Solving Algebra Problems with Geometry Diagrams (APGDs) is still a challenging problem because diagram processing is not studied as intensively as language processing. To work against this challenge, this paper proposes a hologram reasoning scheme and develops a high-performance method for solving APGDs by using this scheme. To reach this goal, it first defines a hologram, being a kind of graph, and proposes a hologram generator to convert a given APGD into a hologram, which represents the entire information of APGD and the relations for solving the problem can be acquired from it by a uniform way. Then HGR, a hologram reasoning method employs a pool of prepared graph models to derive algebraic equations, which is consistent with the geometric theorems. This method is able to be updated by adding new graph models into the pool. Lastly, it employs deep reinforcement learning to enhance the efficiency of model selection from the pool. The entire HGR not only ensures high solution accuracy with fewer reasoning steps but also significantly enhances the interpretability of the solution process by providing descriptions of all reasoning steps. Experimental results demonstrate the effectiveness of HGR in improving both accuracy and interpretability in solving APGDs.

Materials discovery driven by statistical property models is an iterative decision process, during which an initial data collection is extended with new data proposed by a model-informed acquisition function--with the goal to maximize a certain "reward" over time, such as the maximum property value discovered so far. While the materials science community achieved much progress in developing property models that predict well on average with respect to the training distribution, this form of in-distribution performance measurement is not directly coupled with the discovery reward. This is because an iterative discovery process has a shifting reward distribution that is over-proportionally determined by the model performance for exceptional materials. We demonstrate this problem using the example of bulk modulus maximization among double perovskite oxides. We find that the in-distribution predictive performance suggests random forests as superior to Gaussian process regression, while the results are inverse in terms of the discovery rewards. We argue that the lack of proper performance estimation methods from pre-computed data collections is a fundamental problem for improving data-driven materials discovery, and we propose a novel such estimator that, in contrast to na\"ive reward estimation, successfully predicts Gaussian processes with the "expected improvement" acquisition function as the best out of four options in our demonstrational study for double perovskites. Importantly, it does so without requiring the over thousand ab initio computations that were needed to confirm this prediction.

Traditional seismic processing workflows (SPW) are expensive, requiring over a year of human and computational effort. Deep learning (DL) based data-driven seismic workflows (DSPW) hold the potential to reduce these timelines to a few minutes. Raw seismic data (terabytes) and required subsurface prediction (gigabytes) are enormous. This large-scale, spatially irregular time-series data poses seismic data ingestion (SDI) as an unconventional yet fundamental problem in DSPW. Current DL research is limited to small-scale simplified synthetic datasets as they treat seismic data like images and process them with convolution networks. Real seismic data, however, is at least 5D. Applying 5D convolutions to this scale is computationally prohibitive. Moreover, raw seismic data is highly unstructured and hence inherently non-image like. We propose a fundamental shift to move away from convolutions and introduce SESDI: Set Embedding based SDI approach. SESDI first breaks down the mammoth task of large-scale prediction into an efficient compact auxiliary task. SESDI gracefully incorporates irregularities in data with its novel model architecture. We believe SESDI is the first successful demonstration of end-to-end learning on real seismic data. SESDI achieves SSIM of over 0.8 on velocity inversion task on real proprietary data from the Gulf of Mexico and outperforms the state-of-the-art U-Net model on synthetic datasets.

IMAGE: This is a schematic illustration of MEGNet models. Nanoengineers at the University of California San Diego have developed new deep learning models that can accurately predict the properties of molecules and crystals. By enabling almost instantaneous property predictions, these deep learning models provide researchers the means to rapidly scan the nearly-infinite universe of compounds to discover potentially transformative materials for various technological applications, such as high-energy-density Li-ion batteries, warm-white LEDs, and better photovoltaics. To construct their models, a team led by nanoengineering professor Shyue Ping Ong at the UC San Diego Jacobs School of Engineering used a new deep learning framework called graph networks, developed by Google DeepMind, the brains behind AlphaGo and AlphaZero. Graph networks have the potential to expand the capabilities of existing AI technology to perform complicated learning and reasoning tasks with limited experience and knowledge--something that humans are good at.