Composite materials with 3D architectures are desirable in a variety of applications for the capability of tailoring their properties to meet multiple functional requirements. By the arrangement of materials' internal components, structure design is of great significance in tuning the properties of the composites. However, most of the composite structures are proposed by empirical designs following existing patterns. Hindered by the complexity of 3D structures, it is hard to extract customized structures with multiple desired properties from large design space. Here we report a multi-objective driven Wasserstein generative adversarial network (MDWGAN) to implement inverse designs of 3D composite structures according to given geometrical, structural and mechanical requirements. Our framework consists a GAN based network which generates 3D composite structures possessing with similar geometrical and structural features to the target dataset. Besides, multiple objectives are introduced to our framework for the control of mechanical property and isotropy of the composites. Real time calculation of the properties in training iterations is achieved by an accurate surrogate model. We constructed a small and concise dataset to illustrate our framework. With multiple objectives combined by their weight, and the 3D-GAN act as a soft constraint, our framework is proved to be capable of tuning the properties of the generated composites in multiple aspects, while keeping the selected features of different kinds of structures. The feasibility on small dataset and potential scalability on objectives of other properties make our work a novel, effective approach to provide fast, experience free composite structure designs for various functional materials.

Graph neural networks are emerging as promising methods for modeling molecular graphs, in which nodes and edges correspond to atoms and chemical bonds, respectively. Recent studies show that when 3D molecular geometries, such as bond lengths and angles, are available, molecular property prediction tasks can be made more accurate. However, computing of 3D molecular geometries requires quantum calculations that are computationally prohibitive. For example, accurate calculation of 3D geometries of a small molecule requires hours of computing time using density functional theory (DFT). Here, we propose to predict the ground-state 3D geometries from molecular graphs using machine learning methods. To make this feasible, we develop a benchmark, known as Molecule3D, that includes a dataset with precise ground-state geometries of approximately 4 million molecules derived from DFT. We also provide a set of software tools for data processing, splitting, training, and evaluation, etc. Specifically, we propose to assess the error and validity of predicted geometries using four metrics. We implement two baseline methods that either predict the pairwise distance between atoms or atom coordinates in 3D space. Experimental results show that, compared with generating 3D geometries with RDKit, our method can achieve comparable prediction accuracy but with much smaller computational costs. Our Molecule3D is available as a module of the MoleculeX software library (https://github.com/divelab/MoleculeX).

Areas under ROC (AUROC) and precision-recall curves (AUPRC) are common metrics for evaluating classification performance for imbalanced problems. Compared with AUROC, AUPRC is a more appropriate metric for highly imbalanced datasets. While direct optimization of AUROC has been studied extensively, optimization of AUPRC has been rarely explored. In this work, we propose a principled technical method to optimize AUPRC for deep learning. Our approach is based on maximizing the averaged precision (AP), which is an unbiased point estimator of AUPRC. We show that the surrogate loss function for AP is highly non-convex and more complicated than that of AUROC. We cast the objective into a sum of dependent compositional functions with inner functions dependent on random variables of the outer level. We propose efficient adaptive and non-adaptive stochastic algorithms with provable convergence guarantee under mild conditions by using recent advances in stochastic compositional optimization. Extensive experimental results on graphs and image datasets demonstrate that our proposed method outperforms prior methods on imbalanced problems. To the best of our knowledge, our work represents the first attempt to optimize AUPRC with provable convergence.

Pre-symptomatic drought stress prediction is of great relevance in precision plant protection, ultimately helping to meet the challenge of "How to feed a hungry world?". Unfortunately, it also presents unique computational problems in scale and interpretability: it is a temporal, large-scale prediction task, e.g., when monitoring plants over time using hyperspectral imaging, and features are `things' with a `biological' meaning and interpretation and not just mathematical abstractions computable for any data. In this paper we propose Dirichlet-aggregation regression (DAR) to meet the challenge. DAR represents all data by means of convex combinations of only few extreme ones computable in linear time and easy to interpret.Then, it puts a Gaussian process prior on the Dirichlet distributions induced on the simplex spanned by the extremes. The prior can be a function of any observed meta feature such as time, location, type of fertilization, and plant species. We evaluated DAR on two hyperspectral image series of plants over time with about 2 (resp. 5.8) Billion matrix entries. The results demonstrate that DAR can be learned efficiently and predicts stress well before it becomes visible to the human eye.

In many cases it makes sense to model a relationship symmetrically, not implying any particular directionality. Consider the classical example of a recommendation system where the rating of an item by a user should symmetrically be dependent on the attributes of both the user and the item. The attributes of the (known) relationships are also relevant for predicting attributes of entities and for predicting attributes of new relations. In recommendation systems, the exploitation of relational attributes is often referred to as collaborative filtering. Again, in many applications one might prefer to model the collaborative effect in a symmetrical way. In this paper we present a relational model, which is completely symmetrical. The key innovation is that we introduce for each entity (or object) an infinite-dimensional latent variable as part of a Dirichlet process (DP) model. We discuss inference in the model, which is based on a DP Gibbs sampler, i.e., the Chinese restaurant process. We extend the Chinese restaurant process to be applicable to relational modeling. Our approach is evaluated in three applications. One is a recommendation system based on the MovieLens data set. The second application concerns the prediction of the function of yeast genes/proteins on the data set of KDD Cup 2001 using a multi-relational model. The third application involves a relational medical domain. The experimental results show that our model gives significantly improved estimates of attributes describing relationships or entities in complex relational models.

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions between entities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood, information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths, or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental results are achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.

We introduce a Gaussian process (GP) framework, stochastic relational models (SRM), for learning social, physical, and other relational phenomena where interactions betweenentities are observed. The key idea is to model the stochastic structure of entity relationships (i.e., links) via a tensor interaction of multiple GPs, each defined on one type of entities. These models in fact define a set of nonparametric priors on infinite dimensional tensor matrices, where each element represents a relationship between a tuple of entities. By maximizing the marginalized likelihood,information is exchanged between the participating GPs through the entire relational network, so that the dependency structure of links is messaged to the dependency of entities, reflected by the adapted GP kernels. The framework offers a discriminative approach to link prediction, namely, predicting the existences, strengths,or types of relationships based on the partially observed linkage network as well as the attributes of entities (if given). We discuss properties and variants of SRM and derive an efficient learning algorithm. Very encouraging experimental resultsare achieved on a toy problem and a user-movie preference link prediction task. In the end we discuss extensions of SRM to general relational learning tasks.