Related papers: Complex-valued neural operator assisted soliton id…
We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped trap. The system is obtained by means of…
Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…
This study aims to develop surrogate models for accelerating decision making processes associated with carbon capture and storage (CCS) technologies. Selection of sub-surface $CO_2$ storage sites often necessitates expensive and involved…
One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and…
This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…
The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…
Previous graph neural networks (GNNs) usually assume that the graph data is with clean labels for representation learning, but it is not true in real applications. In this paper, we propose a new multi-teacher distillation method based on…
In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…
While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose…
Deep learning models operating in the complex domain are used due to their rich representation capacity. However, most of these models are either restricted to the first quadrant of the complex plane or project the complex-valued data into…
We present a deep-learning-based approach for identifying dark matter haloes in cosmological N-body simulations. Our framework consists of a volumetric Convolutional Neural Network to classify individual simulation particles as either halo…
Drawing inspiration from gradient-based meta-learning methods with infinitely small gradient steps, we introduce Continuous-Time Meta-Learning (COMLN), a meta-learning algorithm where adaptation follows the dynamics of a gradient vector…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Neural Ordinary Differential Equations (Neural ODEs) construct the continuous dynamics of hidden units using ordinary differential equations specified by a neural network, demonstrating promising results on many tasks. However, Neural ODEs…
Recent advances in electron, scanning probe, optical, and chemical imaging and spectroscopy yield bespoke data sets containing the information of structure and functionality of complex systems. In many cases, the resulting data sets are…
Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is…
We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate (BEC), based on a system of three…