arXiv subjects

Yujia Huang

Publications and source records attributed to Yujia Huang.

13 recordsLinked to original sources

arXiv2025

Fourier heuristic PINNs to solve the biharmonic equations based on its coupled scheme

Physics-informed neural networks (PINNs) have been widely utilized for solving a range of partial differential equations (PDEs) in various scientific and engineering disciplines. This paper presents a Fourier heuristic-enhanced PINN (termed FCPINN) designed to address a specific class of biharmonic equations with Dirichlet and Navier boundary conditions. The method achieves this by decomposing the high-order equations into two Poisson equations. FCPINN integrates Fourier spectral theory with a reduced-order formulation for high-order PDEs, significantly improving approximation accuracy and reducing computational complexity. This approach is especially beneficial for problems with intricate boundary constraints and high-dimensional inputs. To assess the effectiveness and robustness of the FCPINN algorithm, we conducted several numerical experiments on both linear and nonlinear biharmonic problems across different Euclidean spaces. The results show that FCPINN provides an optimal trade-off between speed and accuracy for high-order PDEs, surpassing the performance of conventional PINN and deep mixed residual method (MIM) approaches, while also maintaining stability and robustness with varying numbers of hidden layer nodes.

math.NA↗

arXiv2024

Augmented physics informed extreme learning machine to solve the biharmonic equations via Fourier expansions

To address the sensitivity of parameters and limited precision for physics-informed extreme learning machines (PIELM) with common activation functions, such as sigmoid, tangent, and Gaussian, in solving high-order partial differential equations (PDEs) relevant to scientific computation and engineering applications, this work develops a Fourier-induced PIELM (FPIELM) method. This approach aims to approximate solutions for a class of fourth-order biharmonic equations with two boundary conditions on both unitized and non-unitized domains. By carefully calculating the differential and boundary operators of the biharmonic equation on discretized collections, the solution for this high-order equation is reformulated as a linear least squares minimization problem. We further evaluate the FPIELM with varying hidden nodes and scaling factors for uniform distribution initialization, and then determine the optimal range for these two hyperparameters. Numerical experiments and comparative analyses demonstrate that the proposed FPIELM method is more stable, robust, precise, and efficient than other PIELM approaches in solving biharmonic equations across both regular and irregular domains.

math.NA↗

arXiv2024

Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion

We study the problem of symbolic music generation (e.g., generating piano rolls), with a technical focus on non-differentiable rule guidance. Musical rules are often expressed in symbolic form on note characteristics, such as note density or chord progression, many of which are non-differentiable which pose a challenge when using them for guided diffusion. We propose Stochastic Control Guidance (SCG), a novel guidance method that only requires forward evaluation of rule functions that can work with pre-trained diffusion models in a plug-and-play way, thus achieving training-free guidance for non-differentiable rules for the first time. Additionally, we introduce a latent diffusion architecture for symbolic music generation with high time resolution, which can be composed with SCG in a plug-and-play fashion. Compared to standard strong baselines in symbolic music generation, this framework demonstrates marked advancements in music quality and rule-based controllability, outperforming current state-of-the-art generators in a variety of settings. For detailed demonstrations, code and model checkpoints, please visit our project website: https://scg-rule-guided-music.github.io/.

cs.SD↗

arXiv2023

FI-ODE: Certifiably Robust Forward Invariance in Neural ODEs

Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.

cs.LG↗

arXiv2023

Improved test-retest reliability of $\textit{R}_2^*$ and susceptibility quantification using multi-shot multi echo 3D EPI

This study aimed to evaluate the potential of 3D echo-planar imaging (EPI) for improving the reliability of $T_2^*$-weighted ($T_2^*w$) data and quantification of $\textit{R}_2^*$ decay rate and susceptibility ($χ$) compared to conventional gradient echo (GRE)-based acquisition. Eight healthy subjects in a wide age range were recruited. Each subject received repeated scans for both GRE and EPI acquisitions with an isotropic 1 mm resolution at 3 T. Maps of $\textit{R}_2^*$ and $χ$ were quantified and compared using their inter-scan difference to evaluate the test-retest reliability. Inter-protocol differences of $\textit{R}_2^*$ and $χ$ between GRE and EPI were also measured voxel by voxel and in selected ROIs to test the consistency between the two acquisition methods. The quantifications of $\textit{R}_2^*$ and $χ$ using EPI protocols showed increased test-retest reliability with higher EPI factors up to 5 as performed in the experiment and were consistent with those based on GRE. This result suggested multi-shot multi-echo 3D EPI can be a useful alternative acquisition method for $T_2^*w$ MRI and quantification of $\textit{R}_2^*$ and $χ$ with reduced scan time, improved test-retest reliability and similar accuracy compared to commonly used 3D GRE.

