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.

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.