Zero-Shot Semantic Parsing for Instructions

We consider a zero-shot semantic parsing task: parsing instructions into compositional logical forms, in domains that were not seen during training. We present a new dataset with 1,390 examples from 7 application domains (e.g. a calendar or a file manager), each example consisting of a triplet: (a) the application's initial state, (b) an instruction, to be carried out in the context of that state, and (c) the state of the application after carrying out the instruction. We introduce a new training algorithm that aims to train a semantic parser on examples from a set of source domains, so that it can effectively parse instructions from an unknown target domain. We integrate our algorithm into the floating parser of Pasupat and Liang (2015), and further augment the parser with features and a logical form candidate filtering logic, to support zero-shot adaptation. Our experiments with various zero-shot adaptation setups demonstrate substantial performance gains over a non-adapted parser.Comment: ACL 201

Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problems

The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace transform in the complex plane. By requiring the Laplace transform to be analytic on some problem dependent complex half-plane, these modes can be suppressed. The resulting algorithm computes a finite number of coefficients of a series expansion of the Laplace transform, thereby providing an approximation to the exact boundary condition. The resulting error decays super-algebraically with the number of coefficients, so relatively few additional degrees of freedom are sufficient to reduce the error to the level of the discretization error in the interior of the computational domain. The approach shows good results for the Schr\"odinger and the drift-diffusion equation but, in contrast to the one-dimensional case, exhibits instabilities for the wave and Klein-Gordon equation. Numerical examples are shown that demonstrate the good performance in the former and the instabilities in the latter case

Remeshing and Refining with Moving Finite Elements. Application to Nonlinear Wave Problems

The recently proposed String Gradient Weighted Moving Finite Element (SGWMFE) method is extended to include remeshing and refining. The method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to the nonlinear time-dependent two-dimensional shallow water equations, under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation. Such effects are of major importance in geophysical fluid dynamics applications. Two deficiencies of the original SGWMFE method are (1) possible tangling of the mesh which causes the method's failure, and (2) no mechanism for global refinement when necessary due to the constant number of degrees of freedom. Here the method is extended in order to continue computing solutions when the meshes become too distorted, which happens quickly when the flow is rotationally dominant. Optimal rates of convergence are obtained when remeshing is applied. The method is also extended to include refinement to enable handling of new physical phenomena of a smaller scale which may appear during the solution process. It is shown that the errors in time are kept under control when refinement is necessary. Results of the extended method for some example problems of water hump release are presented

High-Order Non-Reflective Boundary Conditions for Disperive Wave Problems in Stratified Media

Proceedings Sixth International Conference on Computer Modelling and Experimental Measurements of Seas and Coastal Regions, Cadiz, Spain, 23-25 June 2003, (C.A. Brebbia, D. Almorza and F. Lo ́pez− Aguayo, eds), pp. 73-82.Problems of linear time-dependent dispersive waves in an unbounded domain are con- sidered. The infinite domain is truncated via an artificial boundary B. A high-order Non-Reflecting Boundary Condition (NRBC) is imposed on B, and the problem is solved by a Finite Difference (FD) scheme in the finite domain. The sequence of NRBCs proposed by Higdon is used. However, in contrast to the original low-order implementation, a new scheme is devised which allows the easy use of a Higdon-type NRBC of any desired order. In addition, the problem is considered for a stratified media. The performance of the scheme is demonstrated via numerical example

High-order boundary conditions for linearized shallow water equations with stratification, dispersion and advection

The two-dimensional linearized shallow water equations are considered in unbounded domains with density stratifications. Wave dispersion and advection effects are slso taken into account. The infinite domain is truncated via a rectangular artificial boundary B, and a high-order Open Boundary Condition (OBC) is imposed on B. Then the problem is solved numerically in the finite domain bounded by B. A recently developed boundary scheme is employed, which is based on a reformulation of the sequence of OBC's originaly proposed by Higdon. The OBCs can easily be used up to any desired order. They are incorporated here in a finite difference scheme. Numerical examples are used to demonstrate the performance and advantages of the computational method, with an emphasis on the effect of stratification

A Simple Numerical Absorbing Layer Method in Elastodynamics

The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions, infinite elements or absorbing layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this Note, a simple and efficient absorbing layer method is proposed in the framework of the Finite Element Method. This method considers Rayleigh/Caughey damping in the absorbing layer and its principle is presented first. The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types (surface waves, body waves) and incidences (normal to grazing). The method is shown to be efficient for different types of elastic waves and may thus be used for various elastodynamic problems in unbounded domains

Open Boundaries for the Nonlinear Schrodinger Equation

We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF) which is used to solve time dependent Nonlinear Schrodinger Equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described. The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability.Comment: 21 pages, 4 figure

Hyperboloidal layers for hyperbolic equations on unbounded domains

We show how to solve hyperbolic equations numerically on unbounded domains by compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate in combination with spatial compactification. We construct a new layer method based on this idea, called the hyperboloidal layer. The method is demonstrated on numerical tests including the one dimensional Maxwell equations using finite differences and the three dimensional wave equation with and without nonlinear source terms using spectral techniques.Comment: 23 pages, 23 figure

Spectral element modeling of three dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core

This paper deals with the spectral element modeling of seismic wave propagation at the global scale. Two aspects relevant to low-frequency studies are particularly emphasized. First, the method is generalized beyond the Cowling approximation in order to fully account for the effects of self-gravitation. In particular, the perturbation of the gravity field outside the Earth is handled by a projection of the spectral element solution onto the basis of spherical harmonics. Second, we propose a new formulation inside the fluid which allows to account for an arbitrary density stratification. It is based upon a decomposition of the displacement into two scalar potentials, and results in a fully explicit fluid-solid coupling strategy. The implementation of the method is carefully detailed and its accuracy is demonstrated through a series of benchmark tests.Comment: Sent to Geophysical Journal International on July 29, 200

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation