Related papers: Learning Heat-based Equations in Self-similar vari…

Block based motion estimation is integral to inter prediction processes performed in hybrid video codecs. Prevalent block matching based methods that are used to compute block motion vectors (MVs) rely on computationally intensive search…

Model Predictive Controllers (MPC) require a good model for the controlled process. In this paper I infer inductive biases about a physical system. I use these biases to derive a new neural network architecture that can model this real…

Brain-inspired learning models attempt to mimic the cortical architecture and computations performed in the neurons and synapses constituting the human brain to achieve its efficiency in cognitive tasks. In this work, we present…

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…

We introduce an approach for solving PDEs over manifolds using physics informed neural networks whose architecture aligns with spectral methods. The networks are trained to take in as input samples of an initial condition, a time stamp and…

We develop a new approach for regularity estimates, especially vorticity estimates, of solutions of the three-dimensional Navier-Stokes equations with periodic initial data, by exploiting carefully formulated linearized vorticity equations.…

Manifold learning is a fundamental problem in machine learning with numerous applications. Most of the existing methods directly learn the low-dimensional embedding of the data in some high-dimensional space, and usually lack the…

In the present paper, we study the long time behaviour of the solutions of the second grade fluids equations in dimension 3. Using scaling variables and energy estimates in weighted Sobolev spaces, we describe the first order asymptotic…

In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly…

We treat the heat equation with singular drift terms and its generalization: the linearized Navier-Stokes system. In the first case, we obtain boundedness of weak solutions for highly singular, "supercritical" data. In the second case, we…

Building's energy consumption prediction is a major concern in the recent years and many efforts have been achieved in order to improve the energy management of buildings. In particular, the prediction of energy consumption in building is…

In everyday life collaboration tasks between human operators and robots, the former necessitate simple ways for programming new skills, the latter have to show adaptive capabilities to cope with environmental changes. The joint use of…

The explosive availability of remote sensing images has challenged supervised classification algorithms such as Support Vector Machines (SVM), as training samples tend to be highly limited due to the expensive and laborious task of ground…

The numerical simulation of the inviscid Burgers' equation is often hindered by spurious oscillations near discontinuities. To mitigate this issue, a viscous term can be introduced, leading to the viscous Burgers' equation. In this work,…

The National Synchrotron Light Source II (NSLS-II) uses highly stable electron beam to produce high-quality X-ray beams with high brightness and low-emittance synchrotron radiation. The traditional algorithm to stabilize the beam applies…

Regularization in modern machine learning is crucial, and it can take various forms in algorithmic design: training set, model family, error function, regularization terms, and optimizations. In particular, the learning rate, which can be…

Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…

We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…

We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…

The training of Support Vector Machines may be a very difficult task when dealing with very large datasets. The memory requirement and the time consumption of the SVMs algorithms grow rapidly with the increase of the data. To overcome these…