Guannan Zhang

Zezhong Zhang, Feng Bao, Guannan Zhang

The Ensemble Score Filter (EnSF) is a score-based diffusion model approach for solving high-dimensional and nonlinear data assimilation problems. While initial applications of EnSF to the Lorenz-96 model and the quasi-geostrophic system showed potential, the current method employs a heuristic weighted sum to combine the prior and the likelihood score functions. This introduces a structural error into the estimation of the posterior score function in the nonlinear setting. This work addresses this challenge by developing an iterative ensemble score filter (IEnSF) that applies an iterative algorithm as an outer loop around the reverse-time stochastic differential equation solver. When the state dynamics or the observation operator is nonlinear, the iterative algorithm can gradually reduce the posterior score estimation error by improving the accuracy of approximating the conditional expectation of the likelihood score function. The number of iterations required depends on the distance between the prior and posterior distributions. Numerical experiments demonstrate that the IEnSF algorithm substantially reduces the error in posterior score estimation in the nonlinear setting and thus improves the accuracy of tracking high-dimensional dynamical systems.

Max Gunzburger, Michael Schneier, Clayton Webster et al.

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. The goal is to recover the entire solution map from the parameter space to the finite element space. To this end, first, a reduced-basis solution using a weak greedy algorithm is constructed, then a DLS approximation is determined by evaluating the reduced-basis approximation instead of the full finite element approximation. The main advantage of the new approach is that one only need apply the DLS operator to the coefficients of the reduced-basis expansion, resulting in huge savings in both the storage of the DLS coefficients and the online cost of evaluating the DLS approximation. In addition, the recently developed quasi-optimal polynomial space is also adopted in the new approach, resulting in superior convergence rates for a wider class of problems than previous analyzed. Numerical experiments are provided that illustrate the theoretical results.

Lei Liu, Xiaoyan Yang, Yue Shen et al.

Memory-augmented Large Language Models (LLMs) have demonstrated remarkable performance in long-term human-machine interactions, which basically relies on iterative recalling and reasoning of history to generate high-quality responses. However, such repeated recall-reason steps easily produce biased thoughts, \textit{i.e.}, inconsistent reasoning results when recalling the same history for different questions. On the contrary, humans can keep thoughts in the memory and recall them without repeated reasoning. Motivated by this human capability, we propose a novel memory mechanism called TiM (Think-in-Memory) that enables LLMs to maintain an evolved memory for storing historical thoughts along the conversation stream. The TiM framework consists of two crucial stages: (1) before generating a response, a LLM agent recalls relevant thoughts from memory, and (2) after generating a response, the LLM agent post-thinks and incorporates both historical and new thoughts to update the memory. Thus, TiM can eliminate the issue of repeated reasoning by saving the post-thinking thoughts as the history. Besides, we formulate the basic principles to organize the thoughts in memory based on the well-established operations, (\textit{i.e.}, insert, forget, and merge operations), allowing for dynamic updates and evolution of the thoughts. Furthermore, we introduce Locality-Sensitive Hashing into TiM to achieve efficient retrieval for the long-term conversations. We conduct qualitative and quantitative experiments on real-world and simulated dialogues covering a wide range of topics, demonstrating that equipping existing LLMs with TiM significantly enhances their performance in generating responses for long-term interactions.

Lin Mu, Guannan Zhang

We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the convection-dominated transport equations with random velocities. We investigate the equations with two types of random fields, i.e., colored noises and discrete white noises, both of which can lead to high-dimensional parametric dependence. The motivation is to use domain decomposition to exploit low-dimensional structures of local problems in the sub-domains, such that the total number of expensive PDE solves can be greatly reduced. Our objective is to develop an efficient model reduction method to simultaneously handle high-dimensionality and irregular behaviors of the stochastic PDEs under consideration. The advantages of our method lie in three aspects: (i) online-offline decomposition, i.e., the online cost is independent of the size of the triangle mesh; (ii) operator approximation for handling non-affine and high-dimensional random fields; (iii) effective strategy to capture irregular behaviors, e.g., sharp transitions of the PDE solution. Two numerical examples will be provided to demonstrate the advantageous performance of our method.

Weifan Wang, Binbin Hu, Zhicheng Peng et al.

Recently, the growth of service platforms brings great convenience to both users and merchants, where the service search engine plays a vital role in improving the user experience by quickly obtaining desirable results via textual queries. Unfortunately, users' uncontrollable search customs usually bring vast amounts of long-tail queries, which severely threaten the capability of search models. Inspired by recently emerging graph neural networks (GNNs) and contrastive learning (CL), several efforts have been made in alleviating the long-tail issue and achieve considerable performance. Nevertheless, they still face a few major weaknesses. Most importantly, they do not explicitly utilize the contextual structure between heads and tails for effective knowledge transfer, and intention-level information is commonly ignored for more generalized representations. To this end, we develop a novel framework GARCIA, which exploits the graph based knowledge transfer and intention based representation generalization in a contrastive setting. In particular, we employ an adaptive encoder to produce informative representations for queries and services, as well as hierarchical structure aware representations of intentions. To fully understand tail queries and services, we equip GARCIA with a novel multi-granularity contrastive learning module, which powers representations through knowledge transfer, structure enhancement and intention generalization. Subsequently, the complete GARCIA is well trained in a pre-training&fine-tuning manner. At last, we conduct extensive experiments on both offline and online environments, which demonstrates the superior capability of GARCIA in improving tail queries and overall performance in service search scenarios.

