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Manifold learning techniques seek to discover structure-preserving mappings of high-dimensional data into low-dimensional spaces. While the new sets of coordinates specified by these mappings can closely parameterize the data, they are…
Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional…
Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…
Discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction and it has two main ingredients: an interpolating basis that is computed from a collection of snapshots of the solution and a set of indices…
Discrete Empirical Interpolation Method (DEIM) is a simple and effective method for reconstructing a function from its incomplete pointwise observations. However, applying DEIM to functions with physically constrained ranges can produce…
This paper introduces a new framework for constructing the Discrete Empirical Interpolation Method DEIM projection operator. The interpolation node selection procedure is formulated using the QR factorization with column pivoting, and it…
In this study we propose a-posteriori error estimation results to approximate the precision loss in quantities of interests computed using reduced order models. To generate the surrogate models we employ Proper Orthogonal Decomposition and…
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…
We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…
Discrete empirical interpolation method (DEIM) estimates a function from its incomplete pointwise measurements. Unfortunately, DEIM suffers large interpolation errors when few measurements are available. Here, we introduce Sparse DEIM…
The discrete empirical interpolation method (DEIM) is a well-established approach, widely used for state reconstruction using sparse sensor/measurement data, nonlinear model reduction, and interpretable feature selection. We introduce the…
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…
Deep Learning has emerged as one of the most significant innovations in machine learning. However, a notable limitation of this field lies in the ``black box" decision-making processes, which have led to skepticism within groups like…
Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…
A genetic algorithm procedure is demonstrated that refines the selection of interpolation points of the discrete empirical interpolation method (DEIM) when used for constructing reduced order models for time dependent and/or parametrized…
In the present paper we consider a 2-D shallow-water equations (SWE) model on a $\beta$-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be…
The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…
The MRI-derived brain network serves as a pivotal instrument in elucidating both the structural and functional aspects of the brain, encompassing the ramifications of diseases and developmental processes. However, prevailing methodologies,…
It has been observed that deep neural networks (DNNs) often use both genuine as well as spurious features. In this work, we propose "Amending Inherent Interpretability via Self-Supervised Masking" (AIM), a simple yet interestingly effective…
The ability for a human to understand an Artificial Intelligence (AI) model's decision-making process is critical in enabling stakeholders to visualize model behavior, perform model debugging, promote trust in AI models, and assist in…