most challenging and intensive areas of ongoing research. This task demands a deep understanding of the system…