You Zhou, Xiujing Lin, Xiang Zhang et al.

Artificial Intelligence (AI) has achieved significant advancements in technology and research with the development over several decades, and is widely used in many areas including computing vision, natural language processing, time-series analysis, speech synthesis, etc. During the age of deep learning, especially with the arise of Large Language Models, a large majority of researchers' attention is paid on pursuing new state-of-the-art (SOTA) results, resulting in ever increasing of model size and computational complexity. The needs for high computing power brings higher carbon emission and undermines research fairness by preventing small or medium-sized research institutions and companies with limited funding in participating in research. To tackle the challenges of computing resources and environmental impact of AI, Green Computing has become a hot research topic. In this survey, we give a systematic overview of the technologies used in Green Computing. We propose the framework of Green Computing and devide it into four key components: (1) Measures of Greenness, (2) Energy-Efficient AI, (3) Energy-Efficient Computing Systems and (4) AI Use Cases for Sustainability. For each components, we discuss the research progress made and the commonly used techniques to optimize the AI efficiency. We conclude that this new research direction has the potential to address the conflicts between resource constraints and AI development. We encourage more researchers to put attention on this direction and make AI more environmental friendly.

Zhaoxin Huan, Ke Ding, Ang Li et al.

Click-through rate (CTR) prediction is a crucial issue in recommendation systems. There has been an emergence of various public CTR datasets. However, existing datasets primarily suffer from the following limitations. Firstly, users generally click different types of items from multiple scenarios, and modeling from multiple scenarios can provide a more comprehensive understanding of users. Existing datasets only include data for the same type of items from a single scenario. Secondly, multi-modal features are essential in multi-scenario prediction as they address the issue of inconsistent ID encoding between different scenarios. The existing datasets are based on ID features and lack multi-modal features. Third, a large-scale dataset can provide a more reliable evaluation of models, fully reflecting the performance differences between models. The scale of existing datasets is around 100 million, which is relatively small compared to the real-world CTR prediction. To address these limitations, we propose AntM$^{2}$C, a Multi-Scenario Multi-Modal CTR dataset based on industrial data from Alipay. Specifically, AntM$^{2}$C provides the following advantages: 1) It covers CTR data of 5 different types of items, providing insights into the preferences of users for different items, including advertisements, vouchers, mini-programs, contents, and videos. 2) Apart from ID-based features, AntM$^{2}$C also provides 2 multi-modal features, raw text and image features, which can effectively establish connections between items with different IDs. 3) AntM$^{2}$C provides 1 billion CTR data with 200 features, including 200 million users and 6 million items. It is currently the largest-scale CTR dataset available. Based on AntM$^{2}$C, we construct several typical CTR tasks and provide comparisons with baseline methods. The dataset homepage is available at https://www.atecup.cn/home.

Zezhong Zhang, Feng Bao, Lili Ju et al.

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as its formulation and/or data of its solution for pre-training. In this work, we propose to construct transferable neural feature spaces from purely function approximation perspectives without using PDE information. The construction of the feature space involves re-parameterization of the hidden neurons and uses auxiliary functions to tune the resulting feature space. Theoretical analysis shows the high quality of the produced feature space, i.e., uniformly distributed neurons. Extensive numerical experiments verify the outstanding performance of our method, including significantly improved transferability, e.g., using the same feature space for various PDEs with different domains and boundary conditions, and the superior accuracy, e.g., several orders of magnitude smaller mean squared error than the state of the art methods.

Yanfang Liu, Minglei Yang, Zezhong Zhang et al.

We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require to use reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the UCI repository.

Junqi Yin, Siming Liang, Siyan Liu et al.

The weather and climate domains are undergoing a significant transformation thanks to advances in AI-based foundation models such as FourCastNet, GraphCast, ClimaX and Pangu-Weather. While these models show considerable potential, they are not ready yet for operational use in weather forecasting or climate prediction. This is due to the lack of a data assimilation method as part of their workflow to enable the assimilation of incoming Earth system observations in real time. This limitation affects their effectiveness in predicting complex atmospheric phenomena such as tropical cyclones and atmospheric rivers. To overcome these obstacles, we introduce a generic real-time data assimilation framework and demonstrate its end-to-end performance on the Frontier supercomputer. This framework comprises two primary modules: an ensemble score filter (EnSF), which significantly outperforms the state-of-the-art data assimilation method, namely, the Local Ensemble Transform Kalman Filter (LETKF); and a vision transformer-based surrogate capable of real-time adaptation through the integration of observational data. The ViT surrogate can represent either physics-based models or AI-based foundation models. We demonstrate both the strong and weak scaling of our framework up to 1024 GPUs on the Exascale supercomputer, Frontier. Our results not only illustrate the framework's exceptional scalability on high-performance computing systems, but also demonstrate the importance of supercomputers in real-time data assimilation for weather and climate predictions. Even though the proposed framework is tested only on a benchmark surface quasi-geostrophic (SQG) turbulence system, it has the potential to be combined with existing AI-based foundation models, making it suitable for future operational implementations.

