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Full waveform inversion (FWI) is a powerful tool for reconstructing material fields based on sparsely measured data obtained by wave propagation. For specific problems, discretizing the material field with a neural network (NN) improves the…

We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…

We present a novel method to model and calculate deformation fields between shapes embedded in $\mathbb{R}^D$. Our framework combines naturally interpolating the two input shapes and calculating correspondences at the same time. The key…

In this paper, we propose a new method called Self-Training with Dynamic Weighting (STDW), which aims to enhance robustness in Gradual Domain Adaptation (GDA) by addressing the challenge of smooth knowledge migration from the source to the…

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…

In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…

We introduce a dimensional splitting method based on the intertwining property of the Radon transform, with a particular focus on its applications related to hyperbolic partial differential equations (PDEs). This dimensional splitting has…

In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…

The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…

Inverse design (ID) is a computational method that systematically explores a design space to find optimal device geometries based on specific performance criteria. In silicon photonics, ID often leads to devices with design features that…

The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…

We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold.…

We consider the inverse problem of reconstructing an unknown function $u$ from a finite set of measurements, under the assumption that $u$ is the trajectory of a transport-dominated problem with unknown input parameters. We propose an…

We propose a method to interpolate Signed Distance Function (SDF) data from a discrete set of samples. Unlike prior work, our approach ensures that the new SDF data values are fully consistent with the input and each other, such that the…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

There is a growing interest in estimating heterogeneous treatment effects across individuals using their high-dimensional feature attributes. Achieving high performance in such high-dimensional heterogeneous treatment effect estimation is…

Seismic full-waveform inversion (FWI), which uses iterative methods to estimate high-resolution subsurface models from seismograms, is a powerful imaging technique in exploration geophysics. In recent years, the computational cost of FWI…