physics.med-ph↗

arXiv2022

Diffusion Models for Adversarial Purification

Adversarial purification refers to a class of defense methods that remove adversarial perturbations using a generative model. These methods do not make assumptions on the form of attack and the classification model, and thus can defend pre-existing classifiers against unseen threats. However, their performance currently falls behind adversarial training methods. In this work, we propose DiffPure that uses diffusion models for adversarial purification: Given an adversarial example, we first diffuse it with a small amount of noise following a forward diffusion process, and then recover the clean image through a reverse generative process. To evaluate our method against strong adaptive attacks in an efficient and scalable way, we propose to use the adjoint method to compute full gradients of the reverse generative process. Extensive experiments on three image datasets including CIFAR-10, ImageNet and CelebA-HQ with three classifier architectures including ResNet, WideResNet and ViT demonstrate that our method achieves the state-of-the-art results, outperforming current adversarial training and adversarial purification methods, often by a large margin. Project page: https://diffpure.github.io.

cs.LG↗

arXiv2021

Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Bounds

Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant. However, such a bound is often loose: it tends to over-regularize the neural network and degrade its natural accuracy. A tighter Lipschitz bound may provide a better tradeoff between natural and certified accuracy, but is generally hard to compute exactly due to non-convexity of the network. In this work, we propose an efficient and trainable \emph{local} Lipschitz upper bound by considering the interactions between activation functions (e.g. ReLU) and weight matrices. Specifically, when computing the induced norm of a weight matrix, we eliminate the corresponding rows and columns where the activation function is guaranteed to be a constant in the neighborhood of each given data point, which provides a provably tighter bound than the global Lipschitz constant of the neural network. Our method can be used as a plug-in module to tighten the Lipschitz bound in many certifiable training algorithms. Furthermore, we propose to clip activation functions (e.g., ReLU and MaxMin) with a learnable upper threshold and a sparsity loss to assist the network to achieve an even tighter local Lipschitz bound. Experimentally, we show that our method consistently outperforms state-of-the-art methods in both clean and certified accuracy on MNIST, CIFAR-10 and TinyImageNet datasets with various network architectures.

cs.LG↗

arXiv2021

Demonstration of neutron radiation-induced nucleation of supercooled water

We present here direct evidence for neutrons causing nucleation of supercooled water. Highly purified water (20 nm filtration) is cooled to well below freezing (as low as -20 degrees C) with a radioactive calibration source of neutrons / gamma-rays either present or removed during each of many control cooling runs for the same volume of water. When it is primarily neutrons irradiating the sample bulk, the non-equilibrium freezing point (also known as the "supercooling point") is, on average, +0.7 degrees C warmer than the control equivalent, with a statistical significance of greater than 5 sigma, with systematic uncertainty included. This effect is not observed with water in the presence of gamma-rays instead of neutrons. While these neutrons should have theoretically had sufficient energy to mount the energy barrier, corroborating our results, their raising of supercooling temperature has never been reported experimentally to the best of our knowledge. The potential to use deeply supercooled solutions, not only water, as metastable detectors for radiation and perhaps dark matter or neutrino physics presents now a new avenue for exploration.

physics.ins-det↗

arXiv2020

Neural Networks with Recurrent Generative Feedback

Neural networks are vulnerable to input perturbations such as additive noise and adversarial attacks. In contrast, human perception is much more robust to such perturbations. The Bayesian brain hypothesis states that human brains use an internal generative model to update the posterior beliefs of the sensory input. This mechanism can be interpreted as a form of self-consistency between the maximum a posteriori (MAP) estimation of an internal generative model and the external environment. Inspired by such hypothesis, we enforce self-consistency in neural networks by incorporating generative recurrent feedback. We instantiate this design on convolutional neural networks (CNNs). The proposed framework, termed Convolutional Neural Networks with Feedback (CNN-F), introduces a generative feedback with latent variables to existing CNN architectures, where consistent predictions are made through alternating MAP inference under a Bayesian framework. In the experiments, CNN-F shows considerably improved adversarial robustness over conventional feedforward CNNs on standard benchmarks.