Yiming Wang, Yu Lin, Xiaodong Zeng et al.

LoRA achieves remarkable resource efficiency and comparable performance when adapting LLMs for specific tasks. Since ChatGPT demonstrated superior performance on various tasks, there has been a growing desire to adapt one model for all tasks. However, the explicit low-rank of LoRA limits the adaptation performance in complex multi-task scenarios. LoRA is dominated by a small number of top singular vectors while fine-tuning decomposes into a set of less important unitary transforms. In this paper, we propose MultiLoRA for better multi-task adaptation by reducing the dominance of top singular vectors observed in LoRA. MultiLoRA scales LoRA modules horizontally and change parameter initialization of adaptation matrices to reduce parameter dependency, thus yields more balanced unitary subspaces. We unprecedentedly construct specialized training data by mixing datasets of instruction follow, natural language understanding, world knowledge, to cover semantically and syntactically different samples. With only 2.5% of additional parameters, MultiLoRA outperforms single LoRA counterparts and fine-tuning on multiple benchmarks and model scales. Further investigation into weight update matrices of MultiLoRA exhibits reduced dependency on top singular vectors and more democratic unitary transform contributions.

Yiming Wang, Yu Lin, Xiaodong Zeng et al.

End users face a choice between privacy and efficiency in current Large Language Model (LLM) service paradigms. In cloud-based paradigms, users are forced to compromise data locality for generation quality and processing speed. Conversely, edge device paradigms maintain data locality but fail to deliver satisfactory performance. In this work, we propose a novel LLM service paradigm that distributes privacy-sensitive computation on edge devices and shared computation in the cloud. Only activations are transmitted between the central cloud and edge devices to ensure data locality. Our core innovation, PrivateLoRA, addresses the challenging communication overhead by exploiting the low rank of residual activations, achieving over 95% communication reduction. Consequently, PrivateLoRA effectively maintains data locality and is extremely resource efficient. Under standard 5G networks, PrivateLoRA achieves throughput over 300% of device-only solutions for 7B models and over 80% of an A100 GPU for 33B models. PrivateLoRA also provides tuning performance comparable to LoRA for advanced personalization. Our approach democratizes access to state-of-the-art generative AI for edge devices, paving the way for more tailored LLM experiences for the general public. To our knowledge, our proposed framework is the first efficient and privacy-preserving LLM solution in the literature.

Ming Fan, Zezhong Zhang, Dan Lu et al.

We introduce GenAI4UQ, a software package for inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting in scientific applications. GenAI4UQ leverages a generative artificial intelligence (AI) based conditional modeling framework to address the limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of model input parameters and generation of output predictions directly from observations. The software's design allows for rapid ensemble forecasting with robust uncertainty quantification, while maintaining high computational and storage efficiency. GenAI4UQ simplifies the model training process through built-in auto-tuning of hyperparameters, making it accessible to users with varying levels of expertise. Its conditional generative framework ensures versatility, enabling applicability across a wide range of scientific domains. At its core, GenAI4UQ transforms the paradigm of inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling. (The code and data are available at https://github.com/patrickfan/GenAI4UQ).

Yichen Li, Qunwei Li, Haozhao Wang et al.

In Federated Learning (FL), the data in each client is typically assumed fixed or static. However, data often comes in an incremental manner in real-world applications, where the data domain may increase dynamically. In this work, we study catastrophic forgetting with data heterogeneity in Federated Incremental Learning (FIL) scenarios where edge clients may lack enough storage space to retain full data. We propose to employ a simple, generic framework for FIL named Re-Fed, which can coordinate each client to cache important samples for replay. More specifically, when a new task arrives, each client first caches selected previous samples based on their global and local importance. Then, the client trains the local model with both the cached samples and the samples from the new task. Theoretically, we analyze the ability of Re-Fed to discover important samples for replay thus alleviating the catastrophic forgetting problem. Moreover, we empirically show that Re-Fed achieves competitive performance compared to state-of-the-art methods.

Zhitian Xie, Yinger Zhang, Chenyi Zhuang et al.

The application of mixture-of-experts (MoE) is gaining popularity due to its ability to improve model's performance. In an MoE structure, the gate layer plays a significant role in distinguishing and routing input features to different experts. This enables each expert to specialize in processing their corresponding sub-tasks. However, the gate's routing mechanism also gives rise to narrow vision: the individual MoE's expert fails to use more samples in learning the allocated sub-task, which in turn limits the MoE to further improve its generalization ability. To effectively address this, we propose a method called Mixture-of-Distilled-Expert (MoDE), which applies moderate mutual distillation among experts to enable each expert to pick up more features learned by other experts and gain more accurate perceptions on their original allocated sub-tasks. We conduct plenty experiments including tabular, NLP and CV datasets, which shows MoDE's effectiveness, universality and robustness. Furthermore, we develop a parallel study through innovatively constructing "expert probing", to experimentally prove why MoDE works: moderate distilling knowledge can improve each individual expert's test performances on their assigned tasks, leading to MoE's overall performance improvement.

Chunjing Gan, Dan Yang, Binbin Hu et al.

Nowadays, the rapid development of mobile economy has promoted the flourishing of online marketing campaigns, whose success greatly hinges on the efficient matching between user preferences and desired marketing campaigns where a well-established Marketing-oriented Knowledge Graph (dubbed as MoKG) could serve as the critical "bridge" for preference propagation. In this paper, we seek to carefully prompt a Large Language Model (LLM) with domain-level knowledge as a better marketing-oriented knowledge miner for marketing-oriented knowledge graph construction, which is however non-trivial, suffering from several inevitable issues in real-world marketing scenarios, i.e., uncontrollable relation generation of LLMs,insufficient prompting ability of a single prompt, the unaffordable deployment cost of LLMs. To this end, we propose PAIR, a novel Progressive prompting Augmented mIning fRamework for harvesting marketing-oriented knowledge graph with LLMs. In particular, we reduce the pure relation generation to an LLM based adaptive relation filtering process through the knowledge-empowered prompting technique. Next, we steer LLMs for entity expansion with progressive prompting augmentation,followed by a reliable aggregation with comprehensive consideration of both self-consistency and semantic relatedness. In terms of online serving, we specialize in a small and white-box PAIR (i.e.,LightPAIR),which is fine-tuned with a high-quality corpus provided by a strong teacher-LLM. Extensive experiments and practical applications in audience targeting verify the effectiveness of the proposed (Light)PAIR.

Xingyu Lu, Zhining Liu, Yanchu Guan et al.

Given the enormous number of users and items, industrial cascade recommendation systems (RS) are continuously expanded in size and complexity to deliver relevant items, such as news, services, and commodities, to the appropriate users. In a real-world scenario with hundreds of thousands requests per second, significant computation is required to infer personalized results for each request, resulting in a massive energy consumption and carbon emission that raises concern. This paper proposes GreenFlow, a practical computation allocation framework for RS, that considers both accuracy and carbon emission during inference. For each stage (e.g., recall, pre-ranking, ranking, etc.) of a cascade RS, when a user triggers a request, we define two actions that determine the computation: (1) the trained instances of models with different computational complexity; and (2) the number of items to be inferred in the stage. We refer to the combinations of actions in all stages as action chains. A reward score is estimated for each action chain, followed by dynamic primal-dual optimization considering both the reward and computation budget. Extensive experiments verify the effectiveness of the framework, reducing computation consumption by 41% in an industrial mobile application while maintaining commercial revenue. Moreover, the proposed framework saves approximately 5000kWh of electricity and reduces 3 tons of carbon emissions per day.

Yuwei Geng, Olena Burkovska, Lili Ju et al.

We propose an efficient end-to-end deep learning method for solving nonlocal Allen-Cahn (AC) and Cahn-Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-based AC or CH phase-field models result in diffuse interfaces between phases, with the only recourse for remediation is to severely refine the spatial grids in the vicinity of the true moving sharp interface whose width is determined by a grid-independent parameter that is substantially larger than the local grid size. In this work, we introduce non-mass conserving nonlocal AC or CH phase-field models with regular, logarithmic, or obstacle double-well potentials. Because of non-locality, some of these models feature totally sharp interfaces separating phases. The discretization of such models can lead to a transition between phases whose width is only a single grid cell wide. Another motivation is to use deep learning approaches to ameliorate the otherwise high cost of solving discretized nonlocal phase-field models. To this end, loss functions of the customized neural networks are defined using the residual of the fully discrete approximations of the AC or CH models, which results from applying a Fourier collocation method and a temporal semi-implicit approximation. To address the long-range interactions in the models, we tailor the architecture of the neural network by incorporating a nonlocal kernel as an input channel to the neural network model. We then provide the results of extensive computational experiments to illustrate the accuracy, structure-preserving properties, predictive capabilities, and cost reductions of the proposed method.

Yao Zhao, Haipeng Zhang, Shiwei Lyu et al.

Uplift modeling is widely used in performance marketing to estimate effects of promotion campaigns (e.g., increase of customer retention rate). Since it is impossible to observe outcomes of a recipient in treatment (e.g., receiving a certain promotion) and control (e.g., without promotion) groups simultaneously (i.e., counter-factual), uplift models are mainly trained on instances of treatment and control groups separately to form two models respectively, and uplifts are predicted by the difference of predictions from these two models (i.e., two-model method). When responses are noisy and the treatment effect is fractional, induced individual uplift predictions will be inaccurate, resulting in targeting undesirable customers. Though it is impossible to obtain the ideal ground-truth individual uplifts, known as Individual Treatment Effects (ITEs), alternatively, an average uplift of a group of users, called Average Treatment Effect (ATE), can be observed from experimental deliveries. Upon this, similar to Multiple Instance Learning (MIL) in which each training sample is a bag of instances, our framework sums up individual user uplift predictions for each bag of users as its bag-wise ATE prediction, and regularizes it to its ATE label, thus learning more accurate individual uplifts. Additionally, to amplify the fractional treatment effect, bags are composed of instances with adjacent individual uplift predictions, instead of random instances. Experiments conducted on two datasets show the effectiveness and universality of the proposed framework.

Minglei Yang, Pengjun Wang, Ming Fan et al.

We introduce a conditional pseudo-reversible normalizing flow for constructing surrogate models of a physical model polluted by additive noise to efficiently quantify forward and inverse uncertainty propagation. Existing surrogate modeling approaches usually focus on approximating the deterministic component of physical model. However, this strategy necessitates knowledge of noise and resorts to auxiliary sampling methods for quantifying inverse uncertainty propagation. In this work, we develop the conditional pseudo-reversible normalizing flow model to directly learn and efficiently generate samples from the conditional probability density functions. The training process utilizes dataset consisting of input-output pairs without requiring prior knowledge about the noise and the function. Our model, once trained, can generate samples from any conditional probability density functions whose high probability regions are covered by the training set. Moreover, the pseudo-reversibility feature allows for the use of fully-connected neural network architectures, which simplifies the implementation and enables theoretical analysis. We provide a rigorous convergence analysis of the conditional pseudo-reversible normalizing flow model, showing its ability to converge to the target conditional probability density function using the Kullback-Leibler divergence. To demonstrate the effectiveness of our method, we apply it to several benchmark tests and a real-world geologic carbon storage problem.

Toan Huynh, Ruth Lopez Fajardo, Guannan Zhang et al.

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

Minglei Yang, Yanfang Liu, Diego del-Castillo-Negrete et al.

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. The performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Zezhong Zhang, Feng Bao, Guannan Zhang

The impressive expressive power of deep neural networks (DNNs) underlies their widespread applicability. However, while the theoretical capacity of deep architectures is high, the practical expressive power achieved through successful training often falls short. Building on the insights gained from Neural ODEs, which explore the depth of DNNs as a continuous variable, in this work, we generalize the traditional fully connected DNN through the concept of continuous width. In the Generalized Deep Neural Network (GDNN), the traditional notion of neurons in each layer is replaced by a continuous state function. Using the finite rank parameterization of the weight integral kernel, we establish that GDNN can be obtained by employing the Integral Activation Transform (IAT) as activation layers within the traditional DNN framework. The IAT maps the input vector to a function space using some basis functions, followed by nonlinear activation in the function space, and then extracts information through the integration with another collection of basis functions. A specific variant, IAT-ReLU, featuring the ReLU nonlinearity, serves as a smooth generalization of the scalar ReLU activation. Notably, IAT-ReLU exhibits a continuous activation pattern when continuous basis functions are employed, making it smooth and enhancing the trainability of the DNN. Our numerical experiments demonstrate that IAT-ReLU outperforms regular ReLU in terms of trainability and better smoothness.

Feng Bao, Zezhong Zhang, Guannan Zhang

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses a mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves a tremendous amount of time spent on training neural networks. High-dimensional Lorenz-96 systems are used to demonstrate the performance of our method. EnSF provides surprising performance, compared with the state-of-the-art Local Ensemble Transform Kalman Filter method, in reliably and efficiently tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimensions) with highly nonlinear observation processes.

Dan Yang, Binbin Hu, Xiaoyan Yang et al.

With the growing popularity of various mobile devices, user targeting has received a growing amount of attention, which aims at effectively and efficiently locating target users that are interested in specific services. Most pioneering works for user targeting tasks commonly perform similarity-based expansion with a few active users as seeds, suffering from the following major issues: the unavailability of seed users for newcoming services and the unfriendliness of black-box procedures towards marketers. In this paper, we design an Entity Graph Learning (EGL) system to provide explainable user targeting ability meanwhile applicable to addressing the cold-start issue. EGL System follows the hybrid online-offline architecture to satisfy the requirements of scalability and timeliness. Specifically, in the offline stage, the system focuses on the heavyweight entity graph construction and user entity preference learning, in which we propose a Three-stage Relation Mining Procedure (TRMP), breaking loose from the expensive seed users. At the online stage, the system offers the ability of user targeting in real-time based on the entity graph from the offline stage. Since the user targeting process is based on graph reasoning, the whole process is transparent and operation-friendly to marketers. Finally, extensive offline experiments and online A/B testing demonstrate the superior performance of the proposed EGL System.

