Related papers: Using Spectral Submanifolds for Optimal Mode Selec…

A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of…

Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…

We illustrate how the recent theory of Spectral Submanifolds (SSM) can capture global bifurcations and complex dynamics in mechanical systems even under delay and spatial discretization. Specifically, we build a parameter-dependent…

Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…

This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…

Inspired by the feedforward multilayer perceptron (FF-MLP), decision tree (DT) and extreme learning machine (ELM), a new classification model, called the subspace learning machine (SLM), is proposed in this work. SLM first identifies a…

In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases,…

The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in chemical kinetic models. The construction of SIMs and many…

A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint,…

This paper introduces a new approach for fine-tuning the predictions of structured state space models (SSMs) at inference time using real-time recurrent learning. While SSMs are known for their efficiency and long-range modeling…

Mechanical metamaterials utilize geometry to achieve exceptional mechanical properties, including those not typically possible for traditional materials. To achieve these properties, it is necessary to identify the proper structures and…

Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable…

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…

Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…

A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…

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…

High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient…