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]: The Convolutional Neural Network (CNN) has been successfully applied in many fields during recent decades; however it lacks the ability to utilize prior domain knowledge when dealing with many realistic problems. We present a framework called Geometric Operator Convolutional Neural Network (GO-CNN) that uses domain knowledge, wherein the kernel of the first convolutional layer is replaced with a kernel generated by a geometric operator function. This framework integrates many conventional geometric operators, which allows it to adapt to a diverse range of problems. Under certain conditions, we theoretically analyze the convergence and the bound of the generalization errors between GO-CNNs and common CNNs. Although the geometric operator convolution kernels have fewer trainable parameters than common convolution kernels, the experimental results indicate that GO-CNN performs more accurately than common CNN on CIFAR-10/100. Furthermore, GO-CNN reduces dependence on the amount of training examples and enhances adversarial stability.
[A]: Traditional image processing algorithms are combined with Convolutional Neural Networks,a new neural network.

[Q]: In high-dimensional reinforcement learning settings with sparse rewards, performing
effective exploration to even obtain any reward signal is an open challenge.
While model-based approaches hold promise of better exploration via planning, it
is extremely difficult to learn a reliable enough Markov Decision Process (MDP)
in high dimensions (e.g., over 10^100 states). In this paper, we propose learning
an abstract MDP over a much smaller number of states (e.g., 10^5), which we can
plan over for effective exploration. We assume we have an abstraction function
that maps concrete states (e.g., raw pixels) to abstract states (e.g., agent position,
ignoring other objects). In our approach, a manager maintains an abstract
MDP over a subset of the abstract states, which grows monotonically through targeted
exploration (possible due to the abstract MDP). Concurrently, we learn a
worker policy to travel between abstract states; the worker deals with the messiness
of concrete states and presents a clean abstraction to the manager. On three of
the hardest games from the Arcade Learning Environment (Montezuma's,
Pitfall!, and Private Eye), our approach outperforms the previous
state-of-the-art by over a factor of 2 in each game. In Pitfall!, our approach is
the first to achieve superhuman performance without demonstrations.
[A]:
We automatically construct and explore a small abstract Markov Decision Process, enabling us to achieve state-of-the-art results on Montezuma's Revenge, Pitfall!, and Private Eye by a significant margin.