Majdi I. Radaideh, Hoang Tran, Lianshan Lin et al.

The mercury constitutive model predicting the strain and stress in the target vessel plays a central role in improving the lifetime prediction and future target designs of the mercury targets at the Spallation Neutron Source (SNS). We leverage the experiment strain data collected over multiple years to improve the mercury constitutive model through a combination of large-scale simulations of the target behavior and the use of machine learning tools for parameter estimation. We present two interdisciplinary approaches for surrogate-based model calibration of expensive simulations using evolutionary neural networks and sparse polynomial expansions. The experiments and results of the two methods show a very good agreement for the solid mechanics simulation of the mercury spallation target. The proposed methods are used to calibrate the tensile cutoff threshold, mercury density, and mercury speed of sound during intense proton pulse experiments. Using strain experimental data from the mercury target sensors, the newly calibrated simulations achieve 7\% average improvement on the signal prediction accuracy and 8\% reduction in mean absolute error compared to previously reported reference parameters, with some sensors experiencing up to 30\% improvement. The proposed calibrated simulations can significantly aid in fatigue analysis to estimate the mercury target lifetime and integrity, which reduces abrupt target failure and saves a tremendous amount of costs. However, an important conclusion from this work points out to a deficiency in the current constitutive model based on the equation of state in capturing the full physics of the spallation reaction. Given that some of the calibrated parameters that show a good agreement with the experimental data can be nonphysical mercury properties, we need a more advanced two-phase flow model to capture bubble dynamics and mercury cavitation.

Yuankai Teng, Zhu Wang, Lili Ju et al.

Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks. Inspired by the Nonlinear Level set Learning (NLL) method that uses the reversible residual network (RevNet), in this paper we propose a new method of Dimension Reduction via Learning Level Sets (DRiLLS) for function approximation. Our method contains two major components: one is the pseudo-reversible neural network (PRNN) module that effectively transforms high-dimensional input variables to low-dimensional active variables, and the other is the synthesized regression module for approximating function values based on the transformed data in the low-dimensional space. The PRNN not only relaxes the invertibility constraint of the nonlinear transformation present in the NLL method due to the use of RevNet, but also adaptively weights the influence of each sample and controls the sensitivity of the function to the learned active variables. The synthesized regression uses Euclidean distance in the input space to select neighboring samples, whose projections on the space of active variables are used to perform local least-squares polynomial fitting. This helps to resolve numerical oscillation issues present in traditional local and global regressions. Extensive experimental results demonstrate that our DRiLLS method outperforms both the NLL and Active Subspace methods, especially when the target function possesses critical points in the interior of its input domain.

Siyan Liu, Pei Zhang, Dan Lu et al.

We propose a novel prediction interval (PI) method for uncertainty quantification, which addresses three major issues with the state-of-the-art PI methods. First, existing PI methods require retraining of neural networks (NNs) for every given confidence level and suffer from the crossing issue in calculating multiple PIs. Second, they usually rely on customized loss functions with extra sensitive hyperparameters for which fine tuning is required to achieve a well-calibrated PI. Third, they usually underestimate uncertainties of out-of-distribution (OOD) samples leading to over-confident PIs. Our PI3NN method calculates PIs from linear combinations of three NNs, each of which is independently trained using the standard mean squared error loss. The coefficients of the linear combinations are computed using root-finding algorithms to ensure tight PIs for a given confidence level. We theoretically prove that PI3NN can calculate PIs for a series of confidence levels without retraining NNs and it completely avoids the crossing issue. Additionally, PI3NN does not introduce any unusual hyperparameters resulting in a stable performance. Furthermore, we address OOD identification challenge by introducing an initialization scheme which provides reasonably larger PIs of the OOD samples than those of the in-distribution samples. Benchmark and real-world experiments show that our method outperforms several state-of-the-art approaches with respect to predictive uncertainty quality, robustness, and OOD samples identification.

Jiaxin Zhang, Sirui Bi, Guannan Zhang

Bayesian experimental design (BED) aims at designing an experiment to maximize the information gathering from the collected data. The optimal design is usually achieved by maximizing the mutual information (MI) between the data and the model parameters. When the analytical expression of the MI is unavailable, e.g., having implicit models with intractable data distributions, a neural network-based lower bound of the MI was recently proposed and a gradient ascent method was used to maximize the lower bound. However, the approach in Kleinegesse et al., 2020 requires a pathwise sampling path to compute the gradient of the MI lower bound with respect to the design variables, and such a pathwise sampling path is usually inaccessible for implicit models. In this work, we propose a hybrid gradient approach that leverages recent advances in variational MI estimator and evolution strategies (ES) combined with black-box stochastic gradient ascent (SGA) to maximize the MI lower bound. This allows the design process to be achieved through a unified scalable procedure for implicit models without sampling path gradients. Several experiments demonstrate that our approach significantly improves the scalability of BED for implicit models in high-dimensional design space.

