arXiv subjects

Yizheng Wang

Publications and source records attributed to Yizheng Wang.

33 records · Page 2Linked to original sources

arXiv2025

Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptation

AI for PDEs has garnered significant attention, particularly Physics-Informed Neural Networks (PINNs). However, PINNs are typically limited to solving specific problems, and any changes in problem conditions necessitate retraining. Therefore, we explore the generalization capability of transfer learning in the strong and energy form of PINNs across different boundary conditions, materials, and geometries. The transfer learning methods we employ include full finetuning, lightweight finetuning, and Low-Rank Adaptation (LoRA). The results demonstrate that full finetuning and LoRA can significantly improve convergence speed while providing a slight enhancement in accuracy.

cs.LG↗

arXiv2025

Energy-based physics-informed neural network for frictionless contact problems under large deformation

Numerical methods for contact mechanics are of great importance in engineering applications, enabling the prediction and analysis of complex surface interactions under various conditions. In this work, we propose an energy-based physics-informed neural network (PINNs) framework for solving frictionless contact problems under large deformation. Inspired by microscopic Lennard-Jones potential, a surface contact energy is used to describe the contact phenomena. To ensure the robustness of the proposed PINN framework, relaxation, gradual loading and output scaling techniques are introduced. In the numerical examples, the well-known Hertz contact benchmark problem is conducted, demonstrating the effectiveness and robustness of the proposed PINNs framework. Moreover, challenging contact problems with the consideration of geometrical and material nonlinearities are tested. It has been shown that the proposed PINNs framework provides a reliable and powerful tool for nonlinear contact mechanics. More importantly, the proposed PINNs framework exhibits competitive computational efficiency to the commercial FEM software when dealing with those complex contact problems. The codes used in this manuscript are available at https://github.com/JinshuaiBai/energy_PINN_Contact.(The code will be available after acceptance)

cs.CE↗

arXiv2024

Applications of Scientific Machine Learning for the Analysis of Functionally Graded Porous Beams

This study investigates different Scientific Machine Learning (SciML) approaches for the analysis of functionally graded (FG) porous beams and compares them under a new framework. The beam material properties are assumed to vary as an arbitrary continuous function. The methods consider the output of a neural network/operator as an approximation to the displacement fields and derive the equations governing beam behavior based on the continuum formulation. The methods are implemented in the framework and formulated by three approaches: (a) the vector approach leads to a Physics-Informed Neural Network (PINN), (b) the energy approach brings about the Deep Energy Method (DEM), and (c) the data-driven approach, which results in a class of Neural Operator methods. Finally, a neural operator has been trained to predict the response of the porous beam with functionally graded material under any porosity distribution pattern and any arbitrary traction condition. The results are validated with analytical and numerical reference solutions. The data and code accompanying this manuscript will be publicly available at https://github.com/eshaghi-ms/DeepNetBeam.

cs.LG↗

arXiv2024

Variational Physics-informed Neural Operator (VINO) for Solving Partial Differential Equations

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or boundary conditions or different input configurations. This study proposes the Variational Physics-Informed Neural Operator (VINO), a deep learning method designed for solving PDEs by minimizing the energy formulation of PDEs. This framework can be trained without any labeled data, resulting in improved performance and accuracy compared to existing deep learning methods and conventional PDE solvers. By discretizing the domain into elements, the variational format allows VINO to overcome the key challenge in physics-informed neural operators, namely the efficient evaluation of the governing equations for computing the loss. Comparative results demonstrate VINO's superior performance, especially as the mesh resolution increases. As a result, this study suggests a better way to incorporate physical laws into neural operators, opening a new approach for modeling and simulating nonlinear and complex processes in science and engineering.

