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Designing nanophotonic structures traditionally grapples with the complexities of discrete parameters, such as real materials, often resorting to costly global optimization methods. This paper introduces an approach that leverages…

Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…

Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…

In this work, we investigate the fundamental trade-off regarding accuracy and parameter efficiency in the parameterization of neural network weights using predictor networks. We present a surprising finding that, when recovering the…

We address the problem of Bayesian inference for parameters in ordinary differential equation (ODE) models based on observational data. Conventional approaches in this setting typically rely on numerical solvers such as the Euler or…

Efficient parameter identification of electrochemical models is crucial for accurate monitoring and control of lithium-ion cells. This process becomes challenging when applied to complex models that rely on a considerable number of…

We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for…

The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…

We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…

We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity and the size of the training dataset. In our experiments,…

X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval…

Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…

In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…

Scanning X-ray nanodiffraction microscopy is a powerful technique for spatially resolving nanoscale structural morphologies by diffraction contrast. One of the critical challenges in experimental nanodiffraction data analysis is posed by…

This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the…

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…

End-to-end deep trainable models are about to exceed the performance of the traditional handcrafted compression techniques on videos and images. The core idea is to learn a non-linear transformation, modeled as a deep neural network,…

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…

This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation…