Alexander Patrick Mathews

Alasdair Tran, Alexander Mathews, Lexing Xie et al.

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the performance gap between pure machine learning approaches to that of the best numerical or hybrid solvers. This is achieved with new representations - separable spectral layers and improved residual connections - and a combination of training strategies such as the Markov assumption, Gaussian noise, and cosine learning rate decay. On several challenging benchmark PDEs on regular grids, structured meshes, and point clouds, the F-FNO can scale to deeper networks and outperform both the FNO and the geo-FNO, reducing the error by 83% on the Navier-Stokes problem, 31% on the elasticity problem, 57% on the airfoil flow problem, and 60% on the plastic forging problem. Compared to the state-of-the-art pseudo-spectral method, the F-FNO can take a step size that is an order of magnitude larger in time and achieve an order of magnitude speedup to produce the same solution quality.

Umanga Bista, Alexander Patrick Mathews, Aditya Krishna Menon et al.

Most work on multi-document summarization has focused on generic summarization of information present in each individual document set. However, the under-explored setting of update summarization, where the goal is to identify the new information present in each set, is of equal practical interest (e.g., presenting readers with updates on an evolving news topic). In this work, we present SupMMD, a novel technique for generic and update summarization based on the maximum mean discrepancy from kernel two-sample testing. SupMMD combines both supervised learning for salience and unsupervised learning for coverage and diversity. Further, we adapt multiple kernel learning to make use of similarity across multiple information sources (e.g., text features and knowledge based concepts). We show the efficacy of SupMMD in both generic and update summarization tasks by meeting or exceeding the current state-of-the-art on the DUC-2004 and TAC-2009 datasets.

Alexander Mathews, Lexing Xie, Xuming He

We simplify sentences with an attentive neural network sequence to sequence model, dubbed S4. The model includes a novel word-copy mechanism and loss function to exploit linguistic similarities between the original and simplified sentences. It also jointly uses pre-trained and fine-tuned word embeddings to capture the semantics of complex sentences and to mitigate the effects of limited data. When trained and evaluated on pairs of sentences from thousands of news articles, we observe a 8.8 point improvement in BLEU score over a sequence to sequence baseline; however, learning word substitutions remains difficult. Such sequence to sequence models are promising for other text generation tasks such as style transfer.