Related papers: OTMol: Robust Molecular Structure Comparison via O…
In online incremental learning, data continuously arrives with substantial distributional shifts, creating a significant challenge because previous samples have limited replay value when learning a new task. Prior research has typically…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…
Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…
Multi-task learning (MTL) aims at solving multiple related tasks simultaneously and has experienced rapid growth in recent years. However, MTL models often suffer from performance degeneration with negative transfer due to learning several…
Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…
Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between…
Context: Dynamical studies of irradiated circumstellar disks require an accurate treatment of radiation transport to, for example, properly determine cooling and fragmentation properties. The radiation transport algorithm should be as fast…
A primal-dual accelerated stochastic gradient descent with variance reduction algorithm (PDASGD) is proposed to solve linear-constrained optimization problems. PDASGD could be applied to solve the discrete optimal transport (OT) problem and…
We address the degree to which machine learning can be used to accurately and transferably predict post-Hartree-Fock correlation energies. Refined strategies for feature design and selection are presented, and the molecular-orbital-based…
Computational methods that operate on three-dimensional molecular structure have the potential to solve important questions in biology and chemistry. In particular, deep neural networks have gained significant attention, but their…
Density functional theory (DFT) is the most widely used method for calculating molecular properties; however, its accuracy is often insufficient for quantitative predictions. Coupled-cluster (CC) theory is the most successful method for…
The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability…
The Gromov-Wasserstein (GW) problem, a variant of the classical optimal transport (OT) problem, has attracted growing interest in the machine learning and data science communities due to its ability to quantify similarity between measures…
Molecular structures are always depicted as 2D printed form in scientific documents like journal papers and patents. However, these 2D depictions are not machine-readable. Due to a backlog of decades and an increasing amount of these…
An equation of Monge-Amp\`ere type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport…
Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
Molecular optimization is a key challenge in drug discovery and material science domain, involving the design of molecules with desired properties. Existing methods focus predominantly on single-property optimization, necessitating…
We present a versatile adaptation of existing dimensionality reduction (DR) objectives, enabling the simultaneous reduction of both sample and feature sizes. Correspondances between input and embedding samples are computed through a…