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Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of Laplacian in simulation of wave equation via finite-difference method. We exploit intrinsic one-to-one similarities between timestepping algorithm with Convolutional Neural Networks (CNNs), and propose to intersperse CNNs between low-fidelity timesteps. Augmenting neural networks with low-fidelity timestepping algorithms may allow us to take large timesteps while limiting the numerical dispersion artifacts. While simulating the wave-equation with low-fidelity timestepping algorithm, by correcting the wavefield several time during propagation, we hope to limit the numerical dispersion artifact introduced by a poor discretization of the Laplacian. As a proof of concept, we demonstrate this principle by correcting for numerical dispersion by keeping the velocity model fixed, and varying the source locations to generate training and testing pairs for our supervised learning algorithm.
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Neural Machine Translation (NMT) has become a popular technology in recent years, and the encoder-decoder framework is the mainstream among all the methods. Its obvious that the quality of the semantic representations from encoding is very crucial and can significantly affect the performance of the model. However, existing unidirectional source-to-target architectures may hardly produce a language-independent representation of the text because they rely heavily on the specific relations of the given language pairs. To alleviate this problem, in this paper, we propose a novel Bi-Decoder Augmented Network (BiDAN) for the neural machine translation task. Besides the original decoder which generates the target language sequence, we add an auxiliary decoder to generate back the source language sequence at the training time. Since each decoder transforms the representations of the input text into its corresponding language, jointly training with two target ends can make the shared encoder has the potential to produce a language-independent semantic space. We conduct extensive experiments on several NMT benchmark datasets and the results demonstrate the effectiveness of our proposed approach.
Accurate numerical solutions for the Schrodinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining Monte Carlo methods with unsupervised training of neural networks has recently been proposed as a promising approach to overcome the curse of dimensionality in this setting and to obtain accurate wavefunctions for individual molecules at a moderately scaling computational cost. These methods currently do not exploit the regularity exhibited by wavefunctions with respect to their molecular geometries. Inspired by recent successful applications of deep transfer learning in machine translation and computer vision tasks, we attempt to leverage this regularity by introducing a weight-sharing constraint when optimizing neural network-based models for different molecular geometries. That is, we restrict the optimization process such that up to 95 percent of weights in a neural network model are in fact equal across varying molecular geometries. We find that this technique can accelerate optimization when considering sets of nuclear geometries of the same molecule by an order of magnitude and that it opens a promising route towards pre-trained neural network wavefunctions that yield high accuracy even across different molecules.
The algorithm for Monte Carlo simulation of parton-level events based on an Artificial Neural Network (ANN) proposed in arXiv:1810.11509 is used to perform a simulation of $Hto 4ell$ decay. Improvements in the training algorithm have been implemented to avoid numerical instabilities. The integrated decay width evaluated by the ANN is within 0.7% of the true value and unweighting efficiency of 26% is reached. While the ANN is not automatically bijective between input and output spaces, which can lead to issues with simulation quality, we argue that the training procedure naturally prefers bijective maps, and demonstrate that the trained ANN is bijective to a very good approximation.
Human intelligence is characterized by a remarkable ability to infer abstract rules from experience and apply these rules to novel domains. As such, designing neural network algorithms with this capacity is an important step toward the development of deep learning systems with more human-like intelligence. However, doing so is a major outstanding challenge, one that some argue will require neural networks to use explicit symbol-processing mechanisms. In this work, we focus on neural networks capacity for arbitrary role-filler binding, the ability to associate abstract roles to context-specific fillers, which many have argued is an important mechanism underlying the ability to learn and apply rules abstractly. Using a simplified version of Ravens Progressive Matrices, a hallmark test of human intelligence, we introduce a sequential formulation of a visual problem-solving task that requires this form of binding. Further, we introduce the Emergent Symbol Binding Network (ESBN), a recurrent neural network model that learns to use an external memory as a binding mechanism. This mechanism enables symbol-like variable representations to emerge through the ESBNs training process without the need for explicit symbol-processing machinery. We empirically demonstrate that the ESBN successfully learns the underlying abstract rule structure of our task and perfectly generalizes this rule structure to novel fillers.
Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree. While effective for relatively short-term time integration, when long time integration of the time-dependent PDEs is sought, the time-space domain may become arbitrarily large and hence training of the neural network may become prohibitively expensive. To this end, we develop a parareal physics-informed neural network (PPINN), hence decomposing a long-time problem into many independent short-time problems supervised by an inexpensive/fast coarse-grained (CG) solver. In particular, the serial CG solver is designed to provide approximate predictions of the solution at discrete times, while initiate many fine PINNs simultaneously to correct the solution iteratively. There is a two-fold benefit from training PINNs with small-data sets rather than working on a large-data set directly, i.e., training of individual PINNs with small-data is much faster, while training the fine PINNs can be readily parallelized. Consequently, compared to the original PINN approach, the proposed PPINN approach may achieve a significant speedup for long-time integration of PDEs, assuming that the CG solver is fast and can provide reasonable predictions of the solution, hence aiding the PPINN solution to converge in just a few iterations. To investigate the PPINN performance on solving time-dependent PDEs, we first apply the PPINN to solve the Burgers equation, and subsequently we apply the PPINN to solve a two-dimensional nonlinear diffusion-reaction equation. Our results demonstrate that PPINNs converge in a couple of iterations with significant speed-ups proportional to the number of time-subdomains employed.
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