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Modern feedforward convolutional neural networks (CNNs) can now solve some computer vision tasks at super-human levels. However, these networks only roughly mimic human visual perception. One difference from human vision is that they do not…
As the computer vision matures into a systems science and engineering discipline, there is a trend in leveraging latest advances in computer graphics simulations for performance evaluation, learning, and inference. However, there is an open…
How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…
Humans are excellent at perceiving illusory outlines. We are readily able to complete contours, shapes, scenes, and even unseen objects when provided with images that contain broken fragments of a connected appearance. In vision science,…
Momentum-based gradients are essential for optimizing advanced machine learning models, as they not only accelerate convergence but also advance optimizers to escape stationary points. While most state-of-the-art momentum techniques utilize…
Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…
One of the main obstacles for developing flexible AI systems is the split between data-based learners and model-based solvers. Solvers such as classical planners are very flexible and can deal with a variety of problem instances and goals…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Visual illusions teach us that what we see is not always what it is represented in the physical world. Its special nature make them a fascinating tool to test and validate any new vision model proposed. In general, current vision models are…
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all…
It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of…
Computational modeling helps neuroscientists to integrate and explain experimental data obtained through neurophysiological and anatomical studies, thus providing a mechanism by which we can better understand and predict the principles of…
We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…
Humans intuitively recognize objects' physical properties and predict their motion, even when the objects are engaged in complicated interactions. The abilities to perform physical reasoning and to adapt to new environments, while intrinsic…
Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…
We show an approach to automated control of machine vision systems based on incremental creation and evaluation of a particular family of influence diagrams that represent hypotheses of imagery interpretation and possible subsequent…
We propose a new variational illusory shape (VIS) model via phase fields and phase transitions. It is inspired by the first-order variational illusory contour (VIC) model proposed by Jung and Shen [{\em J. Visual Comm. Image Repres.}, {\bf…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
This paper presents the first high-order computational fluid dynamics (CFD) simulations of static and spinning golf balls at realistic flow conditions. The present results are shown to capture the complex fluid dynamics inside the dimples…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…