1.1k citations · 2.4k across the 34 of their papers we have counts for
24 papers · 1 filter
Scale-Split Neural Operator for Memory- and Data-Efficient 3D Turbulence Prediction
Shaoxiang Qin, Yucheng Zhao, Zongyi Li +2
Neural surrogates have emerged as fast alternatives to the numerical simulation of three-dimensional turbulence. However, training them at high resolution remains challenging, sinc…
GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training
Haixu Wu, Minghao Guo, Zongyi Li +4
Neural simulators promise efficient surrogates for physics simulation, but scaling them is bottlenecked by the prohibitive cost of generating high-fidelity training data. Pre-train…
Physics-informed Neural-operator Predictive Control for Drag Reduction in Turbulent Flows
Zelin Zhao, Zongyi Li, Kimia Hassibi +5
Assessing turbulence control effects for wall friction numerically is a significant challenge since it requires expensive simulations of turbulent fluid dynamics. We instead propos…
Geometric Operator Learning with Optimal Transport
Xinyi Li, Zongyi Li, Nikola Kovachki +1
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically…
Scale-Consistent Learning for Partial Differential Equations
Zongyi Li, Samuel Lanthaler, Catherine Deng +4
Machine learning (ML) models have emerged as a promising approach for solving partial differential equations (PDEs) in science and engineering. Previous ML models typically cannot…
High precision PINNs in unbounded domains: application to singularity formulation in PDEs
Yixuan Wang, Ziming Liu, Zongyi Li +2
We investigate the high-precision training of Physics-Informed Neural Networks (PINNs) in unbounded domains, with a special focus on applications to singularity formulation in PDEs…
A Library for Learning Neural Operators
Jean Kossaifi, Nikola Kovachki, Zongyi Li +8
We present NeuralOperator, an open-source Python library for operator learning. Neural operators generalize neural networks to maps between function spaces instead of finite-dimens…
Coarse Graining with Neural Operators for Simulating Chaotic Systems
Chuwei Wang, Boris Bonev, Julius Berner +6
Accurately predicting the long-term behavior of chaotic systems is crucial for various applications such as climate modeling. However, achieving such predictions typically requires…
Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs
Md Ashiqur Rahman, Robert Joseph George, Mogab Elleithy +9
Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions…
Neural Operators for Accelerating Scientific Simulations and Design
Kamyar Azizzadenesheli, Nikola Kovachki, Zongyi Li +3
Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require d…
Geometry-Informed Neural Operator for Large-Scale 3D PDEs
Zongyi Li, Nikola Borislavov Kovachki, Chris Choy +8
We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying ge…
FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation
Adarsh Ganeshram, Haydn Maust, Valentin Duruisseaux +6
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs).…
Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEs
Robert Joseph George, Jiawei Zhao, Jean Kossaifi +2
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral lay…
An Adversarial Active Sampling-based Data Augmentation Framework for Manufacturable Chip Design
Mingjie Liu, Haoyu Yang, Zongyi Li +7
Lithography modeling is a crucial problem in chip design to ensure a chip design mask is manufacturable. It requires rigorous simulations of optical and chemical models that are co…
Real-time high-resolution CO geological storage prediction using nested Fourier neural operators
Gege Wen, Zongyi Li, Qirui Long +3
Carbon capture and storage (CCS) plays an essential role in global decarbonization. Scaling up CCS deployment requires accurate and high-resolution modeling of the storage reservoi…
Large Scale Mask Optimization Via Convolutional Fourier Neural Operator and Litho-Guided Self Training
Haoyu Yang, Zongyi Li, Kumara Sastry +5
Machine learning techniques have been extensively studied for mask optimization problems, aiming at better mask printability, shorter turnaround time, better mask manufacturability…
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
Zongyi Li, Daniel Zhengyu Huang, Burigede Liu +1
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is sig…
Physics-Informed Neural Operator for Learning Partial Differential Equations
Zongyi Li, Hongkai Zheng, Nikola Kovachki +5
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric…
Neural Operator: Learning Maps Between Function Spaces
Nikola Kovachki, Zongyi Li, Burigede Liu +4
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of n…
Learning Dissipative Dynamics in Chaotic Systems
Zongyi Li, Miguel Liu-Schiaffini, Nikola Kovachki +5
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many…
Fourier Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural o…
Multipole Graph Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data…
Neural Operator: Graph Kernel Network for Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Eu…
Conditional Linear Regression
Diego Calderon, Brendan Juba, Sirui Li +2
Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. Howev…