相关论文: New Algorithm for Mixmaster Dynamics
We consider parabolic evolution equations with Lipschitz continuous and strongly monotone spatial operators. By introducing an additional variable, we construct an equivalent system where the operator is a Lipschitz continuous mapping from…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often…
Expert systems often operate in domains characterized by class-imbalanced tabular data, where detecting rare but critical instances is essential for safety and reliability. While conventional approaches, such as cost-sensitive learning,…
While deep neural networks show great performance on fitting to the training distribution, improving the networks' generalization performance to the test distribution and robustness to the sensitivity to input perturbations still remain as…
Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of…
The analysis of mixed data has been raising challenges in statistics and machine learning. One of two most prominent challenges is to develop new statistical techniques and methodologies to effectively handle mixed data by making the data…
We propose a BGK-type kinetic model for a binary gas mixture, designed to serve as a kinetic formulation of compressible two-phase fluid dynamics. The model features species-dependent adiabatic exponents, and the relaxation operator is…
We have evaluated the data-efficient Bayesian optimization method for the specific task of injection tuning in a circular accelerator. In this paper, we describe the implementation of this method at the Karlsruhe Research Accelerator with…
Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly…
Artificial intelligence(AI)-assisted method had received much attention in the risk field such as disease diagnosis. Different from the classification of disease types, it is a fine-grained task to classify the medical images as benign or…
We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their…
Training Restricted Boltzmann Machines (RBMs) has been challenging for a long time due to the difficulty of computing precisely the log-likelihood gradient. Over the past decades, many works have proposed more or less successful training…
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…
We present a new method which combines Car-Parrinello and Born-Oppenheimer molecular dynamics in order to accelerate density functional theory based ab-initio simulations. Depending on the system a gain in efficiency of one to two orders of…
The link between BFKL physics and twist-two operators involves an analytical continuation in the spin of the operators away from the physical even integer values. Typically this is done only after obtaining an analytical result for integer…
Modern robotic systems sense the environment geometrically, through sensors like cameras, lidar, and sonar, as well as semantically, often through visual models learned from data, such as object detectors. We aim to develop robots that can…
We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting…
Among all data augmentation techniques proposed so far, linear interpolation of training samples, also called Mixup, has found to be effective for a large panel of applications. Along with improved predictive performance, Mixup is also a…