Jiaxin Zhang, Sirui Bi, Guannan Zhang

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Sirui Bi, Jiaxin Zhang, Guannan Zhang

Topology optimization (TO) is a popular and powerful computational approach for designing novel structures, materials, and devices. Two computational challenges have limited the applicability of TO to a variety of industrial applications. First, a TO problem often involves a large number of design variables to guarantee sufficient expressive power. Second, many TO problems require a large number of expensive physical model simulations, and those simulations cannot be parallelized. To address these issues, we propose a general scalable deep-learning (DL) based TO framework, referred to as SDL-TO, which utilizes parallel schemes in high performance computing (HPC) to accelerate the TO process for designing additively manufactured (AM) materials. Unlike the existing studies of DL for TO, our framework accelerates TO by learning the iterative history data and simultaneously training on the mapping between the given design and its gradient. The surrogate gradient is learned by utilizing parallel computing on multiple CPUs incorporated with a distributed DL training on multiple GPUs. The learned TO gradient enables a fast online update scheme instead of an expensive update based on the physical simulator or solver. Using a local sampling strategy, we achieve to reduce the intrinsic high dimensionality of the design space and improve the training accuracy and the scalability of the SDL-TO framework. The method is demonstrated by benchmark examples and AM materials design for heat conduction. The proposed SDL-TO framework shows competitive performance compared to the baseline methods but significantly reduces the computational cost by a speed up of around 8.6x over the standard TO implementation.

Hoang Tran, Guannan Zhang

The local gradient points to the direction of the steepest slope in an infinitesimal neighborhood. An optimizer guided by the local gradient is often trapped in local optima when the loss landscape is multi-modal. A directional Gaussian smoothing (DGS) approach was recently proposed in (Zhang et al., 2020) and used to define a truly nonlocal gradient, referred to as the DGS gradient, for high-dimensional black-box optimization. Promising results show that replacing the traditional local gradient with the DGS gradient can significantly improve the performance of gradient-based methods in optimizing highly multi-modal loss functions. However, the optimal performance of the DGS gradient may rely on fine tuning of two important hyper-parameters, i.e., the smoothing radius and the learning rate. In this paper, we present a simple, yet ingenious and efficient adaptive approach for optimization with the DGS gradient, which removes the need of hyper-parameter fine tuning. Since the DGS gradient generally points to a good search direction, we perform a line search along the DGS direction to determine the step size at each iteration. The learned step size in turn will inform us of the scale of function landscape in the surrounding area, based on which we adjust the smoothing radius accordingly for the next iteration. We present experimental results on high-dimensional benchmark functions, an airfoil design problem and a game content generation problem. The AdaDGS method has shown superior performance over several the state-of-the-art black-box optimization methods.

Jiaxing Zhang, Hoang Tran, Guannan Zhang

Evolution strategy (ES) has been shown great promise in many challenging reinforcement learning (RL) tasks, rivaling other state-of-the-art deep RL methods. Yet, there are two limitations in the current ES practice that may hinder its otherwise further capabilities. First, most current methods rely on Monte Carlo type gradient estimators to suggest search direction, where the policy parameter is, in general, randomly sampled. Due to the low accuracy of such estimators, the RL training may suffer from slow convergence and require more iterations to reach optimal solution. Secondly, the landscape of reward functions can be deceptive and contains many local maxima, causing ES algorithms to prematurely converge and be unable to explore other parts of the parameter space with potentially greater rewards. In this work, we employ a Directional Gaussian Smoothing Evolutionary Strategy (DGS-ES) to accelerate RL training, which is well-suited to address these two challenges with its ability to i) provide gradient estimates with high accuracy, and ii) find nonlocal search direction which lays stress on large-scale variation of the reward function and disregards local fluctuation. Through several benchmark RL tasks demonstrated herein, we show that DGS-ES is highly scalable, possesses superior wall-clock time, and achieves competitive reward scores to other popular policy gradient and ES approaches.

Jiaxin Zhang, Hoang Tran, Dan Lu et al.

We propose an improved evolution strategy (ES) using a novel nonlocal gradient operator for high-dimensional black-box optimization. Standard ES methods with $d$-dimensional Gaussian smoothing suffer from the curse of dimensionality due to the high variance of Monte Carlo (MC) based gradient estimators. To control the variance, Gaussian smoothing is usually limited in a small region, so existing ES methods lack nonlocal exploration ability required for escaping from local minima. We develop a nonlocal gradient operator with directional Gaussian smoothing (DGS) to address this challenge. The DGS conducts 1D nonlocal explorations along $d$ orthogonal directions in $\mathbb{R}^d$, each of which defines a nonlocal directional derivative as a 1D integral. We then use Gauss-Hermite quadrature, instead of MC sampling, to estimate the $d$ 1D integrals to ensure high accuracy (i.e., small variance). Our method enables effective nonlocal exploration to facilitate the global search in high-dimensional optimization. We demonstrate the superior performance of our method in three sets of examples, including benchmark functions for global optimization, and real-world science and engineering applications.

