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Diffusion models have achieved significant progress in image generation. The pre-trained Stable Diffusion (SD) models are helpful for image deblurring by providing clear image priors. However, directly using a blurry image or pre-deblurred…
Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…
We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory and emerging model discovery tools to find low-dimensional subspaces…
Datasets with significant proportions of noisy (incorrect) class labels present challenges for training accurate Deep Neural Networks (DNNs). We propose a new perspective for understanding DNN generalization for such datasets, by…
Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…
The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…
The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
The modeling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering. It is broadly believed that even with today's computer advances resolving all spatiotemporal scales…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…
We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
We draw on the latest advancements in the physics community to propose a novel method for discovering the governing non-linear dynamics of physical systems in reinforcement learning (RL). We establish that this method is capable of…
Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…
In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large.…