Related papers: PDE-Foam - a probability-density estimation method…

An efficient mixed deterministic/sparse-stochastic plane-wave approach is developed for bandstructure calculations of large supercell periodic generalized-Kohn-Sham density functional theory, for any hybrid-exchange density functional. The…

In this work, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale…

We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which…

This work proposes a mixed learning-based and optimization-based approach to the weighted-sum-rates beamforming problem in a multiple-input multiple-output (MIMO) wireless network. The conventional methods, i.e., the fractional programming…

Document set expansion aims to identify relevant documents from a large collection based on a small set of documents that are on a fine-grained topic. Previous work shows that PU learning is a promising method for this task. However, some…

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…

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…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…

This paper considers the analysis of partial differential equations (PDE) containing multiple random variables. Recently developed collocation methods enable the construction of high-order stochastic solutions by converting a stochastic PDE…

We propose a deformable registration algorithm based on unsupervised learning of a low-dimensional probabilistic parameterization of deformations. We model registration in a probabilistic and generative fashion, by applying a conditional…

We consider a quasilinear degenerate diffusion-reaction system that describes biofilm formation. The model exhibits two non-linear effects: a power law degeneracy as one of the dependent variables vanishes and a super diffusion singularity…

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…

Any order generation of discrete data using masked diffusion models (MDMs) offers a compelling alternative to traditional autoregressive models, especially in domains that lack a natural causal ordering of data. However, current popular…

Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…

This paper presents a proper generalized decomposition (PGD) based reduced-order model of hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-PGD method keeps both advantages of HiDeNN and PGD methods. The automatic…

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and…

This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…

The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions…

In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a…

A density-based topology optimization framework is developed to manipulate characteristic modes of conducting surfaces. The adjoint sensitivity analysis provides an efficient computation of the material gradient utilized by the local…