math.AP↗

arXiv2024

DCEM: A deep complementary energy method for solid mechanics

In recent years, the rapid advancement of deep learning has significantly impacted various fields, particularly in solving partial differential equations (PDEs) in the realm of solid mechanics, benefiting greatly from the remarkable approximation capabilities of neural networks. In solving PDEs, Physics-Informed Neural Networks (PINNs) and the Deep Energy Method (DEM) have garnered substantial attention. The principle of minimum potential energy and complementary energy are two important variational principles in solid mechanics. However, the well-known Deep Energy Method (DEM) is based on the principle of minimum potential energy, but there lacks the important form of minimum complementary energy. To bridge this gap, we propose the deep complementary energy method (DCEM) based on the principle of minimum complementary energy. The output function of DCEM is the stress function, which inherently satisfies the equilibrium equation. We present numerical results using the Prandtl and Airy stress functions, and compare DCEM with existing PINNs and DEM algorithms when modeling representative mechanical problems. The results demonstrate that DCEM outperforms DEM in terms of stress accuracy and efficiency and has an advantage in dealing with complex displacement boundary conditions, which is supported by theoretical analyses and numerical simulations. We extend DCEM to DCEM-Plus (DCEM-P), adding terms that satisfy partial differential equations. Furthermore, we propose a deep complementary energy operator method (DCEM-O) by combining operator learning with physical equations. Initially, we train DCEM-O using high-fidelity numerical results and then incorporate complementary energy. DCEM-P and DCEM-O further enhance the accuracy and efficiency of DCEM.

cs.LG↗

arXiv2024

Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks

AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov-Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in various forms, such as strong form, energy form, and inverse form. While mathematically equivalent, these forms are not computationally equivalent, making the exploration of different PDE formulations significant in computational physics. Thus, we propose different PDE forms based on KAN instead of MLP, termed Kolmogorov-Arnold-Informed Neural Network (KINN) for solving forward and inverse problems. We systematically compare MLP and KAN in various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Our results demonstrate that KINN significantly outperforms MLP regarding accuracy and convergence speed for numerous PDEs in computational solid mechanics, except for the complex geometry problem. This highlights KINN's potential for more efficient and accurate PDE solutions in AI for PDEs.

cs.LG↗

arXiv2024

An Experimental Study on Exploring Strong Lightweight Vision Transformers via Masked Image Modeling Pre-Training

Masked image modeling (MIM) pre-training for large-scale vision transformers (ViTs) has enabled promising downstream performance on top of the learned self-supervised ViT features. In this paper, we question if the \textit{extremely simple} lightweight ViTs' fine-tuning performance can also benefit from this pre-training paradigm, which is considerably less studied yet in contrast to the well-established lightweight architecture design methodology. We use an observation-analysis-solution flow for our study. We first systematically observe different behaviors among the evaluated pre-training methods with respect to the downstream fine-tuning data scales. Furthermore, we analyze the layer representation similarities and attention maps across the obtained models, which clearly show the inferior learning of MIM pre-training on higher layers, leading to unsatisfactory transfer performance on data-insufficient downstream tasks. This finding is naturally a guide to designing our distillation strategies during pre-training to solve the above deterioration problem. Extensive experiments have demonstrated the effectiveness of our approach. Our pre-training with distillation on pure lightweight ViTs with vanilla/hierarchical design ($5.7M$/$6.5M$) can achieve $79.4\%$/$78.9\%$ top-1 accuracy on ImageNet-1K. It also enables SOTA performance on the ADE20K segmentation task ($42.8\%$ mIoU) and LaSOT tracking task ($66.1\%$ AUC) in the lightweight regime. The latter even surpasses all the current SOTA lightweight CPU-realtime trackers.

cs.CV↗

arXiv2023

SBSM-Pro: Support Bio-sequence Machine for Proteins

Proteins play a pivotal role in biological systems. The use of machine learning algorithms for protein classification can assist and even guide biological experiments, offering crucial insights for biotechnological applications. We introduce the Support Bio-Sequence Machine for Proteins (SBSM-Pro), a model purpose-built for the classification of biological sequences. This model starts with raw sequences and groups amino acids based on their physicochemical properties. It incorporates sequence alignment to measure the similarities between proteins and uses a novel multiple kernel learning (MKL) approach to integrate various types of information, utilizing support vector machines for classification prediction. The results indicate that our model demonstrates commendable performance across ten datasets in terms of the identification of protein function and posttranslational modification. This research not only exemplifies state-of-the-art work in protein classification but also paves avenues for new directions in this domain, representing a beneficial endeavor in the development of platforms tailored for the classification of biological sequences. SBSM-Pro is available for access at http://lab.malab.cn/soft/SBSM-Pro/.

