Related papers: Discrete Empirical Interpolation Method with Upper…

The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…

Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…

Only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes. The BEM-based Finite Element Method is one of the new discretization strategies, which make use of and benefits from the flexibility of these…

High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify…

High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…

Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately…

Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

Optimization of DR-submodular functions has experienced a notable surge in significance in recent times, marking a pivotal development within the domain of non-convex optimization. Motivated by real-world scenarios, some recent works have…

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…

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising…

Imperfections in X-ray imaging systems can limit their performance, especially in High Energy Density (HED) or Inertial Fusion Energy (IFE)-relevant experiments that are typically single shot, by introducing structured, non-stationary…

Empirical Green's functions (EGFs) extracted from seismic ambient noise have been widely used to image Earth's interior structures, and the resolution of EGF-based tomography depends on the spatial density of seismic stations. However, due…

Numerous dual-energy CT (DECT) techniques have been developed in the past few decades. Dual-energy CT (DECT) statistical iterative reconstruction (SIR) has demonstrated its potential for reducing noise and increasing accuracy. Our lab…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…

A trigonometric interpolation algorithm for non-periodic functions has been recently proposed and applied to study general ordinary differential equation (ODE). This paper enhances the algorithm to approximate functions in $2$-dim space.…

This paper investigates two fundamental problems that arise when utilizing Intrinsic Motivation (IM) for reinforcement learning in Reward-Free Pre-Training (RFPT) tasks and Exploration with Intrinsic Motivation (EIM) tasks: 1) how to design…