Related papers: Deep neural operator for learning transient respon…

Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of…

Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each…

Deep learning has achieved incredible success over the past years, especially in various challenging predictive spatio-temporal analytics (PSTA) tasks, such as disease prediction, climate forecast, and traffic prediction, where intrinsic…

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…

Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…

Learning to capture feature relations effectively and efficiently is essential in click-through rate (CTR) prediction of modern recommendation systems. Most existing CTR prediction methods model such relations either through tedious…

The purpose of the current work is the development of a so-called physics-encoded Fourier neural operator (PeFNO) for surrogate modeling of the quasi-static equilibrium stress field in solids. Rather than accounting for constraints from…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

Lithium-ion batteries exhibit nonlinear voltage dynamics across varying operating conditions and aging states, making accurate modeling essential for estimation, control, and health monitoring. This work compares two data-driven frameworks…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

Continuum models for ion transport through polyamide nanopores require solving partial differential equations (PDEs) through complex pore geometries. Resolving spatiotemporal features at this length and time-scale can make solving these…

Controlling nonlinear dynamics is a long-standing problem in engineering. Harnessing known physical information to accelerate or constrain stochastic learning pursues a new paradigm of scientific machine learning. By linearizing nonlinear…

Reprogrammable mechanical metamaterials, composed of a lattice of discretely adaptive elements, are emerging as a promising platform for mechanical intelligence. To operate in unknown environments, such structures must go beyond passive…

We study the use of deep learning techniques to reconstruct the kinematics of the neutral current deep inelastic scattering (DIS) process in electron-proton collisions. In particular, we use simulated data from the ZEUS experiment at the…

This paper designs an Operator Learning framework to approximate the dynamic response of synchronous generators. One can use such a framework to (i) design a neural-based generator model that can interact with a numerical simulator of the…

Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and…

Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model…

Porous materials -- natural or engineered -- often exhibit dual pore-network structures that govern processes such as mineral exploration and hydrocarbon recovery from tight shales. Double porosity/permeability (DPP) mathematical models…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…