arXiv subjects

Zecheng Zhang

Publications and source records attributed to Zecheng Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Enhancing Visual Question Answering through Ranking-Based Hybrid Training and Multimodal Fusion

Visual Question Answering (VQA) is a challenging task that requires systems to provide accurate answers to questions based on image content. Current VQA models struggle with complex questions due to limitations in capturing and integrating multimodal information effectively. To address these challenges, we propose the Rank VQA model, which leverages a ranking-inspired hybrid training strategy to enhance VQA performance. The Rank VQA model integrates high-quality visual features extracted using the Faster R-CNN model and rich semantic text features obtained from a pre-trained BERT model. These features are fused through a sophisticated multimodal fusion technique employing multi-head self-attention mechanisms. Additionally, a ranking learning module is incorporated to optimize the relative ranking of answers, thus improving answer accuracy. The hybrid training strategy combines classification and ranking losses, enhancing the model's generalization ability and robustness across diverse datasets. Experimental results demonstrate the effectiveness of the Rank VQA model. Our model significantly outperforms existing state-of-the-art models on standard VQA datasets, including VQA v2.0 and COCO-QA, in terms of both accuracy and Mean Reciprocal Rank (MRR). The superior performance of Rank VQA is evident in its ability to handle complex questions that require understanding nuanced details and making sophisticated inferences from the image and text. This work highlights the effectiveness of a ranking-based hybrid training strategy in improving VQA performance and lays the groundwork for further research in multimodal learning methods.

cs.CV↗

arXiv2024

Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Model

Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself provides an additional modality to identify the system. The utilization of symbolic expressions along side time-series samples allows for the development of multimodal predictive neural networks. A key challenge with current approaches is that the symbolic information, i.e. the equations, must be manually preprocessed (simplified, rearranged, etc.) to match and relate to the existing token library, which increases costs and reduces flexibility, especially when dealing with new differential equations. We propose a new token library based on SymPy to encode differential equations as an additional modality for time-series models. The proposed approach incurs minimal cost, is automated, and maintains high prediction accuracy for forecasting tasks. Additionally, we include a Bayesian filtering module that connects the different modalities to refine the learned equation. This improves the accuracy of the learned symbolic representation and the predicted time-series.

cs.LG↗

arXiv2024

PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

cs.LG↗

arXiv2024

Image anomaly detection and prediction scheme based on SSA optimized ResNet50-BiGRU model

Image anomaly detection is a popular research direction, with many methods emerging in recent years due to rapid advancements in computing. The use of artificial intelligence for image anomaly detection has been widely studied. By analyzing images of athlete posture and movement, it is possible to predict injury status and suggest necessary adjustments. Most existing methods rely on convolutional networks to extract information from irrelevant pixel data, limiting model accuracy. This paper introduces a network combining Residual Network (ResNet) and Bidirectional Gated Recurrent Unit (BiGRU), which can predict potential injury types and provide early warnings by analyzing changes in muscle and bone poses from video images. To address the high complexity of this network, the Sparrow search algorithm was used for optimization. Experiments conducted on four datasets demonstrated that our model has the smallest error in image anomaly detection compared to other models, showing strong adaptability. This provides a new approach for anomaly detection and predictive analysis in images, contributing to the sustainable development of human health and performance.

cs.CV↗

arXiv2024

Deep Analysis of Time Series Data for Smart Grid Startup Strategies: A Transformer-LSTM-PSO Model Approach

Grid startup, an integral component of the power system, holds strategic importance for ensuring the reliability and efficiency of the electrical grid. However, current methodologies for in-depth analysis and precise prediction of grid startup scenarios are inadequate. To address these challenges, we propose a novel method based on the Transformer-LSTM-PSO model. This model uniquely combines the Transformer's self-attention mechanism, LSTM's temporal modeling capabilities, and the parameter tuning features of the particle swarm optimization algorithm. It is designed to more effectively capture the complex temporal relationships in grid startup schemes. Our experiments demonstrate significant improvements, with our model achieving lower RMSE and MAE values across multiple datasets compared to existing benchmarks, particularly in the NYISO Electric Market dataset where the RMSE was reduced by approximately 15% and the MAE by 20% compared to conventional models. Our main contribution is the development of a Transformer-LSTM-PSO model that significantly enhances the accuracy and efficiency of smart grid startup predictions. The application of the Transformer-LSTM-PSO model represents a significant advancement in smart grid predictive analytics, concurrently fostering the development of more reliable and intelligent grid management systems.

