Related papers: Automated code generation for discontinuous Galerk…
As the basis of generative AI, an autoregressive model requires the generation of a new token depending on all the previously generated tokens, which brings high quality but also restricts the model to generate tokens one by one, forming a…
We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has…
Creating high performance implementations of deep learning primitives on CPUs is a challenging task. Multiple considerations including multi-level cache hierarchy, and wide SIMD units of CPU platforms influence the choice of program…
We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…
Deep learning methods have recently achieved great empirical success on machine translation, dialogue response generation, summarization, and other text generation tasks. At a high level, the technique has been to train end-to-end neural…
Programming robots is a complicated and time-consuming task. A robot is essentially a real-time, distributed embedded system. Often, control and communication paths within the system are tightly coupled to the actual physical configuration…
We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…
We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general…
Probabilistic programming languages represent complex data with intermingled models in a few lines of code. Efficient inference algorithms in probabilistic programming languages make possible to build unified frameworks to compute…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation…
We propose GANCoder, an automatic programming approach based on Generative Adversarial Networks (GAN), which can generate the same functional and logical programming language codes conditioned on the given natural language utterances. The…
Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the…
The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to…
Compilers convert between representations -- usually, from higher-level, human writable code to lower-level, machine-readable code. A compiler backend is the portion of the compiler containing optimizations and code generation routines for…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…
Human reasoning can distill principles from observed patterns and generalize them to explain and solve novel problems. The most powerful artificial intelligence systems lack explainability and symbolic reasoning ability, and have therefore…
Automatic code generation has recently attracted large attention and is becoming more significant to the software development process. Solutions based on Machine Learning and Artificial Intelligence are being used to increase human and…