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.

[Q]: 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.
[A]: 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.


[Q]: Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be captured from images, from which similarities between different drugs applied at different dosages can be quantified. The general approach is to find a function mapping the images to an embedding space of manageable dimensionality whose geometry captures relevant features of the input images. An important known issue for such methods is separating relevant biological signal from nuisance variation. For example, the embedding vectors tend to be more correlated for cells that were cultured and imaged during the same week than for cells from a different week, despite having identical drug compounds applied in both cases. In this case, the particular batch a set of experiments were conducted in constitutes the domain of the data; an ideal set of image embeddings should contain only the relevant biological information (e.g. drug effects). We develop a general framework for adjusting the image embeddings in order to `forget' domain-specific information while preserving relevant biological information. To do this, we minimize a loss function based on distances between marginal distributions (such as the Wasserstein distance) of embeddings across domains for each replicated treatment. For the dataset presented, the replicated treatment is the negative control. We find that for our transformed embeddings (1) the underlying geometric structure is not only preserved but the embeddings also carry improved biological signal (2) less domain-specific information is present.
[A]: We correct nuisance variation for image embeddings across different domains, preserving only relevant information.


[Q]: We present a Neural Program Search, an algorithm to generate programs from natural language description and a small number of input / output examples. The algorithm combines methods from Deep Learning and Program Synthesis fields by designing rich domain-specific language (DSL) and defining efficient search algorithm guided by a Seq2Tree model on it. To evaluate the quality of the approach we also present a semi-synthetic dataset of descriptions with test examples and corresponding programs. We show that our algorithm significantly outperforms sequence-to-sequence model with attention baseline.
[A]:
Program synthesis from natural language description and input / output examples via Tree-Beam Search over Seq2Tree model