29 research outputs found
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs
While physics-informed neural networks (PINNs) have been proven effective for
low-dimensional partial differential equations (PDEs), the computational cost
remains a hurdle in high-dimensional scenarios. This is particularly pronounced
when computing high-order and high-dimensional derivatives in the
physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian
noise for stochastic smoothing of the original neural net model, enabling Monte
Carlo methods for derivative approximation, eliminating the need for costly
auto-differentiation. Despite its computational efficiency in high dimensions,
RS-PINN introduces biases in both loss and gradients, negatively impacting
convergence, especially when coupled with stochastic gradient descent (SGD). We
present a comprehensive analysis of biases in RS-PINN, attributing them to the
nonlinearity of the Mean Squared Error (MSE) loss and the PDE nonlinearity. We
propose tailored bias correction techniques based on the order of PDE
nonlinearity. The unbiased RS-PINN allows for a detailed examination of its
pros and cons compared to the biased version. Specifically, the biased version
has a lower variance and runs faster than the unbiased version, but it is less
accurate due to the bias. To optimize the bias-variance trade-off, we combine
the two approaches in a hybrid method that balances the rapid convergence of
the biased version with the high accuracy of the unbiased version. In addition,
we present an enhanced implementation of RS-PINN. Extensive experiments on
diverse high-dimensional PDEs, including Fokker-Planck, HJB, viscous Burgers',
Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off
and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are
provided for selecting biased, unbiased, or hybrid versions, depending on the
dimensionality and nonlinearity of the specific PDE problem.Comment: 21 pages, 5 figure
ePointDA: An End-to-End Simulation-to-Real Domain Adaptation Framework for LiDAR Point Cloud Segmentation
Due to its robust and precise distance measurements, LiDAR plays an important
role in scene understanding for autonomous driving. Training deep neural
networks (DNNs) on LiDAR data requires large-scale point-wise annotations,
which are time-consuming and expensive to obtain. Instead, simulation-to-real
domain adaptation (SRDA) trains a DNN using unlimited synthetic data with
automatically generated labels and transfers the learned model to real
scenarios. Existing SRDA methods for LiDAR point cloud segmentation mainly
employ a multi-stage pipeline and focus on feature-level alignment. They
require prior knowledge of real-world statistics and ignore the pixel-level
dropout noise gap and the spatial feature gap between different domains. In
this paper, we propose a novel end-to-end framework, named ePointDA, to address
the above issues. Specifically, ePointDA consists of three modules:
self-supervised dropout noise rendering, statistics-invariant and
spatially-adaptive feature alignment, and transferable segmentation learning.
The joint optimization enables ePointDA to bridge the domain shift at the
pixel-level by explicitly rendering dropout noise for synthetic LiDAR and at
the feature-level by spatially aligning the features between different domains,
without requiring the real-world statistics. Extensive experiments adapting
from synthetic GTA-LiDAR to real KITTI and SemanticKITTI demonstrate the
superiority of ePointDA for LiDAR point cloud segmentation.Comment: Accepted by AAAI 202
A Finger-Shaped Tactile Sensor for Fabric Surfaces Evaluation by 2-Dimensional Active Sliding Touch
Sliding tactile perception is a basic function for human beings to determine the mechanical properties of object surfaces and recognize materials. Imitating this process, this paper proposes a novel finger-shaped tactile sensor based on a thin piezoelectric polyvinylidene fluoride (PVDF) film for surface texture measurement. A parallelogram mechanism is designed to ensure that the sensor applies a constant contact force perpendicular to the object surface, and a 2-dimensional movable mechanical structure is utilized to generate the relative motion at a certain speed between the sensor and the object surface. By controlling the 2-dimensional motion of the finger-shaped sensor along the object surface, small height/depth variation of surface texture changes the output charge of PVDF film then surface texture can be measured. In this paper, the finger-shaped tactile sensor is used to evaluate and classify five different kinds of linen. Fast Fourier Transformation (FFT) is utilized to get original attribute data of surface in the frequency domain, and principal component analysis (PCA) is used to compress the attribute data and extract feature information. Finally, low dimensional features are classified by Support Vector Machine (SVM). The experimental results show that this finger-shaped tactile sensor is effective and high accurate for discriminating the five textures
Invariant Information Bottleneck for Domain Generalization
Invariant risk minimization (IRM) has recently emerged as a promising
alternative for domain generalization. Nevertheless, the loss function is
difficult to optimize for nonlinear classifiers and the original optimization
objective could fail when pseudo-invariant features and geometric skews exist.
