40 citations · 61 across the 12 of their papers we have counts for
12 papers
Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization
Xiangming Huang, Guannan Zhang, Lu Lu +1
The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Ge…
Learning the detector in optical tomography
Zijian Wang, Andreas Hauptmann, Lu Lu +1
We propose a method to reconstruct the optical absorption of a highly-scattering medium probed by diffuse light. The method consists of learning the optical detection system and th…
RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations
Weihang Ouyang, Min Zhu, Wei Xiong +2
Physics-informed neural networks (PINNs) and neural operators, two leading scientific machine learning (SciML) paradigms, have emerged as powerful tools for solving partial differe…
Stochastic Operator Network: A Stochastic Maximum Principle Based Approach to Operator Learning
Ryan Bausback, Jingqiao Tang, Lu Lu +2
We develop a novel framework for uncertainty quantification in operator learning, the Stochastic Operator Network (SON). SON combines the stochastic optimal control concepts of the…
Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators
Weihang Ouyang, Yeonjong Shin, Si-Wei Liu +1
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial c…
Identifying Trustworthiness Challenges in Deep Learning Models for Continental-Scale Water Quality Prediction
Xiaobo Xia, Xiaofeng Liu, Jiale Liu +5
Water quality is foundational to environmental sustainability, ecosystem resilience, and public health. Deep learning offers transformative potential for large-scale water quality…
Rapid aerodynamic prediction of swept wings via physics-embedded transfer learning
Yunjia Yang, Runze Li, Yufei Zhang +2
Machine learning-based models provide a promising way to rapidly acquire transonic swept wing flow fields but suffer from large computational costs in establishing training dataset…
Challenges in Training PINNs: A Loss Landscape Perspective
Pratik Rathore, Weimu Lei, Zachary Frangella +2
This paper explores challenges in training Physics-Informed Neural Networks (PINNs), emphasizing the role of the loss landscape in the training process. We examine difficulties in…
Speeding up and reducing memory usage for scientific machine learning via mixed precision
Joel Hayford, Jacob Goldman-Wetzler, Eric Wang +1
Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neura…
ROAM: memory-efficient large DNN training via optimized operator ordering and memory layout
Huiyao Shu, Ang Wang, Ziji Shi +3
As deep learning models continue to increase in size, the memory requirements for training have surged. While high-level techniques like offloading, recomputation, and compression…
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
Lu Lu, Raphael Pestourie, Steven G. Johnson +1
Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine l…
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
Pengzhan Jin, Lu Lu, Yifa Tang +1
The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and gene…