In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
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Question: Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, the uses have been restricted by the fact the training data are obtained using PDE solvers. Thereby, the uses were limited to domains, where the PDE solver was applicable, but no further. 

 We present methods for training on small domains, while applying the trained models on larger domains, with consistency constraints ensuring the solutions are physically meaningful even at the boundary of the small domains. We demonstrate the results on an air-pollution forecasting model for Dublin, Ireland.

Answer: We present RNNs for training surrogate models of PDEs, wherein consistency constraints ensure the solutions are physically meaningful, even when the training uses much smaller domains than the trained model is applied to.


Question: Deep neural networks (DNNs) had great success on NLP tasks such as language modeling, machine translation and certain question answering (QA) tasks. However, the success is limited at more knowledge intensive tasks such as QA from a big corpus. Existing end-to-end deep QA models (Miller et al., 2016; Weston et al., 2014) need to read the entire text after observing the question, and therefore their complexity in responding a question is linear in the text size. This is prohibitive for practical tasks such as QA from Wikipedia, a novel, or the Web. We propose to solve this scalability issue by using symbolic meaning representations, which can be indexed and retrieved efficiently with complexity that is independent of the text size. More specifically, we use sequence-to-sequence models to encode knowledge symbolically and generate programs to answer questions from the encoded knowledge. We apply our approach, called the N-Gram Machine (NGM), to the bAbI tasks (Weston et al., 2015) and a special version of them (“life-long bAbI”) which has stories of up to 10 million sentences. Our experiments show that NGM can successfully solve both of these tasks accurately and efficiently. Unlike fully differentiable memory models, NGM’s time complexity and answering quality are not affected by the story length. The whole system of NGM is trained end-to-end with REINFORCE (Williams, 1992). To avoid high variance in gradient estimation, which is typical in discrete latent variable models, we use beam search instead of sampling. To tackle the exponentially large search space, we use a stabilized auto-encoding objective and a structure tweak procedure to iteratively reduce and refine the search space.


Answer: We propose a framework that learns to encode knowledge symbolically and generate programs to reason about the encoded knowledge.


Question: We propose a novel score-based approach to learning a directed acyclic graph (DAG) from observational data. We adapt a recently proposed continuous constrained optimization formulation to allow for nonlinear relationships between variables using neural networks. This extension allows to model complex interactions while being more global in its search compared to other greedy approaches. In addition to comparing our method to existing continuous optimization methods, we provide missing empirical comparisons to nonlinear greedy search methods. On both synthetic and real-world data sets, this new method outperforms current continuous methods on most tasks while being competitive with existing greedy search methods on important metrics for causal inference.

Answer:
We are proposing a new score-based approach to structure/causal learning leveraging neural networks and a recent continuous constrained formulation to this problem