Zhiwei Fang

Zhiwei Fang, Sifan Wang, Paris Perdikaris

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parametrized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1})$, where $d$ is the domain's dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Our numerical experiments show the effectiveness of parametrized complex geometries and unbounded problems.

Zhiwei Fang, Sifan Wang, Paris Perdikaris

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems. In this work, we present a new training paradigm referred to as "gradient boosting" (GB), which significantly enhances the performance of physics informed neural networks (PINNs). Rather than learning the solution of a given PDE using a single neural network directly, our algorithm employs a sequence of neural networks to achieve a superior outcome. This approach allows us to solve problems presenting great challenges for traditional PINNs. Our numerical experiments demonstrate the effectiveness of our algorithm through various benchmarks, including comparisons with finite element methods and PINNs. Furthermore, this work also unlocks the door to employing ensemble learning techniques in PINNs, providing opportunities for further improvement in solving PDEs.

Xin Zhao, Zhiwei Fang, Yuchen Guo et al.

A combinatorial recommender (CR) system feeds a list of items to a user at a time in the result page, in which the user behavior is affected by both contextual information and items. The CR is formulated as a combinatorial optimization problem with the objective of maximizing the recommendation reward of the whole list. Despite its importance, it is still a challenge to build a practical CR system, due to the efficiency, dynamics, personalization requirement in online environment. In particular, we tear the problem into two sub-problems, list generation and list evaluation. Novel and practical model architectures are designed for these sub-problems aiming at jointly optimizing effectiveness and efficiency. In order to adapt to online case, a bootstrap algorithm forming an actor-critic reinforcement framework is given to explore better recommendation mode in long-term user interaction. Offline and online experiment results demonstrate the efficacy of proposed JDRec framework. JDRec has been applied in online JD recommendation, improving click through rate by 2.6% and synthetical value for the platform by 5.03%. We will publish the large-scale dataset used in this study to contribute to the research community.

Oliver Hennigh, Susheela Narasimhan, Mohammad Amin Nabian et al.

We present SimNet, an AI-driven multi-physics simulation framework, to accelerate simulations across a wide range of disciplines in science and engineering. Compared to traditional numerical solvers, SimNet addresses a wide range of use cases - coupled forward simulations without any training data, inverse and data assimilation problems. SimNet offers fast turnaround time by enabling parameterized system representation that solves for multiple configurations simultaneously, as opposed to the traditional solvers that solve for one configuration at a time. SimNet is integrated with parameterized constructive solid geometry as well as STL modules to generate point clouds. Furthermore, it is customizable with APIs that enable user extensions to geometry, physics and network architecture. It has advanced network architectures that are optimized for high-performance GPU computing, and offers scalable performance for multi-GPU and multi-Node implementation with accelerated linear algebra as well as FP32, FP64 and TF32 computations. In this paper we review the neural network solver methodology, the SimNet architecture, and the various features that are needed for effective solution of the PDEs. We present real-world use cases that range from challenging forward multi-physics simulations with turbulence and complex 3D geometries, to industrial design optimization and inverse problems that are not addressed efficiently by the traditional solvers. Extensive comparisons of SimNet results with open source and commercial solvers show good correlation.

Jun Fu, Jing Liu, Haijie Tian et al.

In this paper, we address the scene segmentation task by capturing rich contextual dependencies based on the selfattention mechanism. Unlike previous works that capture contexts by multi-scale features fusion, we propose a Dual Attention Networks (DANet) to adaptively integrate local features with their global dependencies. Specifically, we append two types of attention modules on top of traditional dilated FCN, which model the semantic interdependencies in spatial and channel dimensions respectively. The position attention module selectively aggregates the features at each position by a weighted sum of the features at all positions. Similar features would be related to each other regardless of their distances. Meanwhile, the channel attention module selectively emphasizes interdependent channel maps by integrating associated features among all channel maps. We sum the outputs of the two attention modules to further improve feature representation which contributes to more precise segmentation results. We achieve new state-of-the-art segmentation performance on three challenging scene segmentation datasets, i.e., Cityscapes, PASCAL Context and COCO Stuff dataset. In particular, a Mean IoU score of 81.5% on Cityscapes test set is achieved without using coarse data. We make the code and trained model publicly available at https://github.com/junfu1115/DANet

Congchi Yin, Qian Yu, Zhiwei Fang et al.

Recent major milestones have successfully reconstructed natural language from non-invasive brain signals (e.g. functional Magnetic Resonance Imaging (fMRI) and Electroencephalogram (EEG)) across subjects. However, we find current dataset splitting strategies for cross-subject brain-to-text decoding are wrong. Specifically, we first demonstrate that all current splitting methods suffer from data leakage problem, which refers to the leakage of validation and test data into training set, resulting in significant overfitting and overestimation of decoding models. In this study, we develop a right cross-subject data splitting criterion without data leakage for decoding fMRI and EEG signal to text. Some SOTA brain-to-text decoding models are re-evaluated correctly with the proposed criterion for further research.

Xiaoxiao Xu, Chen Yang, Qian Yu et al.

We propose a general Variational Embedding Learning Framework (VELF) for alleviating the severe cold-start problem in CTR prediction. VELF addresses the cold start problem via alleviating over-fits caused by data-sparsity in two ways: learning probabilistic embedding, and incorporating trainable and regularized priors which utilize the rich side information of cold start users and advertisements (Ads). The two techniques are naturally integrated into a variational inference framework, forming an end-to-end training process. Abundant empirical tests on benchmark datasets well demonstrate the advantages of our proposed VELF. Besides, extended experiments confirmed that our parameterized and regularized priors provide more generalization capability than traditional fixed priors.

Zhiwei Fang, Justin Zhang, Xiu Yang

In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the surface differential operators so that PINN's loss value will be an indicator of the residue of the surface PDEs. Numerical experiments verify efficacy of our algorithm.