Yao Xuan’s research while affiliated with University of California, Santa Barbara and other places

Generating learning-friendly representations for points in space is a fundamental and long-standing problem in ML. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D/3D Euclidean space as a high-dimensional vector, and has been successfully applied to various geospatial prediction and generative tasks. However, all current 2D and 3D location encoders are designed to model point distances in Euclidean space. So when applied to large-scale real-world GPS coordinate datasets, which require distance metric learning on the spherical surface, both types of models can fail due to the map projection distortion problem (2D) and the spherical-to-Euclidean distance approximation error (3D). To solve these problems, we propose a multi-scale location encoder called Sphere2Vec which can preserve spherical distances when encoding point coordinates on a spherical surface. We developed a unified view of distance-reserving encoding on spheres based on the DFS. We also provide theoretical proof that the Sphere2Vec preserves the spherical surface distance between any two points, while existing encoding schemes do not. Experiments on 20 synthetic datasets show that Sphere2Vec can outperform all baseline models on all these datasets with up to 30.8% error rate reduction. We then apply Sphere2Vec to three geo-aware image classification tasks - fine-grained species recognition, Flickr image recognition, and remote sensing image classification. Results on 7 real-world datasets show the superiority of Sphere2Vec over multiple location encoders on all three tasks. Further analysis shows that Sphere2Vec outperforms other location encoder models, especially in the polar regions and data-sparse areas because of its nature for spherical surface distance preservation. Code and data are available at https://gengchenmai.github.io/sphere2vec-website/.

We propose a general-purpose spherical location encoder, Sphere2Vec, which, as far as we know, is the first location encoder which aims at preserving spherical distance. • We provide a theoretical proof about the spherical-distance-kept nature of Sphere2Vec. • We provide theoretical proof to show why the previous 2D location encoders and NeRF-style 3D location encoders cannot model spherical distance correctly. • We first construct 20 synthetic datasets based on the mixture of von Mises-Fisher (MvMF) distributions and show that Sphere2Vec can outperform all baseline models including the state-of-the-art (SOTA) 2D location encoders and NeRF-style 3D location encoders on all these datasets with an up to 30.8% error rate reduction. • Next, we conduct extensive experiments on seven real-world datasets for three geo-aware image classification tasks. Results show that Sphere2Vec outperforms all baseline models on all datasets. • Further analysis shows that Sphere2Vec is able to produce finer-grained and compact spatial distributions, and does significantly better than 2D and 3D Euclidean location encoders in the polar regions and areas with sparse training samples. A B S T R A C T Generating learning-friendly representations for points in space is a fundamental and long-standing problem in machine learning. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D or 3D Euclidean space as a high-dimensional vector, and has been successfully applied to various (geo)spatial prediction and generative tasks. However, all current 2D and 3D location encoders are designed to model point distances in Euclidean space. So when applied to large-scale real-world GPS coordinate datasets (e.g., species or satellite images taken all over the world), which require distance metric learning on the spherical surface, both types of models can fail due to the map projection distortion problem (2D) and the spherical-to-Euclidean distance approximation error (3D). To solve these problems, we propose a multi-scale location en-coder called Sphere2Vec which can preserve spherical distances when encoding point coordinates on a spherical surface. We developed a unified view of distance-reserving encoding on spheres based on the Double Fourier Sphere (DFS). We also provide theoretical proof that the Sphere2Vec encoding preserves the spherical surface distance between any two points, while existing encoding schemes such as Space2Vec and NeRF do not. Experiments on 20 synthetic datasets show that Sphere2Vec can outperform all baseline models including the state-of-the-art (SOTA) 2D location encoder (i.e., Space2Vec) and 3D encoder NeRF on all these datasets with up to 30.8% error rate reduction. We then apply Sphere2Vec to three geo-aware image classification tasks-fine-grained species recognition, Flickr image recognition, and remote sensing image classification. Results on 7 real-world datasets show the superiority of Sphere2Vec over multiple 2D and 3D location encoders on all three tasks. Further analysis shows that Sphere2Vec outperforms other location encoder models, especially in the polar regions and data-sparse areas because of its nature for spherical surface distance preservation. Code and data of this work are available at https://gengchenmai.github.io/sphere2vec-website/.

A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in the work of Xuan et al. [J. Comput. Phys. 443, 110519 (2021)]. Several innovations and improvements are proposed. (1) A Sobolev space-trained, convolutional neural network is employed to handle the exponential dimension increase of the discretized, local average monomer density fields and to strongly enforce both spatial translation and rotation invariance of the predicted, field-theoretic intensive Hamiltonian. (2) A generative adversarial network (GAN) is introduced to efficiently and accurately predict saddle point, local average monomer density fields without resorting to gradient descent methods that employ the training set. This GAN approach yields important savings of both memory and computational cost. (3) The proposed machine learning framework is successfully applied to 2D cell size optimization as a clear illustration of its broad potential to accelerate the exploration of parameter space for discovering polymer nanostructures. Extensions to three-dimensional phase discovery appear to be feasible.

A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in [1]. Several innovations and improvements are proposed. (1) A Sobolev space-trained, convolutional neural network (CNN) is employed to handle the exponential dimension increase of the discretized, local average monomer density fields and to strongly enforce both spatial translation and rotation invariance of the predicted, field-theoretic intensive Hamiltonian. (2) A generative adversarial network (GAN) is introduced to efficiently and accurately predict saddle point, local average monomer density fields without resorting to gradient descent methods that employ the training set. This GAN approach yields important savings of both memory and computational cost. (3) The proposed machine learning framework is successfully applied to 2D cell size optimization as a clear illustration of its broad potential to accelerate the exploration of parameter space for discovering polymer nanostructures. Extensions to three-dimensional phase discovery appear to be feasible.

