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This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

Traditional methods of linking large language models (LLMs) to knowledge bases via the semantic similarity search often fall short of capturing complex relational dynamics. To address these limitations, we introduce AutoKG, a lightweight…

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…

Knowledge Graph (KG) is a flexible structure that is able to describe the complex relationship between data entities. Currently, most KG embedding models are trained based on negative sampling, i.e., the model aims to maximize some…

We study the global strong solutions to a 3-dimensional parabolic-hyperbolic Keller-Segel model with initial data close to a stable equilibrium with perturbations belonging to $L^2(\mathbb R^3)\times H^1(\mathbb{R}^3)$. We obtain global…

The density-matrix renormalization-group (DMRG) algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the…

Deep Neural Networks (DNN) could forget the knowledge about earlier tasks when learning new tasks, and this is known as \textit{catastrophic forgetting}. While recent continual learning methods are capable of alleviating the catastrophic…

Accurately predicting drug-target binding affinity (DTA) in silico is a key task in drug discovery. Most of the conventional DTA prediction methods are simulation-based, which rely heavily on domain knowledge or the assumption of having the…

We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a way of training…

A central challenge in computational catalysis is the identification of low-energy and chemically plausible adsorption configurations, as these directly affect adsorption energies, reaction pathways, and catalytic performance. Existing…

We present a Kernel Ridge Regression (KRR) based supervised learning method combined with Genetic Algorithms (GAs) for the calculation of quasiparticle energies within Many-Body Green's Functions Theory. These energies representing…

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic…

An overarching challenge in rheology is to develop constitutive models for complex fluids for which we lack accurate first principles theory. A further challenge is that most experiments probing dynamical structure and rheology do so only…

Reconstructing 3D fluid velocity fields from sparse 2D video observations is a highly ill-posed inverse problem, demanding both transport consistency with observed motion and physical validity under fluid laws. Existing methods typically…

In this paper, we improve the original Lagrange multiplier approach \cite{ChSh22,ChSh_II22} and introduce a new energy correction approach to construct a class of robust, positivity/bound-preserving, mass conserving and energy dissipative…

3D Gaussian Splatting (3DGS) has emerged as a promising 3D reconstruction technique. The traditional 3DGS training pipeline follows three sequential steps: Gaussian densification, Gaussian projection, and color splatting. Despite its…

In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure…

Compressed Sensing MRI (CS-MRI) has provided theoretical foundations upon which the time-consuming MRI acquisition process can be accelerated. However, it primarily relies on iterative numerical solvers which still hinders their adaptation…

Knowledge Graph-based Retrieval-Augmented Generation (KG-RAG) significantly enhances the reasoning capabilities of LargeLanguage Models by leveraging structured knowledge. However, existing KG-RAG frameworks typically operate as open-loop…

In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all time. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS)…