Inspired by IRM, in this paper we propose a novel formulation for domain
generalization, dubbed invariant information bottleneck (IIB). IIB aims at
minimizing invariant risks for nonlinear classifiers and simultaneously
mitigating the impact of pseudo-invariant features and geometric skews.
Specifically, we first present a novel formulation for invariant causal
prediction via mutual information. Then we adopt the variational formulation of
the mutual information to develop a tractable loss function for nonlinear
classifiers. To overcome the failure modes of IRM, we propose to minimize the
mutual information between the inputs and the corresponding representations.
IIB significantly outperforms IRM on synthetic datasets, where the
pseudo-invariant features and geometric skews occur, showing the effectiveness
of proposed formulation in overcoming failure modes of IRM. Furthermore,
experiments on DomainBed show that IIB outperforms baselines by on
average across real datasets.Comment: AAAI 202
Structural Distortion of g-C<sub>3</sub>N<sub>4</sub> Induced by N-Defects for Enhanced Photocatalytic Hydrogen Evolution
Hydrogen evolution by photocatalytic technology has been one of the most promising and attractive solutions, and can harvest and convert the abundant solar energy into green, renewable hydrogen energy. As a new kind of photocatalytic material, graphitic carbon nitride (g-C3N4) has drawn much attention in photocataluytic H2 production due to its visible light response, ease of preparation and good stability. For a higher photocatalyic performance, N defects were introduced in to the traditional g-C3N4 in this work. The existence of N defects was proved by adequate material characterization. Significantly, a new absorption region at around 500 nm of N-deficient g-C3N4 appeared, revealing the exciting n-Ï€* transition of lone pair electrons. The photocatalytic H2 production performance of N-deficient g-C3N4 was increased by 5.8 times. The enhanced photocatalytic performance of N-deficient g-C3N4 was attributed to the enhanced visible light absorption, as well as the promoted separation of photo-generated carries and increased specific surface area
Maternal prenatal screening programs that predict trisomy 21, trisomy 18, and neural tube defects in offspring
Objective To determine the efficacy of three different maternal screening programs (first-trimester screening [FTS], individual second-trimester screening [ISTS], and first- and second-trimester combined screening [FSTCS]) in predicting offspring with trisomy 21, trisomy 18, and neural tube defects (NTDs). Methods A retrospective cohort involving 108,118 pregnant women who received prenatal screening tests during the first (9–13+6 weeks) and second trimester (15–20+6 weeks) in Hangzhou, China from January–December 2019, as follows: FTS, 72,096; ISTS, 36,022; and FSTCS, 67,631 gravidas. Result The high and intermediate risk positivity rates for trisomy 21 screening with FSTCS (2.40% and 5.57%) were lower than ISTS (9.02% and 16.14%) and FTS (2.71% and 7.19%); there were statistically significant differences in the positivity rates among the screening programs (all P 0.05). The positive predictive values (PPVs) for trisomy 21 and 18 were highest with FTS, while the false positive rate (FPR) was lowest with FSTCS. Conclusion FSTCS was superior to FTS and ISTS screening and substantially reduced the number of high risk pregnancies for trisomy 21 and 18; however, FSTCS was not significantly different in detecting fetal trisomy 21 and 18 and other confirmed cases with chromosomal abnormalities
Maternal prenatal screening programs that predict trisomy 21, trisomy 18, and neural tube defects in offspring.
ObjectiveTo determine the efficacy of three different maternal screening programs (first-trimester screening [FTS], individual second-trimester screening [ISTS], and first- and second-trimester combined screening [FSTCS]) in predicting offspring with trisomy 21, trisomy 18, and neural tube defects (NTDs).MethodsA retrospective cohort involving 108,118 pregnant women who received prenatal screening tests during the first (9-13+6 weeks) and second trimester (15-20+6 weeks) in Hangzhou, China from January-December 2019, as follows: FTS, 72,096; ISTS, 36,022; and FSTCS, 67,631 gravidas.ResultThe high and intermediate risk positivity rates for trisomy 21 screening with FSTCS (2.40% and 5.57%) were lower than ISTS (9.02% and 16.14%) and FTS (2.71% and 7.19%); there were statistically significant differences in the positivity rates among the screening programs (all P 0.05). The positive predictive values (PPVs) for trisomy 21 and 18 were highest with FTS, while the false positive rate (FPR) was lowest with FSTCS.ConclusionFSTCS was superior to FTS and ISTS screening and substantially reduced the number of high risk pregnancies for trisomy 21 and 18; however, FSTCS was not significantly different in detecting fetal trisomy 21 and 18 and other confirmed cases with chromosomal abnormalities