Jiaxin Zhang, Xianglin Liu, Sirui Bi et al.

High entropy alloys (HEAs) have been increasingly attractive as promising next-generation materials due to their various excellent properties. It's necessary to essentially characterize the degree of chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed and demonstrated on the accurate and efficient prediction of configurational energy of high entropy alloys. The proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. Given limited data calculated by first-principles calculations, Bayesian regularized regression not only offers an accurate and stable prediction but also effectively quantifies the uncertainties associated with EPI parameters. Compared with the arbitrary determination of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence we can place in statistical estimates of configurational energy when data are sparse.

Peter Jantsch, Clayton G. Webster, Guannan Zhang

This work focuses on weighted Lagrange interpolation on an unbounded domain, and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line, and can be extended to unbounded domains with the introduction of a weight function $w:\mathbb{R}\rightarrow [0,1]$. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares, and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.

Hoang A. Tran, Clayton G. Webster, Guannan Zhang

There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as well as the model inadequacy. However, the application of Bayesian inference to systematically quantify the uncertainties in parameters, by means of exploring posterior probability density functions (PPDFs), has been hindered by the prohibitively daunting computational cost associated with the large number of model executions, in addition to daunting computation time per one turbulence simulation. In this effort, we perform in this paper an adaptive hierarchical sparse grid surrogate modeling approach to Bayesian inference of large eddy simulation (LES). First, an adaptive hierarchical sparse grid surrogate for the output of forward models is constructed using a relatively small number of model executions. Using such surrogate, the likelihood function can be rapidly evaluated at any point in the parameter space without simulating the computationally expensive LES model. This method is essentially similar to those developed in [62] for geophysical and groundwater models, but is adjusted and applied here for a much more challenging problem of uncertainty quantification of turbulence models. Through a numerical demonstration of the Smagorinsky model of two-dimensional flow around a cylinder at sub-critical Reynolds number, our approach is proven to significantly reduce the number of costly LES executions without losing much accuracy in the posterior probability estimation. Here, the model parameters are calibrated against synthetic data related to the mean flow velocity and Reynolds stresses at different locations in the flow wake. The influence of the user-elected LES parameters on the quality of output data will be discussed.

Feng Bao, Yanzhao Cao, Clayton Webster et al.

In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the optimal filter over a deterministic state space grid and is developed from samples of the current state obtained by solving the state equation implicitly. The purpose of the meshfree approximation is to improve the efficiency of the implicit filter in moderately high-dimensional problems. The construction of the algorithm includes generation of random state space points and a meshfree interpolation method. Numerical experiments show the effectiveness and efficiency of our algorithm.

Guannan Zhang, Weidong Zhao, Clayton Webster et al.

We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by Lèvy processes with jumps. The nonlocal diffusion problem under consideration is converted to a BSDE,for which numerical schemes are developed and applied directly. As a stochastic approach, the proposed method does not require the solution of linear systems, which allows for embarrassingly parallel implementations and also enables adaptive approximation techniques to be incorporated in a straightforward fashion. Moreover, our method is more accurate than classic stochastic approaches due to the use of high-order temporal and spatial discretization schemes. In addition, our approach can handle a broad class of problems with general nonlinear forcing terms as long as they are globally Lipchitz continuous. Rigorous error analysis of the new method is provided as several numerical examples that illustrate the effectiveness and efficiency of the proposed approach.

Diego Galindo, Peter Jantsch, Clayton G. Webster et al.

This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC approaches considered in this effort consist of sequentially constructed multi-dimensional Lagrange interpolant in the random parametric domain, formulated by collocating on a set of points so that the resulting approximation is defined in a hierarchical sequence of polynomial spaces of increasing fidelity. Our acceleration approach exploits the construction of the SC interpolant to accelerate the underlying ensemble of deterministic solutions. Specifically, we predict the solution of the parametrized PDE at each collocation point on the current level of the SC approximation by evaluating each sample with a previously assembled lower fidelity interpolant, and then use such predictions to provide deterministic (linear or nonlinear) iterative solvers with improved initial approximations. As a concrete example, we develop our approach in the context of SC approaches that employ sparse tensor products of globally defined Lagrange polynomials on nested one-dimensional Clenshaw-Curtis abscissas. This work also provides a rigorous computational complexity analysis of the resulting fully discrete sparse grid SC approximation, with and without acceleration, which demonstrates the effectiveness of our proposed methodology in reducing the total number of iterations of a conjugate gradient solution of the finite element systems at each collocation point. Numerical examples include both linear and nonlinear parametrized PDEs, which are used to illustrate the theoretical results and the improved efficiency of this technique compared with several others.