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A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
The Constraint-satisfaction problem (CSP) is fundamental in mathematics, physics, and theoretical computer science. Continuous local search (CLS) solvers, as recent advancements, can achieve highly competitive results on certain classes of…
Balanced Singular Perturbation Approximation (SPA) is a model order reduction method for linear time-invariant systems that guarantees asymptotic stability and for which there exists an a priori error bound. In that respect, it is similar…
Constraint Satisfaction Problem (CSP) is a framework for modeling and solving a variety of real-world problems. Once the problem is expressed as a finite set of constraints, the goal is to find the variables' values satisfying them. Even…
Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…
Sensors producing 3D point clouds such as 3D laser scanners and RGB-D cameras are widely used in robotics, be it for autonomous driving or manipulation. Aligning point clouds produced by these sensors is a vital component in such…
The dynamic factors in the environment will lead to the decline of camera localization accuracy due to the violation of the static environment assumption of SLAM algorithm. Recently, some related works generally use the combination of…
We present a Transformer-based framework for Constraint Satisfaction Problems (CSPs). CSPs find use in many applications and thus accelerating their solution with machine learning is of wide interest. Most existing approaches rely on…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the…
The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that…
Deep Convolutional Neural Networks (CNN) has achieved significant success in computer vision field. However, the high computational cost of the deep complex models prevents the deployment on edge devices with limited memory and…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it.…
For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are…
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
The power spectral density (PSD) function is commonly used to specify seismometer performance. It is derived from the FFT of acceleration and correction is made for the transfer function of the instrument that generated the data. As with…