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There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…
As the deep learning revolution marches on, self-supervised learning has garnered increasing attention in recent years thanks to its remarkable representation learning ability and the low dependence on labeled data. Among these varied…
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…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
The presence of measurement error is a widespread issue which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the…
In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…
Directed energy deposition (DED), a metal additive manufacturing process, is highly susceptible to process-induced defects such as geometric deviations, lack of fusion, and poor surface finish. This work presents a build-height-synchronized…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…
We introduce a novel type of approximation spaces for functions with values in a nonlinear manifold. The discrete functions are constructed by piecewise polynomial interpolation in a Euclidean embedding space, and then projecting pointwise…
Proper orthogonal decomposition methods for model reduction utilize information about the solution at certain time and parameter points to generate a reduced space basis. In this paper, we compare two proper orthogonal decomposition methods…
We investigate the properties of the simultaneous projection method as applied to countably infinitely many closed and linear subspaces of a real Hilbert space. We establish the optimal error bound for linear convergence of this method,…
This paper presents Deep Networks for Improved Segmentation Edges (DeNISE), a novel data enhancement technique using edge detection and segmentation models to improve the boundary quality of segmentation masks. DeNISE utilizes the inherent…
Debiased inference for high-dimensional regression models has received substantial recent attention to ensure regularized estimators have valid inference. All existing methods focus on achieving Neyman orthogonality through explicitly…
We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs). In the presence of…
Accurate 6D object pose estimation is vital for robotics, augmented reality, and scene understanding. For seen objects, high accuracy is often attainable via per-object fine-tuning but generalizing to unseen objects remains a challenge. To…
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging…
Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…
Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational…