Related papers: Equivariant Neural Simulators for Stochastic Spati…
Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries. By construction ENNs cannot produce lower symmetry outputs given a higher symmetry input. However, symmetry…
Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…
This work investigates use of equivariant neural networks as efficient and high-performance frameworks for image reconstruction and denoising in nuclear medicine. Our work aims to tackle limitations of conventional Convolutional Neural…
This thesis introduces PEMS2, an improvement to PEMS (Parallel External Memory System). PEMS executes Bulk-Synchronous Parallel (BSP) algorithms in an External Memory (EM) context, enabling computation with very large data sets which exceed…
Molecular dynamics (MD) simulations are a central tool in science and engineering enabling the study of dynamical behavior and the link between microscopic structure and macroscopic function. Their high computational cost, however, has…
This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…
Numerical simulation is an essential tool in many areas of science and engineering, but its performance often limits application in practice or when used to explore large parameter spaces. On the other hand, surrogate deep learning models,…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
Equivariant Graph Neural Networks (EGNNs) have emerged as a promising approach in Multi-Agent Reinforcement Learning (MARL), leveraging symmetry guarantees to greatly improve sample efficiency and generalization. However, real-world…
Animals are known to make efficient probabilistic inferences based on uncertain and noisy information from the outside world. Although it is known that generic neural networks can perform near-optimal point estimation by probabilistic…
A key objective in spatial statistics is to simulate from the distribution of a spatial process at a selection of unobserved locations conditional on observations (i.e., a predictive distribution) to enable spatial prediction and…
Neuromorphic and quantum computing have recently emerged as promising paradigms for advancing artificial intelligence, each offering complementary strengths. Neuromorphic systems built on spiking neurons excel at processing time series data…
Identifying the obstacle space is crucial for path planning. However, generating an accurate obstacle space remains a significant challenge due to various sources of uncertainty, including motion, behavior, and perception limitations. Even…
We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…
Equivariant neural networks have been widely used in a variety of applications due to their ability to generalize well in tasks where the underlying data symmetries are known. Despite their successes, such networks can be difficult to…
Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…
Despite the superiority of convolutional neural networks demonstrated in time series modeling and forecasting, it has not been fully explored on the design of the neural network architecture and the tuning of the hyper-parameters. Inspired…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…
Machine learning potentials have achieved great success in accelerating atomistic simulations. Many of them relying on atom-centered local descriptors are natural for parallelization. More recent message passing neural network (MPNN) models…