q-bio.QM↗

arXiv2023

ZoomTrack: Target-aware Non-uniform Resizing for Efficient Visual Tracking

Recently, the transformer has enabled the speed-oriented trackers to approach state-of-the-art (SOTA) performance with high-speed thanks to the smaller input size or the lighter feature extraction backbone, though they still substantially lag behind their corresponding performance-oriented versions. In this paper, we demonstrate that it is possible to narrow or even close this gap while achieving high tracking speed based on the smaller input size. To this end, we non-uniformly resize the cropped image to have a smaller input size while the resolution of the area where the target is more likely to appear is higher and vice versa. This enables us to solve the dilemma of attending to a larger visual field while retaining more raw information for the target despite a smaller input size. Our formulation for the non-uniform resizing can be efficiently solved through quadratic programming (QP) and naturally integrated into most of the crop-based local trackers. Comprehensive experiments on five challenging datasets based on two kinds of transformer trackers, \ie, OSTrack and TransT, demonstrate consistent improvements over them. In particular, applying our method to the speed-oriented version of OSTrack even outperforms its performance-oriented counterpart by 0.6% AUC on TNL2K, while running 50% faster and saving over 55% MACs. Codes and models are available at https://github.com/Kou-99/ZoomTrack.

cs.CV↗

arXiv2023

Multi-scale modeling in thermal conductivity of Polyurethane incorporated with Phase Change Materials using Physics-Informed Neural Networks

Polyurethane (PU) possesses excellent thermal properties, making it an ideal material for thermal insulation. Incorporating Phase Change Materials (PCMs) capsules into Polyurethane (PU) has proven to be an effective strategy for enhancing building envelopes. This innovative design substantially enhances indoor thermal stability and minimizes fluctuations in indoor air temperature. To investigate the thermal conductivity of the PU-PCM foam composite, we propose a hierarchical multi-scale model utilizing Physics-Informed Neural Networks (PINNs). This model allows accurate prediction and analysis of the material's thermal conductivity at both the meso-scale and macro-scale. By leveraging the integration of physics-based knowledge and data-driven learning offered by PINNs, we effectively tackle inverse problems and address complex multi-scale phenomena. Furthermore, the obtained thermal conductivity data facilitates the optimization of material design. To fully consider the occupants' thermal comfort within a building envelope, we conduct a case study evaluating the performance of this optimized material in a single room. Simultaneously, we predict the energy consumption associated with this scenario. All outcomes demonstrate the promising nature of this design, enabling passive building energy design and significantly improving occupants' comfort. The successful development of this PINNs-based multi-scale model holds immense potential for advancing our understanding of PU-PCM's thermal properties. It can contribute to the design and optimization of materials for various practical applications, including thermal energy storage systems and insulation design in advanced building envelopes.

physics.comp-ph↗

arXiv2023

Optimizing Carbon Storage Operations for Long-Term Safety

To combat global warming and mitigate the risks associated with climate change, carbon capture and storage (CCS) has emerged as a crucial technology. However, safely sequestering CO2 in geological formations for long-term storage presents several challenges. In this study, we address these issues by modeling the decision-making process for carbon storage operations as a partially observable Markov decision process (POMDP). We solve the POMDP using belief state planning to optimize injector and monitoring well locations, with the goal of maximizing stored CO2 while maintaining safety. Empirical results in simulation demonstrate that our approach is effective in ensuring safe long-term carbon storage operations. We showcase the flexibility of our approach by introducing three different monitoring strategies and examining their impact on decision quality. Additionally, we introduce a neural network surrogate model for the POMDP decision-making process to handle the complex dynamics of the multi-phase flow. We also investigate the effects of different fidelity levels of the surrogate model on decision qualities.

