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In this paper, we first propose a novel method for transferring material transformations across different scenes. Building on disentangled Neural Radiance Field (NeRF) representations, our approach learns to map Bidirectional Reflectance…

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately,…

In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…

Many datasets are obtained as a resolution trade-off between two adversarial dimensions; for example between the frequency and the temporal resolutions for the spectrogram of an audio signal, and between the number of wavelengths and the…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

In this paper, we present a meshless hybrid method combining the Generalized Finite Difference (GFD) and Finite Difference based Radial Basis Function (RBF-FD) approaches to solve non-homogeneous partial differential equations (PDEs)…

Trajectory data is essential for various applications as it records the movement of vehicles. However, publicly available trajectory datasets remain limited in scale due to privacy concerns, which hinders the development of trajectory data…

Deploying machine learning in open environments presents the challenge of encountering diverse test inputs that differ significantly from the training data. These out-of-distribution samples may exhibit shifts in local or global features…

Diffusion models (DMs) excel in image generation but suffer from slow inference and training-inference discrepancies. Although gradient-based solvers for DMs accelerate denoising inference, they often lack theoretical foundations in…

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…

Color plays an important role in human visual perception, reflecting the spectrum of objects. However, the existing infrared and visible image fusion methods rarely explore how to handle multi-spectral/channel data directly and achieve high…

A hybrid asymptotic-numerical method is presented for obtaining the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two-dimensional domain with reflective boundaries. As…

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…

Nonnegative Matrix Factorization (NMF) is a powerful tool for decomposing mixtures of audio signals in the Time-Frequency (TF) domain. In applications such as source separation, the phase recovery for each extracted component is a major…

A deep learning-assisted inversion method is proposed to solve the inhomogeneous background imaging problem. Three non-iterative methods, namely the distorted-Born (DB) major current coefficients method, the DB modified Born approximation…