Xiaohui Xie

Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We develop a Bilevel Local Operator Learning framework for Bayesian inference in PDEs (B-BiLO). At the upper level, we sample parameters from the posterior via Hamiltonian Monte Carlo, while at the lower level we fine-tune a neural network via low-rank adaptation (LoRA) to approximate the solution operator locally. B-BiLO enables efficient gradient-based sampling without synthetic data or adjoint equations and avoids sampling in high-dimensional weight space, as in Bayesian neural networks, by optimizing weights deterministically. We analyze errors from approximate lower-level optimization and establish their impact on posterior accuracy. Numerical experiments across PDE models, including tumor growth, demonstrate that B-BiLO achieves accurate and efficient uncertainty quantification. MSC Classification: 65M32, 62F15, 68T07

We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to locally approximate the PDE solution operator in the neighborhood of a given set of PDE parameters, which enables an accurate approximation of the descent direction for the upper level optimization problem. The lower level loss function includes the least-square penalty of both the residual and its derivative with respect to the PDE parameters. We apply gradient descent simultaneously on both the upper and lower level optimization problems, leading to an effective and fast algorithm. The method, which we refer to as BiLO (Bilevel Local Operator learning), is also able to efficiently infer unknown functions in the PDEs through the introduction of an auxiliary variable. We provide a theoretical analysis that justifies our approach. Through extensive experiments over multiple PDE systems, we demonstrate that our method enforces strong PDE constraints, is robust to sparse and noisy data, and eliminates the need to balance the residual and the data loss, which is inherent to the soft PDE constraints in many existing methods.

Graph Neural Networks (GNNs) have demonstrated impressive performance across various graph-structured datasets and applications. However, their message-passing mechanisms primarily capture local information, limiting their ability to model long-range dependencies. While existing approaches enhance aggregation methods to incorporate local neighbor features, expanding the receptive field in globally aware GNNs increases model complexity, complicating the training of highcomplexity architectures. Community information, which uncovers the intrinsic graph structure, can address these limitations. To this end, we propose a Community-Aware Graph Neural Network (CAG) framework that leverages contrastive learning to enhance global feature extraction through community-aware modeling. To handle challenges such as heterogeneous community sizes and noise, CAG employs a Community Subgraph Explorer guided by Monte Carlo tree search, which identifies dense subgraphs as representative structures to mitigate noise. Extensive experiments show that CAG substantially improves GNN performance in node classification, outperforming backbone models with stateof-the-art accuracy gains (+4.09% by CAG (GCN) on CiteSeer) while maintaining acceptable computational overhead compared to backbone models. Our findings underscore the efficacy of community-aware frameworks in enhancing global information aggregation in traditional GNNs.

In this study, we propose MoME, a Mixture of Visual Language Medical Experts, for Medical Image Segmentation. MoME adapts the successful Mixture of Experts (MoE) paradigm, widely used in Large Language Models (LLMs), for medical vision-language tasks. The architecture enables dynamic expert selection by effectively utilizing multi-scale visual features tailored to the intricacies of medical imagery, enriched with textual embeddings. This work explores a novel integration of vision-language models for this domain. Utilizing an assembly of 10 datasets, encompassing 3,410 CT scans, MoME demonstrates strong performance on a comprehensive medical imaging segmentation benchmark. Our approach explores the integration of foundation models for medical imaging, benefiting from the established efficacy of MoE in boosting model performance by incorporating textual information. Demonstrating competitive precision across multiple datasets, MoME explores a novel architecture for achieving robust results in medical image analysis.

Single-view novel view synthesis, the task of generating images from new viewpoints based on a single reference image, is important but challenging in computer vision. Recent advancements in novel view synthesis have leveraged Denoising Diffusion Probabilistic Models for their exceptional ability to produce high-fidelity images. However, current diffusion-based methods typically utilize camera pose matrices to globally and implicitly enforce 3D constraints, which can lead to inconsistencies in images generated from varying viewpoints, particularly in regions with complex textures and structures. To address these limitations, we present Light Field Diffusion, a novel conditional diffusion-based approach that transcends the conventional reliance on camera pose matrices. Starting from the camera pose matrices, Light Field Diffusion transforms them into light field encodings, with the same shape as the reference image, to describe the direction of each ray. By integrating the light field encoding with the reference image, our method imposes local pixel-wise constraints within the diffusion process, fostering enhanced view consistency. Our approach not only involves training Image Light Field Diffusion on the ShapeNet Car dataset but also includes fine-tuning a pre-trained latent diffusion model on the Objaverse dataset, which enables our Latent Light Field Diffusion model to exhibit remarkable zero-shot generalization capabilities across out-of-distribution datasets like the Ray-traced multi-view synthetic dataset, Google Scanned Objects dataset, and in-the-wild images. Experiments demonstrate that Light Field Diffusion produces high-fidelity images and achieves superior consistency in complex regions, outperforming existing novel view synthesis methods.

Retinal hemorrhage (RH) is a significant clinical finding with various etiologies, necessitating accurate classification for effective management. This study aims to externally validate deep learning (DL) models, specifically FastVit_SA12 and ResNet18, for distinguishing between traumatic and medical causes of RH using diverse fundus photography datasets. A comprehensive dataset was compiled, including private collections from South Korea and Virginia, alongside publicly available datasets such as RFMiD, BRSET, and DeepEyeNet. The models were evaluated on a total of 2661 images, achieving high performance metrics. FastVit_SA12 demonstrated an overall accuracy of 96.99%, with a precision of 0.9935 and recall of 0.9723 for medical cases, while ResNet18 achieved a 94.66% accuracy with a precision of 0.9893. A Grad-CAM analysis revealed that ResNet18 emphasized global vascular patterns, such as arcuate vessels, while FastVit_SA12 focused on clinically relevant areas, including the optic disk and hemorrhagic regions. Medical cases showed localized activations, whereas trauma-related images displayed diffuse patterns across the fundus. Both models exhibited strong sensitivity and specificity, indicating their potential utility in clinical settings for accurate RH diagnosis. This study underscores the importance of external validation in enhancing the reliability and applicability of AI models in ophthalmology, paving the way for improved patient care and outcomes.

Protein language models have shown great promise in predicting protein structure, function, and the effects of missense variants on protein fitness. However, their use has been limited by the substantial computational resources required. In this work, we focus on improving the computational efficiency of protein language models (PLMs), specifically the Evolutionary Scale Modeling (ESM) family, to increase the accessibility of PLMs. By implementing optimizations such as FlashAttention and Partition-Attention, a novel technique designed to handle proteins of variable length, we achieved a 16-fold speedup in inference time and reduced memory usage by 3 to 14 times for long proteins. Additionally, 4-bit quantization applied to billion-parameter models led to a 2 to 3 times reduction in memory consumption with minimal performance loss in the missense variant effect prediction task. Training efficiency was also improved, with a 6-fold reduction in runtime achieved through activation checkpointing and the DeepSpeed Zero-Offload strategy. For fine-tuning, we employed parameter-efficient methods, enabling state-of-the-art predictions of protein properties and functions by training only the model head or a small fraction of adapter weights. For instance, we achieved a Spearman’s correlation coefficient of 70% in melting point prediction and an 87% area under the precision-recall curve (AU-PRC) for transcription factor prediction. Our efficient ESM (ESME) implementation significantly lowers the barrier to using these powerful models, making them accessible to academic laboratories with limited computational resources. The ESME implementation is available on PyPI ( pypi.org/project/esm-efficient ) and GitHub ( github.com/uci-cbcl/esm-efficient ).