cs.LG↗

arXiv2024

RelBench: A Benchmark for Deep Learning on Relational Databases

We present RelBench, a public benchmark for solving predictive tasks over relational databases with graph neural networks. RelBench provides databases and tasks spanning diverse domains and scales, and is intended to be a foundational infrastructure for future research. We use RelBench to conduct the first comprehensive study of Relational Deep Learning (RDL) (Fey et al., 2024), which combines graph neural network predictive models with (deep) tabular models that extract initial entity-level representations from raw tables. End-to-end learned RDL models fully exploit the predictive signal encoded in primary-foreign key links, marking a significant shift away from the dominant paradigm of manual feature engineering combined with tabular models. To thoroughly evaluate RDL against this prior gold-standard, we conduct an in-depth user study where an experienced data scientist manually engineers features for each task. In this study, RDL learns better models whilst reducing human work needed by more than an order of magnitude. This demonstrates the power of deep learning for solving predictive tasks over relational databases, opening up many new research opportunities enabled by RelBench.

cs.LG↗

arXiv2024

Theoretical Analysis of Meta Reinforcement Learning: Generalization Bounds and Convergence Guarantees

This research delves deeply into Meta Reinforcement Learning (Meta RL) through a exploration focusing on defining generalization limits and ensuring convergence. By employing a approach this article introduces an innovative theoretical framework to meticulously assess the effectiveness and performance of Meta RL algorithms. We present an explanation of generalization limits measuring how well these algorithms can adapt to learning tasks while maintaining consistent results. Our analysis delves into the factors that impact the adaptability of Meta RL revealing the relationship, between algorithm design and task complexity. Additionally we establish convergence assurances by proving conditions under which Meta RL strategies are guaranteed to converge towards solutions. We examine the convergence behaviors of Meta RL algorithms across scenarios providing a comprehensive understanding of the driving forces behind their long term performance. This exploration covers both convergence and real time efficiency offering a perspective, on the capabilities of these algorithms.

cs.LG↗

arXiv2024

Automatic News Generation and Fact-Checking System Based on Language Processing

This paper explores an automatic news generation and fact-checking system based on language processing, aimed at enhancing the efficiency and quality of news production while ensuring the authenticity and reliability of the news content. With the rapid development of Natural Language Processing (NLP) and deep learning technologies, automatic news generation systems are capable of extracting key information from massive data and generating well-structured, fluent news articles. Meanwhile, by integrating fact-checking technology, the system can effectively prevent the spread of false news and improve the accuracy and credibility of news. This study details the key technologies involved in automatic news generation and factchecking, including text generation, information extraction, and the application of knowledge graphs, and validates the effectiveness of these technologies through experiments. Additionally, the paper discusses the future development directions of automatic news generation and fact-checking systems, emphasizing the importance of further integration and innovation of technologies. The results show that with continuous technological optimization and practical application, these systems will play an increasingly important role in the future news industry, providing more efficient and reliable news services.

cs.CL↗

arXiv2024

Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose \textit{ReSample}, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

cs.CV↗

arXiv2024

MODNO: Multi Operator Learning With Distributed Neural Operators

The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, recent advances have rapidly expanded this to include the approximation of multiple operators using foundation models equipped with millions or billions of trainable parameters, leading to the research of multi-operator learning (MOL). In this paper, we present a novel distributed training approach aimed at enabling a single neural operator with significantly fewer parameters to effectively tackle multi-operator learning challenges, all without incurring additional average costs. Our method is applicable to various neural operators, such as Deep Operator Neural Networks (DON). The core idea is to independently learn the output basis functions for each operator using its dedicated data, while simultaneously centralizing the learning of the input function encoding shared by all operators using the entire dataset. Through a systematic study of five numerical examples, we compare the accuracy and cost of training a single neural operator for each operator independently versus training a MOL model using our proposed method. Our results demonstrate enhanced efficiency and satisfactory accuracy. Moreover, our approach illustrates that some operators with limited data can be more effectively constructed with the aid of data from analogous operators through MOL learning. This highlights another MOL's potential to bolster operator learning.

cs.LG↗

arXiv2024

Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks

In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we enhance the uncertainty quantification frameworks (B-DeepONet and Prob-DeepONet) previously proposed by the authors by using split conformal prediction. By combining conformal prediction with our Prob- and B-DeepONets, we effectively quantify uncertainty by generating rigorous confidence intervals for DeepONet prediction. Additionally, we design a novel Quantile-DeepONet that allows for a more natural use of split conformal prediction. We refer to this distribution-free effective uncertainty quantification framework as split conformal Quantile-DeepONet regression. Finally, we demonstrate the effectiveness of the proposed methods using various ordinary, partial differential equation numerical examples, and multi-fidelity learning.

cs.LG↗

arXiv2023

D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. In our study, we propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. We demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present four numerical examples to validate its performance.

math.NA↗

arXiv2023

Restoring the Discontinuous Heat Equation Source Using Sparse Boundary Data and Dynamic Sensors

