1.1k citations · 4.1k across the 92 of their papers we have counts for
59 papers · 1 filter
Large-Scale 3D Ground-Motion Synthesis with Physics-Inspired Latent Operator Flow Matching
Yaozhong Shi, Grigorios Lavrentiadis, Konstantinos Tsalouchidis +5
Earthquake hazard analysis and design of spatially distributed infrastructure, such as power grids and energy pipeline networks, require scenario-specific ground-motion time histor…
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…
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…
Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
Julius Berner, Miguel Liu-Schiaffini, Jean Kossaifi +4
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function sp…
Mesh-Informed Neural Operator : A Transformer Generative Approach
Yaozhong Shi, Zachary E. Ross, Domniki Asimaki +1
Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential…
Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks
Ali Hariri, Álvaro Arroyo, Alessio Gravina +6
ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness…
Guided Diffusion Sampling on Function Spaces with Applications to PDEs
Jiachen Yao, Abbas Mammadov, Julius Berner +4
We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This i…
Enabling Automatic Differentiation with Mollified Graph Neural Operators
Ryan Y. Lin, Julius Berner, Valentin Duruisseaux +5
Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However,…
Stochastic Process Learning via Operator Flow Matching
Yaozhong Shi, Zachary E. Ross, Domniki Asimaki +1
Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for lea…
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…
Exploring the design space of deep-learning-based weather forecasting systems
Shoaib Ahmed Siddiqui, Jean Kossaifi, Boris Bonev +4
Despite tremendous progress in developing deep-learning-based weather forecasting systems, their design space, including the impact of different design choices, is yet to be well u…
Dynamical Measure Transport and Neural PDE Solvers for Sampling
Jingtong Sun, Julius Berner, Lorenz Richter +4
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we…
Universal Functional Regression with Neural Operator Flows
Yaozhong Shi, Angela F. Gao, Zachary E. Ross +1
Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a pr…
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…
Calibrated Uncertainty Quantification for Operator Learning via Conformal Prediction
Ziqi Ma, Kamyar Azizzadenesheli, Anima Anandkumar
Operator learning has been increasingly adopted in scientific and engineering applications, many of which require calibrated uncertainty quantification. Since the output of operato…
Neural Operators with Localized Integral and Differential Kernels
Miguel Liu-Schiaffini, Julius Berner, Boris Bonev +3
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Four…
Equivariant Graph Neural Operator for Modeling 3D Dynamics
Minkai Xu, Jiaqi Han, Aaron Lou +6
Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to…
Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs
Jean Kossaifi, Nikola Kovachki, Kamyar Azizzadenesheli +1
Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by…
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…
Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces
Miguel Liu-Schiaffini, Clare E. Singer, Nikola Kovachki +4
Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems. For instance, increased greenhouse gas concentr…
Guaranteed Approximation Bounds for Mixed-Precision Neural Operators
Renbo Tu, Colin White, Jean Kossaifi +5
Neural operators, such as Fourier Neural Operators (FNO), form a principled approach for learning solution operators for PDEs and other mappings between function spaces. However, m…
Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
Xuan Zhang, Limei Wang, Jacob Helwig +60
Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating…
Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo
Haque Ishfaq, Qingfeng Lan, Pan Xu +4
We present a scalable and effective exploration strategy based on Thompson sampling for reinforcement learning (RL). One of the key shortcomings of existing Thompson sampling algor…
Score-based Diffusion Models in Function Space
Jae Hyun Lim, Nikola B. Kovachki, Ricardo Baptista +10
Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a r…