18 citations · 47 across the 18 of their papers we have counts for
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Operator Learning Using Weak Supervision from Walk-on-Spheres
Hrishikesh Viswanath, Hong Chul Nam, Xi Deng +3
Training neural PDE solvers is often bottlenecked by expensive data generation or unstable physics-informed neural network (PINN) involving challenging optimization landscapes due…
Self-Supervised Learning via Flow-Guided Neural Operator on Time-Series Data
Duy Nguyen, Jiachen Yao, Jiayun Wang +2
Self-supervised learning (SSL) is a powerful paradigm for learning from unlabeled time-series data. However, popular methods such as masked autoencoders (MAEs) rely on reconstructi…
Decoupled Diffusion Sampling for Inverse Problems on Function Spaces
Thomas Y. L. Lin, Jiachen Yao, Lufang Chiang +2
We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics im…
Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching
Denis Blessing, Lorenz Richter, Julius Berner +2
Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have i…
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…
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,…
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…
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…
Learning Lagrangian Interaction Dynamics with Sampling-Based Model Order Reduction
Hrishikesh Viswanath, Yue Chang, Aleksey Panas +3
Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant…
Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing
Bingliang Zhang, Wenda Chu, Julius Berner +3
Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where…
Solving Poisson Equations using Neural Walk-on-Spheres
Hong Chul Nam, Julius Berner, Anima Anandkumar
We propose Neural Walk-on-Spheres (NWoS), a novel neural PDE solver for the efficient solution of high-dimensional Poisson equations. Leveraging stochastic representations and Walk…
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…
DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training
Zhongkai Hao, Chang Su, Songming Liu +6
Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the…
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…