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In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…

We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity…

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Motion imitation is a pivotal and effective approach for humanoid robots to achieve a more diverse range of complex and expressive movements, making their performances more human-like. However, the significant differences in kinematics and…

We introduce a Bayesian (deep) model-based reinforcement learning method (RoMBRL) that can capture model uncertainty to achieve sample-efficient policy optimisation. We propose to formulate the model-based policy optimisation problem as a…

Augmenting reinforcement learning with imitation learning is often hailed as a method by which to improve upon learning from scratch. However, most existing methods for integrating these two techniques are subject to several strong…

Efficient trajectory generation is crucial for autonomous systems; however, current numerical methods often struggle to handle periodic behaviors effectively, particularly when the onboard sensors require equidistant temporal sampling. This…

Brownian dynamics of colloidal particles on complex surfaces has found important applications in diverse physical, chemical and biological processes. However, current Brownian dynamics simulation algorithms mostly work for relatively simple…

In this study, a novel machine learning algorithm, restricted Boltzmann machine (RBM), is introduced. The algorithm is applied for the spectral classification in astronomy. RBM is a bipartite generative graphical model with two separate…

Humans excel at robust bipedal walking in complex natural environments. In each step, they adequately tune the interaction of biomechanical muscle dynamics and neuronal signals to be robust against uncertainties in ground conditions.…

A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…

This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its covariance operator, asymptotically accurate up to the…

Motivation: In systems biology, modelling strategies aim to decode how molecular components interact to generate dynamical behaviour. Boolean modelling is more and more used, but the description of the dynamics from two-levels components…

Due to the visual ambiguity, purely kinematic formulations on monocular human motion capture are often physically incorrect, biomechanically implausible, and can not reconstruct accurate interactions. In this work, we focus on exploiting…

NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation. While the method yields visually compelling…

We pursue an early stopping technique that helps Gaussian Restricted Boltzmann Machines (GRBMs) to gain good natural image representations in terms of overcompleteness and data fitting. GRBMs are widely considered as an unsuitable model for…

This work develops a comprehensive mathematical theory for a class of stochastic processes whose local regularity adapts dynamically in response to their own state. We first introduce and rigorously analyze a time-varying fractional…

Jumping poses a significant challenge for quadruped robots, despite being crucial for many operational scenarios. While optimisation methods exist for controlling such motions, they are often time-consuming and demand extensive knowledge of…

Existing techniques for motion imitation often suffer a certain level of latency due to their computational overhead or a large set of correspondence samples to search. To achieve real-time imitation with small latency, we present a…