This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been established that utilizing sparse boundary flux data can enable source recovery, the presence of a limited number of observation sensors poses a challenge for accurately tracing the inverse quantity of interest. To overcome this limitation, we introduce a sampling algorithm grounded in Langevin dynamics that incorporates dynamic sensors to capture the flux information. Furthermore, we propose and discuss two distinct sensor migration strategies. Remarkably, our findings demonstrate that even with only two observation sensors at our disposal, it remains feasible to successfully reconstruct the high-dimensional unknown parameters.

math.NA↗

arXiv2023

PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single solution operator (i.e., the mapping from input parametrized functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Additionally, observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our method, called Predicting Operators and Symbolic Expressions (PROSE), learns maps from multimodal inputs to multimodal outputs, capable of generating both numerical predictions and mathematical equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations using a single trained network. Detailed experiments demonstrate that the network benefits from its multimodal nature, resulting in improved prediction accuracy and better generalization. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms. PROSE provides a new neural network framework for differential equations which allows for more flexibility and generality in learning operators and governing equations from data.

cs.LG↗

arXiv2023

On Learning the Dynamical Response of Nonlinear Control Systems with Deep Operator Networks

We propose a Deep Operator Network~(DeepONet) framework to learn the dynamic response of continuous-time nonlinear control systems from data. To this end, we first construct and train a DeepONet that approximates the control system's local solution operator. Then, we design a numerical scheme that recursively uses the trained DeepONet to simulate the control system's long/medium-term dynamic response for given control inputs and initial conditions. We accompany the proposed scheme with an estimate for the error bound of the associated cumulative error. Furthermore, we design a data-driven Runge-Kutta~(RK) explicit scheme that uses the DeepONet forward pass and automatic differentiation to better approximate the system's response when the numerical scheme's step size is sufficiently small. Numerical experiments on the predator-prey, pendulum, and cart pole systems confirm that our DeepONet framework learns to approximate the dynamic response of nonlinear control systems effectively.

math.DS↗

arXiv2023

Bayesian deep operator learning for homogenized to fine-scale maps for multiscale PDE

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many inexpensive computational methods for obtaining coarse-scale solutions. Additionally, in many real-world applications, fine-scale solutions can only be observed at a limited number of locations. In order to obtain approximations or predictions of fine-scale solutions over general regions of interest, we propose to learn the operator mapping from coarse-scale solutions to fine-scale solutions using a limited number (and possibly noisy) observations of the fine-scale solutions. The approach is to train multi-fidelity homogenization maps using mathematically motivated neural operators. The operator learning framework can efficiently obtain the solution of multiscale PDEs at any arbitrary point, making our proposed framework a mesh-free solver. We verify our results on multiple numerical examples showing that our approach is an efficient mesh-free solver for multiscale PDEs.

math.NA↗

arXiv2023

A discretization-invariant extension and analysis of some deep operator networks

We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a connection between this discretization-invariant neural operator network and those discussed before. The discretization-invariance property of the operator network implies that different input functions can be sampled using various sensor locations within the same training and testing phases. Additionally, since the network learns a ``basis'' for the input and output function spaces, our approach enables the evaluation of input functions on different discretizations. To evaluate the performance of the proposed discretization-invariant neural operator, we focus on challenging examples from multiscale partial differential equations. Our experimental results indicate that the method achieves lower prediction errors compared to previous networks and benefits from its discretization-invariant property.

math.NA↗

arXiv2023

Fast Replica Exchange Stochastic Gradient Langevin Dynamics

Application of the replica exchange (i.e., parallel tempering) technique to Langevin Monte Carlo algorithms, especially stochastic gradient Langevin dynamics (SGLD), has scored great success in non-convex learning problems, but one potential limitation is the computational cost caused by running multiple chains. Upon observing that a large variance of the gradient estimator in SGLD essentially increases the temperature of the stationary distribution, we propose expediting tempering schemes for SGLD by directly estimating the bias caused by the stochastic gradient estimator. This simple idea enables us to simulate high-temperature chains at a negligible computational cost (compared to that of the low-temperature chain) while preserving the convergence to the target distribution. Our method is fundamentally different from the recently proposed m-reSGLD (multi-variance replica exchange SGLD) method in that the latter suffers from the low accuracy of the gradient estimator (e.g., the chain can fail to converge to the target) while our method benefits from it. Further, we derive a swapping rate that can be easily evaluated, providing another significant improvement over m-reSGLD. To theoretically demonstrate the advantage of our method, we develop convergence bounds in Wasserstein distances. Numerical examples for Gaussian mixture and inverse PDE models are also provided, which show that our method can converge quicker than the vanilla multi-variance replica exchange method.

math.NA↗