cs.AI↗

arXiv2023

BINN: A deep learning approach for computational mechanics problems based on boundary integral equations

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are approximated using neural networks and solved through a training process. The loss function is chosen as the residuals of the boundary integral equations. Regularization techniques are adopted to efficiently evaluate the weakly singular and Cauchy principle integrals in boundary integral equations. Potential problems and elastostatic problems are mainly concerned in this article as a demonstration. The proposed method has several outstanding advantages: First, the dimensions of the original problem are reduced by one, thus the freedoms are greatly reduced. Second, the proposed method does not require any extra treatment to introduce the boundary conditions, since they are naturally considered through the boundary integral equations. Therefore, the method is suitable for complex geometries. Third, BINN is suitable for problems on the infinite or semi-infinite domains. Moreover, BINN can easily handle heterogeneous problems with a single neural network without domain decomposition.

cs.LG↗

arXiv2022

CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries

We propose a conservative energy method based on neural networks with subdomains for solving variational problems (CENN), where the admissible function satisfying the essential boundary condition without boundary penalty is constructed by the radial basis function (RBF), particular solution neural network, and general neural network. The loss term is the potential energy, optimized based on the principle of minimum potential energy. The loss term at the interfaces has the lower order derivative compared to the strong form PINN with subdomains. The advantage of the proposed method is higher efficiency, more accurate, and less hyperparameters than the strong form PINN with subdomains. Another advantage of the proposed method is that it can apply to complex geometries based on the special construction of the admissible function. To analyze its performance, the proposed method CENN is used to model representative PDEs, the examples include strong discontinuity, singularity, complex boundary, non-linear, and heterogeneous problems. Furthermore, it outperforms other methods when dealing with heterogeneous problems.

math.NA↗

arXiv2022

A POMDP Model for Safe Geological Carbon Sequestration

Geological carbon capture and sequestration (CCS), where CO$_2$ is stored in subsurface formations, is a promising and scalable approach for reducing global emissions. However, if done incorrectly, it may lead to earthquakes and leakage of CO$_2$ back to the surface, harming both humans and the environment. These risks are exacerbated by the large amount of uncertainty in the structure of the storage formation. For these reasons, we propose that CCS operations be modeled as a partially observable Markov decision process (POMDP) and decisions be informed using automated planning algorithms. To this end, we develop a simplified model of CCS operations based on a 2D spillpoint analysis that retains many of the challenges and safety considerations of the real-world problem. We show how off-the-shelf POMDP solvers outperform expert baselines for safe CCS planning. This POMDP model can be used as a test bed to drive the development of novel decision-making algorithms for CCS operations.

physics.geo-ph↗

arXiv2022

PETS-SWINF: A regression method that considers images with metadata based Neural Network for pawpularity prediction on 2021 Kaggle Competition "PetFinder.my"

Millions of stray animals suffer on the streets or are euthanized in shelters every day around the world. In order to better adopt stray animals, scoring the pawpularity (cuteness) of stray animals is very important, but evaluating the pawpularity of animals is a very labor-intensive thing. Consequently, there has been an urgent surge of interest to develop an algorithm that scores pawpularity of animals. However, the dataset in Kaggle not only has images, but also metadata describing images. Most methods basically focus on the most advanced image regression methods in recent years, but there is no good method to deal with the metadata of images. To address the above challenges, the paper proposes an image regression model called PETS-SWINF that considers metadata of the images. Our results based on a dataset of Kaggle competition, "PetFinder.my", show that PETS-SWINF has an advantage over only based images models. Our results shows that the RMSE loss of the proposed model on the test dataset is 17.71876 but 17.76449 without metadata. The advantage of the proposed method is that PETS-SWINF can consider both low-order and high-order features of metadata, and adaptively adjust the weights of the image model and the metadata model. The performance is promising as our leadboard score is ranked 15 out of 3545 teams (Gold medal) currently for 2021 Kaggle competition on the challenge "PetFinder.my".

cs.CV↗