We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting...
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The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the gro...
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Surface reconstruction is a classical process in industrial engineering and manufacturing, particularly in reverse engineering, where the goal is to obtain a digital model from a physical object. For that purpose, the...
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Surface reconstruction is a classical process in industrial engineering and manufacturing, particularly in reverse engineering, where the goal is to obtain a digital model from a physical object. For that purpose, the real object is typically scanned or digitized and the resulting point cloud is then fitted to mathematical surfaces through numerical optimization. The choice of the approximating functions is crucial for the accuracy of the process. Real-world objects such as manufactured workpieces often require complex nonlinear approximating functions, which are not well suited for standard numerical methods. In a previous paper presented at the ISMSI 2023 conference, we addressed this issue by using manually selected approximation functions via optimization through the cuckoo search algorithm with Lévy flights. Building upon that work, this paper presents an enhanced and extended method for surface reconstruction by using height-map surfaces obtained through a combination of exponential, polynomial and logarithmic functions. A feasible approach for this goal is to consider continuous bivariate distribution functions, which ensures consistent models along with good mathematical properties for the output shapes, such as smoothness and integrability. However, this approach leads to a difficult multivariate, constrained, multimodal continuous nonlinear optimization problem. To tackle this issue, we apply particle swarm optimization, a popular swarm intelligence technique for continuous optimization. The method is hybridized with a local search procedure for further improvement of the solutions and applied to a benchmark of 15 illustrative examples of point clouds fitted to different surface models. The performance of the method is analyzed through several computational experiments. The numerical and graphical results show that the method is able to recover the shape of the point clouds accurately and automatically. Furthermore, our approach outperforms other alternati
Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to address these challenges. This paper ta...
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Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to address these challenges. This paper takes model predictive control, a popular optimal control method, as the primary example to survey recent progress that leverages machine learning techniques to empower optimal control solvers. We also discuss some of the main challenges encountered when applying machine learning to develop more robust optimal control algorithms.
In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic...
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In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniquen...
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Dynamic programming equations for mean field control problems with a separable structure are Eikonal type equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension ...
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An accurate force field is the key to the success of all molecular mechanics simulations on organic polymers and biomolecules. Accuracy beyond density functional theory is often needed to describe the intermolecular i...
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A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are *** initialization schemes as well as...
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A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are *** initialization schemes as well as general regimes for the network width and training data size are *** the overparametrized regime,it is shown that gradient descent dynamics can achieve zero training loss exponentially fast regardless of the quality of the *** addition,it is proved that throughout the training process the functions represented by the neural network model are uniformly close to those of a kernel *** general values of the network width and training data size,sharp estimates of the generalization error are established for target functions in the appropriate reproducing kernel Hilbert space.
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud...
ISBN:
(纸本)9781713871088
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes.
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