Search Results for author:
Found 18 papers, 14 papers with code
PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks
While physics-informed neural networks (PINNs) have become a popular deep learning framework for tackling forward and inverse problems governed by partial differential equations (PDEs), their performance is known to degrade when larger and deeper neural network architectures are employed.
Learning Only On Boundaries: a Physics-Informed Neural operator for Solving Parametric Partial Differential Equations in Complex Geometries
By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain.
An Expert's Guide to Training Physics-informed Neural Networks
Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints.
PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems
We develop a tool, which we name Protoplanetary Disk Operator Network (PPDONet), that can predict the solution of disk-planet interactions in protoplanetary disks in real-time.
Ensemble learning for Physics Informed Neural Networks: a Gradient Boosting approach
While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems.
Random Weight Factorization Improves the Training of Continuous Neural Representations
Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals.
Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling
In this paper, we provide a novel perspective of failure modes of PINNs by hypothesizing that training PINNs relies on successful "propagation" of solution from initial and/or boundary condition points to interior points.
Respecting causality is all you need for training physics-informed neural networks
While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior.
Fast PDE-constrained optimization via self-supervised operator learning
Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering.
Improved architectures and training algorithms for deep operator networks
In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel (NTK) theory, and reveal a bias that favors the approximation of functions with larger magnitudes.
Long-time integration of parametric evolution equations with physics-informed DeepONets
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering.
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets
Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces.
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features.
When and why PINNs fail to train: A neural tangent kernel perspective
In this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent.
Deep learning of free boundary and Stefan problems
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering.
Understanding and mitigating gradient pathologies in physics-informed neural networks
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge.
An overlapping-free leaf segmentation method for plant point clouds
The proposed method can also facilitate the automatic traits estimation of each single leaf (such as the leaf area, length, and width), which has potential to become a highly effective tool for plant research and agricultural engineering.
An Integrated Image Filter for Enhancing Change Detection Results
In this paper, we present an integrated filter which comprises a weighted local guided image filter and a weighted spatiotemporal tree filter.
