Related papers: Rigorous numerical models for the dynamics of comp…
The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical…
Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…
We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. An SRNN models the Hamiltonian function of the system by a neural network and…
In this paper we propose a deep recurrent architecture for the probabilistic modelling of high-frequency market prices, important for the risk management of automated trading systems. Our proposed architecture incorporates probabilistic…
Convolutional Neural Networks (CNNs) achieved great cognitive performance at the expense of considerable computation load. To relieve the computation load, many optimization works are developed to reduce the model redundancy by identifying…
Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
We investigate how a residual network can learn to predict the dynamics of interacting shapes purely as an image-to-image regression task. With a simple 2d physics simulator, we generate short sequences composed of rectangles put in motion…
Neural networks are powerful tools for data-driven modeling of complex dynamical systems, enhancing predictive capability for control applications. However, their inherent nonlinearity and black-box nature challenge control designs that…
Matching two images while estimating their relative geometry is a key step in many computer vision applications. For decades, a well-established pipeline, consisting of SIFT, RANSAC, and 8-point algorithm, has been used for this task.…
Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to…
Many problems in Physics and Chemistry are formulated as the minimization of a functional. Therefore, methods for solving these problems typically require differentiating maps whose input and/or output are functions -- commonly referred to…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
Recurrent neural networks (RNNs) are widely employed to model complex dynamical systems due to their hidden-state structure, which inherently captures temporal dependencies. This work presents a hybrid zonotope-based approach for computing…
Deep learning for predicting or generating 3D human pose sequences is an active research area. Previous work regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain,…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On…
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
Point sets matching method is very important in computer vision, feature extraction, fingerprint matching, motion estimation and so on. This paper proposes a robust point sets matching method. We present an iterative algorithm that is…