Neural network representation learning for spatial data (e.g., points, polylines, polygons, and networks) is a common need for geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in representation learning for points, polylines, and networks, whereas little progress has been made for polygons, especially complex polygonal geometries. In this work, we focus on developing a general-purpose polygon encoding model, which can encode a polygonal geometry (with or without holes, single or multipolygons) into an embedding space. The result embeddings can be leveraged directly (or finetuned) for downstream tasks such as shape classification, spatial relation prediction, building pattern classification, cartographic building generalization, and so on. To achieve model generalizability guarantees, we identify a few desirable properties that the encoder should satisfy: loop origin invariance, trivial vertex invariance, part permutation invariance, and topology awareness. We explore two different designs for the encoder: one derives all representations in the spatial domain and can naturally capture local structures of polygons; the other leverages spectral domain representations and can easily capture global structures of polygons. For the spatial domain approach we propose ResNet1D, a 1D CNN-based polygon encoder, which uses circular padding to achieve loop origin invariance on simple polygons. For the spectral domain approach we develop NUFTspec based on Non-Uniform Fourier Transformation (NUFT), which naturally satisfies all the desired properties. We conduct experiments on two different tasks: 1) polygon shape classification based on the commonly used MNIST dataset; 2) polygon-based spatial relation prediction based on two new datasets (DBSR-46K and DBSR-cplx46K) constructed from OpenStreetMap and DBpedia. Our results show that NUFTspec and ResNet1D outperform multiple existing baselines with significant margins. While ResNet1D suffers from model performance degradation after shape-invariance geometry modifications, NUFTspec is very robust to these modifications due to the nature of the NUFT representation. NUFTspec is able to jointly consider all parts of a multipolygon and their spatial relations during prediction while ResNet1D can recognize the shape details which are sometimes important for classification. This result points to a promising research direction of combining spatial and spectral representations.

Neural network representation learning for spatial data is a common need for geographic artificial intelligence (GeoAI) problems. In recent years, many advancements have been made in representation learning for points, polylines, and networks, whereas little progress has been made for polygons, especially complex polygonal geometries. In this work, we focus on developing a general-purpose polygon encoding model, which can encode a polygonal geometry (with or without holes, single or multipolygons) into an embedding space. The result embeddings can be leveraged directly (or finetuned) for downstream tasks such as shape classification, spatial relation prediction, and so on. To achieve model generalizability guarantees, we identify a few desirable properties: loop origin invariance, trivial vertex invariance, part permutation invariance, and topology awareness. We explore two different designs for the encoder: one derives all representations in the spatial domain; the other leverages spectral domain representations. For the spatial domain approach, we propose ResNet1D, a 1D CNN-based polygon encoder, which uses circular padding to achieve loop origin invariance on simple polygons. For the spectral domain approach, we develop NUFTspec based on Non-Uniform Fourier Transformation (NUFT), which naturally satisfies all the desired properties. We conduct experiments on two tasks: 1) shape classification based on MNIST; 2) spatial relation prediction based on two new datasets - DBSR-46K and DBSR-cplx46K. Our results show that NUFTspec and ResNet1D outperform multiple existing baselines with significant margins. While ResNet1D suffers from model performance degradation after shape-invariance geometry modifications, NUFTspec is very robust to these modifications due to the nature of the NUFT.

Game theory has been an effective tool in the control of disease spread and in suggesting optimal policies at both individual and area levels. In this AMS Notices article, we focus on the decision-making development for the intervention of COVID-19, aiming to provide mathematical models and efficient machine learning methods, and justifications for related policies that have been implemented in the past and explain how the authorities' decisions affect their neighboring regions from a game theory viewpoint.

Generating learning-friendly representations for points in a 2D space is a fundamental and long-standing problem in machine learning. Recently, multi-scale encoding schemes (such as Space2Vec) were proposed to directly encode any point in 2D space as a high-dimensional vector, and has been successfully applied to various (geo)spatial prediction tasks. However, a map projection distortion problem rises when applying location encoding models to large-scale real-world GPS coordinate datasets (e.g., species images taken all over the world) - all current location encoding models are designed for encoding points in a 2D (Euclidean) space but not on a spherical surface, e.g., earth surface. To solve this problem, we propose a multi-scale location encoding model called Sphere2V ec which directly encodes point coordinates on a spherical surface while avoiding the mapprojection distortion problem. We provide theoretical proof that the Sphere2Vec encoding preserves the spherical surface distance between any two points. We also developed a unified view of distance-reserving encoding on spheres based on the Double Fourier Sphere (DFS). We apply Sphere2V ec to the geo-aware image classification task. Our analysis shows that Sphere2V ec outperforms other 2D space location encoder models especially on the polar regions and data-sparse areas for image classification tasks because of its nature for spherical surface distance preservation.

A new framework that leverages data obtained from self-consistent field theory (SCFT) simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. Deep neural networks are adapted and trained in Sobolev space to better capture the saddle point nature of the SCFT approximation. The proposed approach consists of two main problems: 1) the learning of an approximation to the effective Hamiltonian as a function of the average monomer density fields and the relevant physical parameters and 2) the prediction of saddle density fields given the polymer parameters. There is an additional challenge: the effective Hamiltonian has to be invariant under shifts (and rotations in 2D and 3D). A data-enhancing approach and an appropriate regularization are introduced to effectively achieve said invariance. In this first study, the focus is on one-dimensional (in physical space) systems to allow for a thorough exploration and development of the proposed methodology.