cs.LG↗

arXiv2019

Out-of-Distribution Detection Using Neural Rendering Generative Models

Out-of-distribution (OoD) detection is a natural downstream task for deep generative models, due to their ability to learn the input probability distribution. There are mainly two classes of approaches for OoD detection using deep generative models, viz., based on likelihood measure and the reconstruction loss. However, both approaches are unable to carry out OoD detection effectively, especially when the OoD samples have smaller variance than the training samples. For instance, both flow based and VAE models assign higher likelihood to images from SVHN when trained on CIFAR-10 images. We use a recently proposed generative model known as neural rendering model (NRM) and derive metrics for OoD. We show that NRM unifies both approaches since it provides a likelihood estimate and also carries out reconstruction in each layer of the neural network. Among various measures, we found the joint likelihood of latent variables to be the most effective one for OoD detection. Our results show that when trained on CIFAR-10, lower likelihood (of latent variables) is assigned to SVHN images. Additionally, we show that this metric is consistent across other OoD datasets. To the best of our knowledge, this is the first work to show consistently lower likelihood for OoD data with smaller variance with deep generative models.

cs.LG↗

arXiv2018

Accurate color imaging of pathology slides using holography and absorbance spectrum estimation of histochemical stains

Holographic microscopy presents challenges for color reproduction due to the usage of narrow-band illumination sources, which especially impacts the imaging of stained pathology slides for clinical diagnoses. Here, an accurate color holographic microscopy framework using absorbance spectrum estimation is presented. This method uses multispectral holographic images acquired and reconstructed at a small number (e.g., three to six) of wavelengths, estimates the absorbance spectrum of the sample, and projects it onto a color tristimulus. Using this method, the wavelength selection is optimized to holographically image 25 pathology slide samples with different tissue and stain combinations to significantly reduce color errors in the final reconstructed images. The results can be used as a practical guide for various imaging applications and, in particular, to correct color distortions in holographic imaging of pathology samples spanning different dyes and tissue types.

physics.med-ph↗

arXiv2017

Semantic-driven Generation of Hyperlapse from $360^\circ$ Video

We present a system for converting a fully panoramic ($360^\circ$) video into a normal field-of-view (NFOV) hyperlapse for an optimal viewing experience. Our system exploits visual saliency and semantics to non-uniformly sample in space and time for generating hyperlapses. In addition, users can optionally choose objects of interest for customizing the hyperlapses. We first stabilize an input $360^\circ$ video by smoothing the rotation between adjacent frames and then compute regions of interest and saliency scores. An initial hyperlapse is generated by optimizing the saliency and motion smoothness followed by the saliency-aware frame selection. We further smooth the result using an efficient 2D video stabilization approach that adaptively selects the motion model to generate the final hyperlapse. We validate the design of our system by showing results for a variety of scenes and comparing against the state-of-the-art method through a user study.

cs.CV↗

arXiv2017

Pose Invariant Embedding for Deep Person Re-identification

Pedestrian misalignment, which mainly arises from detector errors and pose variations, is a critical problem for a robust person re-identification (re-ID) system. With bad alignment, the background noise will significantly compromise the feature learning and matching process. To address this problem, this paper introduces the pose invariant embedding (PIE) as a pedestrian descriptor. First, in order to align pedestrians to a standard pose, the PoseBox structure is introduced, which is generated through pose estimation followed by affine transformations. Second, to reduce the impact of pose estimation errors and information loss during PoseBox construction, we design a PoseBox fusion (PBF) CNN architecture that takes the original image, the PoseBox, and the pose estimation confidence as input. The proposed PIE descriptor is thus defined as the fully connected layer of the PBF network for the retrieval task. Experiments are conducted on the Market-1501, CUHK03, and VIPeR datasets. We show that PoseBox alone yields decent re-ID accuracy and that when integrated in the PBF network, the learned PIE descriptor produces competitive performance compared with the state-of-the-art approaches.

cs.CV↗